Seat No -

Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 2. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One
Q.no 3. Turing machine is more powerful than (a) Finite automata, (b) Push down
automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Neither (a) nor (b)

Q.no 4. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 5. A grammar G=(V, T, P, S) is __________ if every production taken one of the

two forms: B->aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 6. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 7. Construct a regular expression for the language that contains strings
having at least one pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*
C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

Q.no 8. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 9. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 10. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 11. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA

D : accepted by Turing machine

Q.no 12. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions
C : Reachable symbols

D : Non Unit productions

Q.no 13. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 14. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 15. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 16. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 17. Finite state machine can recognize

A : any grammar

B : only context-free grammar

C : context free grammar and regualr grammar

D : only regular grammar

Q.no 18. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 19. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 20. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 21. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb
Q.no 22. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 23. A PDA machine configuration (p, w, y) can be correctly represented as

A : unprocessed input, stack content, current state

B : current state, unprocessed input, stack content

C : current state, stack content, unprocessed input

D : stack content, current state, unprocessed input

Q.no 24. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 25. The production of the form A->B , where A and B are non terminals is
called

A : Null production

B : Greibach Normal Form

C : Unit production

D : Chomsky Normal Form

Q.no 26. Recursively enumerable languages are …….. , whereas recursive

languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 27. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 28. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 29. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 30. Which productions will generate even length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 31. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 32. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 33. The difference between number of states in FA for regular expression (a
+ b) and (a + b) * is:

A:1

B:2

C:3

D:0

Q.no 34. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 35. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7

B : 10
C : 12

D : 11

Q.no 36.

A:

B:

C:

D:

Q.no 37. The maximum number of transitions which can be performed over a
state in a DFA having alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 38. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 39. Which of the following statement(s) are correct? (a) All languages can be
generated by CFG, (b) Any regular language has an equivalent CFG, (c) Some non
regular languages cannot be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)
D : Both (b) and (c)

Q.no 40. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 41. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 42. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 43. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 44. The output of Moore machine can be defined as

A:
B:

C:

D : state and its input

Q.no 45. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 46. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 47. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa
Q.no 48. Consider the following statements.
I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 49. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 50. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 51. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?
A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 52. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 53.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 54. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition
D : May be correct

Q.no 55. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:

C:
D:

Q.no 56. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 57. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 58. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 59. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 60. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*
Answer for Question No 1. is d

Answer for Question No 2. is a

Answer for Question No 3. is c

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is c

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is a

Answer for Question No 12. is b

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is b

Answer for Question No 17. is d

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is d

Answer for Question No 29. is d

Answer for Question No 30. is b

Answer for Question No 31. is c

Answer for Question No 32. is c

Answer for Question No 33. is a

Answer for Question No 34. is d

Answer for Question No 35. is c

Answer for Question No 36. is d

Answer for Question No 37. is c

Answer for Question No 38. is b

Answer for Question No 39. is d

Answer for Question No 40. is b

Answer for Question No 41. is c

Answer for Question No 42. is c

Answer for Question No 43. is c

Answer for Question No 44. is a

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is a

Answer for Question No 48. is d

Answer for Question No 49. is a

Answer for Question No 50. is a

Answer for Question No 51. is d

Answer for Question No 52. is b

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is c

Answer for Question No 56. is b

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is b

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. A deterministic Turing machine is

A : Ambiguous Turing Machine

B : Unambiguous Turing Machine

C : Non-Deterministic Finite Automata

D : Deterministic Finite Automata

Q.no 2. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 3. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 4. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 5. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 6. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 7. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA
D : accepted by Turing machine

Q.no 8. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 9. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 10. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 11. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 12. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar
D : Type 3 grammar

Q.no 13. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 14. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 15. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 16.

A : L*

B:

C:L
D:

Q.no 17. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 18. Which one of the following languages over the alphabet {0, 1} is
described by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 19. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 20. Turing Machine also behaves like General purpose computer and that TM
is known as _______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 21. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 22. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined

Q.no 23. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 24. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 25. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 26. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which the total number of a’s is
divisible by 2.

A : ((a+b)(a+b))*
B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 27. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is
undecidable. The statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3

Q.no 28. The minimum number of productions required to produce a language

consisting of palindrome strings over T={a,b} is

A:3

B:7

C:5

D:6

Q.no 29. Which of the regular expressions correspond to the given problem
statement: Express the identifiers in C Programming language where l=letters
d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 30. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 31. Which is a wrong satatement?

A : A regular language is produced by union of two regular languages

B : The concatenation of two regular languages is regular

C : The Kleene closure of a regular language is regular

D : The complement of a regular language is also a regular language

Q.no 32. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 33. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 34. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 35. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say
Q.no 36. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 37. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 38. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory

machine.

Q.no 39. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:

C:

D:
Q.no 40. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 41. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 42. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 43. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 44. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 45.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 46. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable
B : Undecidable

C : Computable

D : Recognizable

Q.no 47. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 48. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 49. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:

Q.no 50. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.
A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 51. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 52. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 53. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 54. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)
D : (a . b) (a . b)

Q.no 55. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 56. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 57. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 58. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?
A : 10

B : 11

C : 12

D : 15

Q.no 59.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 60. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Answer for Question No 1. is b

Answer for Question No 2. is d

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is b

Answer for Question No 7. is a

Answer for Question No 8. is d

Answer for Question No 9. is b

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is d

Answer for Question No 13. is d

Answer for Question No 14. is a

Answer for Question No 15. is c

Answer for Question No 16. is b

Answer for Question No 17. is d

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is c

Answer for Question No 21. is b

Answer for Question No 22. is b

Answer for Question No 23. is d

Answer for Question No 24. is a

Answer for Question No 25. is b

Answer for Question No 26. is c

Answer for Question No 27. is d

Answer for Question No 28. is c

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is d

Answer for Question No 32. is b

Answer for Question No 33. is b

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is a

Answer for Question No 38. is d

Answer for Question No 39. is a

Answer for Question No 40. is a

Answer for Question No 41. is b

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is d

Answer for Question No 45. is b

Answer for Question No 46. is b

Answer for Question No 47. is c

Answer for Question No 48. is b

Answer for Question No 49. is c

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is d

Answer for Question No 53. is d

Answer for Question No 54. is b

Answer for Question No 55. is c

Answer for Question No 56. is b

Answer for Question No 57. is c

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Linear Bounded Automaton is a

A : Finite Automaton

B : Turing Machine

C : Push down Automaton

D : Deterministic Finite Automata

Q.no 2. Minimal finite automata need _____________ no. of final states

A:1

B:2

C:3

D : Depends on problem

Q.no 3. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 4. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 5. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 6. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 7. If T1 and T2 are two Turing machines, the composite can be represented
using the expression

A : T1 T2

B : T2 T1
C : T1 X T2

D : T2 X T1

Q.no 8. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 9. In Parse Tree, Root represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 10. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 11. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 12. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 13.

A:R

B:

C : R*

D:

Q.no 14. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 15. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 16. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 17. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 18. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 19. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 20. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 21. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is
undecidable. The statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3
Q.no 22. Number of external states of a UTM should be atleast

A:1

B:2

C:3

D:4

Q.no 23. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*

B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 24. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 25. Unrestricted grammar is also called_______ Grammar

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 26. The complexity class P consist of all the decision problems that can be
solved by ___________using polynomial amount of computation time.

A : Push Down automata

B : DFA

C : NDFA

D : Deterministic Turing machine

Q.no 27. The complement of a language will only be defined when and only when
the __________ over the language is defined.

A : String

B : Word

C : Alphabet

D : Grammar

Q.no 28. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 29. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 30. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 31. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 32. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 33. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 34. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 35. The operations of PDA never work on elements other than top of the
stack.

A : false

B : true

C : may be

D : cannot say

Q.no 36. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 37. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 38. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 39. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 40. For a DFA accepting binary numbers whose decimal equivalent is
divisible by 4, what are all the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 41. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 42. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 43. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 44. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard
Q.no 45. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 46. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:
B:

C:

D:

Q.no 47.
A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 48. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 49. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 50. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:

Q.no 51. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 52. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 53. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 54. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 55. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 56. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3
B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 57.

A:A

B:B

C:C

D:D

Q.no 58. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 59. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 60. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable
Answer for Question No 1. is b

Answer for Question No 2. is d

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is a

Answer for Question No 8. is b

Answer for Question No 9. is c

Answer for Question No 10. is b

Answer for Question No 11. is a

Answer for Question No 12. is b

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is a

Answer for Question No 18. is b

Answer for Question No 19. is b

Answer for Question No 20. is d

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is b

Answer for Question No 24. is c

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is d

Answer for Question No 29. is a

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is b

Answer for Question No 33. is b

Answer for Question No 34. is a

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is c

Answer for Question No 38. is b

Answer for Question No 39. is a

Answer for Question No 40. is d

Answer for Question No 41. is d

Answer for Question No 42. is b

Answer for Question No 43. is c

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is c

Answer for Question No 50. is a

Answer for Question No 51. is d

Answer for Question No 52. is a

Answer for Question No 53. is c

Answer for Question No 54. is b

Answer for Question No 55. is b

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 2. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition
Q.no 3. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 4. Which of the following case does not exist in complexity theory?

A : Best case

B : Worst case

C : Average case

D : Null case

Q.no 5. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 6. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 7. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 8. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 9. The finite automata  is called NFA when there exists____________ for a
specific input from current state to next state

A : Single path

B : Multiple paths

C : Only two paths

D : Three paths

Q.no 10. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 11. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 12. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 13. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 14. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 15. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 16. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 17. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2
D : type 3

Q.no 18. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 19. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 20. Can we convert PDA to equivalent CFG?

A : yes

B : no

C : maybe

D : never

Q.no 21. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 22. The total number of states and transitions required to form a Moore
machine that processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5
C : 2 and 4

D : 2 and 5

Q.no 23. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 24. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 25. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 26.

A:

B:
C:

D : {0, 1}

Q.no 27. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 28. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 29. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 30. Which productions will generate even length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 31. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown
automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing

Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 32. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 33.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the
right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform
the right movement.

Q.no 34. Which of the regular expressions correspond to the given problem
statement: Express the identifiers in C Programming language where l=letters
d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*
Q.no 35. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 36. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 37. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 38. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 39. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite
automata

B : Every language defined by finite automata can also be defined by regular

expression
C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 40. The minimum number of productions required to produce a language

consisting of palindrome strings over T={a,b} is

A:3

B:7

C:5

D:6

Q.no 41. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 42. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 43. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *
C:a(a+b)*b

D : b (a + b ) * a

Q.no 44. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 45. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 46. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:
Q.no 47.

A:A

B:B

C:C

D:D

Q.no 48. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 49. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 50. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 51. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 52. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:
B:

C:

D:

Q.no 53. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 54. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 55. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 56. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct
B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 57.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 58. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 59. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable
D : X1 – X3 is recursively enumerable

Q.no 60. Transition function of NFA machine is given by

A:

B:

C:

D:
Answer for Question No 1. is b

Answer for Question No 2. is c

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is b

Answer for Question No 10. is d

Answer for Question No 11. is b

Answer for Question No 12. is b

Answer for Question No 13. is c

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is c

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is d

Answer for Question No 24. is b

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is c

Answer for Question No 28. is b

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is b

Answer for Question No 32. is c

Answer for Question No 33. is a

Answer for Question No 34. is c

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is d

Answer for Question No 38. is b

Answer for Question No 39. is d

Answer for Question No 40. is c

Answer for Question No 41. is b

Answer for Question No 42. is c

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is c

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is c

Answer for Question No 55. is d

Answer for Question No 56. is b

Answer for Question No 57. is a

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 2. Are the given two patterns equivalent?

(1) gray | grey (2) gr(a|e)y

A : yes

B : no

C : may be

D : cannot say

Q.no 3. Those problems that require large amount of computational resources that are
practically not feasible to solve, these problems are known as _________
A : Decidable

B : Undecidable

C : Tractable

D : Intractable

Q.no 4. Which of the following regular expressions represents the set of strings which
do not contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 5. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 6.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 7. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*

D:

Q.no 8. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 9. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 10. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational

D : Computable

Q.no 11. The decision problem is the function from string to ______________

A : char

B :  int

C :  boolean

D : float

Q.no 12. Turing Machine also behaves like General purpose computer and that TM is
known as _______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 13. Top-down parsers use the grammar

A : LL(K)
B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 14. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 15. The transition a Push down automaton makes is additionally dependent upon
the:

A : Current State

B : input tape

C : stack

D : terminals

Q.no 16. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 17. The finite automata  is called NFA when there exists____________ for a specific
input from current state to next state

A : Single path

B : Multiple paths

C : Only two paths

D : Three paths

Q.no 18. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 19. Which of the following case does not exist in complexity theory?

A : Best case

B : Worst case

C : Average case

D : Null case

Q.no 20. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 21. The RE in which any number of 0′s is followed by any number of 1′s followed
by any number of 2′s is

A : (0+1+2)*

B : 0*1*2*

C : 0* + 1 + 2

D : (0+1)*2*

Q.no 22. Which is a wrong satatement?

A : A regular language is produced by union of two regular languages

B : The concatenation of two regular languages is regular

C : The Kleene closure of a regular language is regular

D : The complement of a regular language is also a regular language

Q.no 23. Recursively enumerable languages are …….. , whereas recursive languages are
…....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 24. The set of all strings over alphabet = {a,b} in which all strings having bbbb as
substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 25. Which of the following statement is false?

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 26. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 27. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 28. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 29. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 30. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 31. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 32. For a DFA accepting binary numbers whose decimal equivalent is divisible by
4, what are all the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 33. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined
Q.no 34. The complexity class P consist of all the decision problems that can be solved
by ___________using polynomial amount of computation time.

A : Push Down automata

B : DFA

C : NDFA

D : Deterministic Turing machine

Q.no 35. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 36. It is less complex to prove the closure properties over regular languages using

A : NFA

B : DFA

C : PDA

D : Canot be said

Q.no 37. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 38. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 39. The automaton which allows transformation to a new state without consuming
any input symbols:
A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 40. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 41. The regular expression denotes a language comprising all possible strings of
even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 42. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 43. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2
Q.no 44. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 45. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 46. The lexical analysis for a modern computer language such as Java needs the
power of which one of the following machine models in a necessary and sufficient
sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 47. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s
is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 48. Transition function of Epsilon-NFA machine is given by

A:
B:

C:

D:

Q.no 49. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 50. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 51. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:
C:

D:

Q.no 52. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 53. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 54. Which Transition table of Turing Machine is correct to check well formedness
of parentheses?
A:

B:

C:

D:

Q.no 55. CFG is not closed under

A : Kleene closure
B : Concatenation

C : Complement

D : Union

Q.no 56. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 57. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 58. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 59. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R
are the two other problems not known to be in NP. Which one of the following
statements is true if Q is polynomial time reducible to S and S is the polynomial time
reducible to R?

A : Q is NP-complete
B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 60. The set of all strings over alphabet ={a,b} in which a single a followed by any
number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*
Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is d

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is a

Answer for Question No 11. is c

Answer for Question No 12. is c

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is c

Answer for Question No 16. is d

Answer for Question No 17. is b

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is b

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is c

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is a

Answer for Question No 29. is d

Answer for Question No 30. is c

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is b

Answer for Question No 34. is d

Answer for Question No 35. is a

Answer for Question No 36. is a

Answer for Question No 37. is d

Answer for Question No 38. is c

Answer for Question No 39. is c

Answer for Question No 40. is c

Answer for Question No 41. is d

Answer for Question No 42. is a

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is c

Answer for Question No 48. is c

Answer for Question No 49. is d

Answer for Question No 50. is d

Answer for Question No 51. is b

Answer for Question No 52. is d

Answer for Question No 53. is c

Answer for Question No 54. is a

Answer for Question No 55. is c

Answer for Question No 56. is a

Answer for Question No 57. is d

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 2. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable
Q.no 3. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 4. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 5. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what
does S represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 6. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 7. Which of the following are the actions that operates on stack top?

A : only push
B : only pop

C : only push and pop

D : push, pop and replace

Q.no 8. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 9. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.

A : true

B : false

C : Cannot say

D : May be

Q.no 10. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 11.

A:R

B:

C : R*
D:

Q.no 12. What is the Regular Expression Matching Zero or More Specific
Characters

A:x

B:#

C:*

D:&

Q.no 13. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 14. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5

Q.no 15. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 16. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*
C : (x* + y)

D : (xy)*

Q.no 17. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 18. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 19. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 20.

A:

B:

C:0

D:1

Q.no 21. Which of the following is the restricted model of Turing machines (a)
Turing machine with semi-infinite tape, (b) Multi stack machine, (c) Offline
Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 22. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 23. The set of all strings over alphabet = {a,b} in which all strings having
bbbb as substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 24. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which any occurrence of the
symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*

Q.no 25. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 26. Construct a regular expression for the language that contains strings
having even number of 0’s followed by odd number of 1’s over {0, 1}.

A : (00)* 1 (11)*

B : ((0+1)(0+1))*

C : (0+1)*

D : (001)*

Q.no 27. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 28. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 29. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 30.
A:

B:

C:

D : {0, 1}

Q.no 31. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 32.

A:

B:

C:

D:

Q.no 33. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 34. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?
A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 35. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 36. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 37. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 38. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is
undecidable. The statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3
Q.no 39. For a DFA accepting binary numbers whose decimal equivalent is
divisible by 4, what are all the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 40. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 41. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*
Q.no 42.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 43. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 44. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa
Q.no 45. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 46. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 47. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 48. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 49. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab
B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 50. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 51. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 52. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 53. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)
D : (a . b) (a . b)

Q.no 54. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 55. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 56. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of
A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 57. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 58. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 59. Transition function of NFA machine is given by

A:

B:

C:

D:
Q.no 60. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA
Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is d

Answer for Question No 8. is d

Answer for Question No 9. is a

Answer for Question No 10. is a

Answer for Question No 11. is b

Answer for Question No 12. is c

Answer for Question No 13. is b

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is b

Answer for Question No 17. is a

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is a

Answer for Question No 24. is b

Answer for Question No 25. is a

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is d

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is d

Answer for Question No 33. is c

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is d

Answer for Question No 38. is d

Answer for Question No 39. is d

Answer for Question No 40. is b

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is a

Answer for Question No 45. is a

Answer for Question No 46. is c

Answer for Question No 47. is d

Answer for Question No 48. is b

Answer for Question No 49. is d

Answer for Question No 50. is d

Answer for Question No 51. is c

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is d

Answer for Question No 55. is b

Answer for Question No 56. is c

Answer for Question No 57. is a

Answer for Question No 58. is b

Answer for Question No 59. is d

Answer for Question No 60. is c

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 2. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 3. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 4. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 5. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 6. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what
does S represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 7. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 8. A->aA| a| b
The number of steps to generate aab are

A:2

B:3

C:4

D:5

Q.no 9. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 10. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 11. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 12. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 13. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 14. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 15. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.

A : true

B : false

C : Cannot say

D : May be

Q.no 16. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 17. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing

Q.no 18. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 19. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 20. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 21. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 22. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb
C : (a+b)* bb

D : (a+b)+ bb

Q.no 23. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 24. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 25. Which of the following statement(s) are correct? (a) All languages can be
generated by CFG, (b) Any regular language has an equivalent CFG, (c) Some non
regular languages cannot be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 26. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 27. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 28. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 29. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 30. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 31. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 32. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 33. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 34. A context free language is called ambiguous if (a) It has two or more
leftmost derivations for the same string. (b) It has two or more rightmost
derivations for the same string. (c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 35. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)
Q.no 36. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 37. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 38. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent

deterministic Turing machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 39. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 40. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:
B:

C:

D:

Q.no 41. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 42. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 43. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 44. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)
B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 45. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 46. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 47. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 48. Transition function of NFA machine is given by

A:

B:

C:
D:

Q.no 49.

A:A

B:B

C:C

D:D

Q.no 50. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 51. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab
D : ababbbbbab

Q.no 52. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 53. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 54. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II
D : Only I and III

Q.no 55. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:

B:

C:
D:

Q.no 56. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 57. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 58. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 59. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 60. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard
Answer for Question No 1. is a

Answer for Question No 2. is d

Answer for Question No 3. is b

Answer for Question No 4. is c

Answer for Question No 5. is d

Answer for Question No 6. is b

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is c

Answer for Question No 10. is a

Answer for Question No 11. is c

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is a

Answer for Question No 18. is c

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is c

Answer for Question No 23. is b

Answer for Question No 24. is d

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is d

Answer for Question No 29. is d

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is b

Answer for Question No 34. is c

Answer for Question No 35. is d

Answer for Question No 36. is a

Answer for Question No 37. is c

Answer for Question No 38. is b

Answer for Question No 39. is b

Answer for Question No 40. is a

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is d

Answer for Question No 47. is a

Answer for Question No 48. is d

Answer for Question No 49. is b

Answer for Question No 50. is b

Answer for Question No 51. is d

Answer for Question No 52. is d

Answer for Question No 53. is c

Answer for Question No 54. is d

Answer for Question No 55. is a

Answer for Question No 56. is d

Answer for Question No 57. is c

Answer for Question No 58. is c

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 2. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 3. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 4. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 5. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA

D : accepted by Turing machine

Q.no 6. Which of the following regular expressions represents the set of strings
which do not contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 7. Which of the following does not belong to the language if input alphabet
set is a,b

A:a

B:b

C : epsilon

D:c
Q.no 8. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 9. Finite state machine can recognize

A : any grammar

B : only context-free grammar

C : context free grammar and regualr grammar

D : only regular grammar

Q.no 10. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 11. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 12. Transition function of DFA machine maps.

A:

B:

C:
D:

Q.no 13. A language L is said to be ____________ if there is a turing machine M such

that L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 14. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 15. A grammar G=(V, T, P, S) is __________ if every production taken one of the
two forms: B->aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 16. Given the expression, is there some assignment of true and false values
to the variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 17. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 18. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 19. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 20. A two-way infinite tape Turing machine is ________ superior than the basic
model of the Turing machine in terms of power.

A : More

B : Less

C : No way

D : Very Much

Q.no 21. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 22. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 23. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 24. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 25. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 26. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.
A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 27. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D :  Unrestricted

Q.no 28. Is the language preserved in all the steps while eliminating epsilon
transitions from a NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 29. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory

machine.

Q.no 30. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 31. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 32. A context free language is called ambiguous if (a) It has two or more
leftmost derivations for the same string. (b) It has two or more rightmost
derivations for the same string. (c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 33. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 34. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 35. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 36. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 37. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is
undecidable. The statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3

Q.no 38. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 39. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 40. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7
B : 10

C : 12

D : 11

Q.no 41. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 42. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 43. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:
Q.no 44.

A:A

B:B

C:C

D:D

Q.no 45. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 46. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011
Q.no 47. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 48. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 49. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 50. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab
D : ababbbbbab

Q.no 51. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 52. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 53. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15
Q.no 54. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 55. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine
Q.no 56. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 57. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 58. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 59. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 60. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Answer for Question No 1. is b

Answer for Question No 2. is d

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is d

Answer for Question No 7. is d

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is a

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is b

Answer for Question No 14. is b

Answer for Question No 15. is b

Answer for Question No 16. is a

Answer for Question No 17. is a

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is c

Answer for Question No 21. is b

Answer for Question No 22. is b

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is a

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is d

Answer for Question No 30. is d

Answer for Question No 31. is d

Answer for Question No 32. is c

Answer for Question No 33. is c

Answer for Question No 34. is d

Answer for Question No 35. is c

Answer for Question No 36. is b

Answer for Question No 37. is d

Answer for Question No 38. is d

Answer for Question No 39. is b

Answer for Question No 40. is c

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is c

Answer for Question No 44. is b

Answer for Question No 45. is d

Answer for Question No 46. is c

Answer for Question No 47. is d

Answer for Question No 48. is d

Answer for Question No 49. is c

Answer for Question No 50. is d

Answer for Question No 51. is d

Answer for Question No 52. is b

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is c

Answer for Question No 58. is c

Answer for Question No 59. is c

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 2. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 3. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 4. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 5. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 6. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 7. RR* can be expressed in which of the forms:

A : R+

B : R-

C : R+ U R-

D:R

Q.no 8. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 9. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 10. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 11. Those problems that require large amount of computational resources
that are practically not feasible to solve, these problems are known as _________

A : Decidable

B : Undecidable

C : Tractable

D : Intractable

Q.no 12. Which of the production rule can be accepted by Chomsky grammar. (i)
A->BC, (ii) A->a

A : only i

B : only ii

C : both i and ii
D : neither i nor ii

Q.no 13. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 14. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 15. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing

Q.no 16. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 17. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 18. The minimum number of states required to recognize an octal number
divisible by 3 is

A:1

B:3

C:5

D:7

Q.no 19. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 20. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 21. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 22. Construct a regular expression for the language that contains strings
having no pair of consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 23. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 24. A context free language is called ambiguous if (a) It has two or more
leftmost derivations for the same string. (b) It has two or more rightmost
derivations for the same string. (c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 25. Which of the functions are not performed by the Turing machine after
reading a symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 26. Which among the following is equivalent to the given regular expression
01*+1

A : (01)*+1
B : 0((1)*+1)

C : (0(1)*)+1

D : ((0*1)1*)*

Q.no 27. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 28. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 29. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 30. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 31. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 32. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 33. Which of the following statement is false?

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 34. What does it mean when we say that an algorithm X is asymptotically
more efficient than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 35. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 36. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively

enumerable.

D : The complement of a context-free language is context-free.

Q.no 37. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 38. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 39. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 40. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite
automata

B : Every language defined by finite automata can also be defined by regular

expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 41. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 42. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 43. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 44. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?
A:

B:

C:

D:
Q.no 45. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 46. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 47. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:
B:

C:

D:
Q.no 48.

A:A

B:B

C:C

D:D

Q.no 49. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:
C:

D:

Q.no 50. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 51. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 52. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 53. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 54. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 55. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 56.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 57. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb
D : abbaabbaa

Q.no 58. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 59. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 60. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*
Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is c

Answer for Question No 6. is a

Answer for Question No 7. is a

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is d

Answer for Question No 12. is d

Answer for Question No 13. is c

Answer for Question No 14. is c

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is c

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is a

Answer for Question No 24. is c

Answer for Question No 25. is d

Answer for Question No 26. is c

Answer for Question No 27. is a

Answer for Question No 28. is c

Answer for Question No 29. is c

Answer for Question No 30. is a

Answer for Question No 31. is b

Answer for Question No 32. is c

Answer for Question No 33. is c

Answer for Question No 34. is b

Answer for Question No 35. is d

Answer for Question No 36. is a

Answer for Question No 37. is b

Answer for Question No 38. is d

Answer for Question No 39. is c

Answer for Question No 40. is d

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is a

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is a

Answer for Question No 48. is b

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is c

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is a

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 2. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing
Q.no 3. A->aA| a| b
The number of steps to generate aab are

A:2

B:3

C:4

D:5

Q.no 4. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 5. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 6. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 7. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 8. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 9. Which one of the following languages over the alphabet {0, 1} is described
by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 10. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 11. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 12. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous
C : regular

D : context free grammar

Q.no 13. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 14. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 15. If T1 and T2 are two Turing machines, the composite can be represented
using the expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 16. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 17. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 18. Finite state machine can recognize

A : any grammar

B : only context-free grammar

C : context free grammar and regualr grammar

D : only regular grammar

Q.no 19. A boolean formula is said to be in Conjuctive Normal Form (CNF) if it can
represented as

A : e1 V e2 V e3

B : e1 Ʌ e2 V e3

C : e1 V e2 Ʌ e3

D : e1 Ʌ e2 Ʌ e3

Q.no 20. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 21. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 22. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 23. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 24. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 25. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 26. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 27. The travelling salesman problem can be solved using _________

A : A spanning tree
B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 28. The complement of a language will only be defined when and only when
the __________ over the language is defined.

A : String

B : Word

C : Alphabet

D : Grammar

Q.no 29. Which among the following is equivalent to the given regular expression
01*+1

A : (01)*+1

B : 0((1)*+1)

C : (0(1)*)+1

D : ((0*1)1*)*

Q.no 30. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D :  Unrestricted

Q.no 31. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 32. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 33. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 34. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 35. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 36. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4
D : 2, 3, 4

Q.no 37. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 38. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 39. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 40. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 41. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?
A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 42. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 43.

A:A

B:B

C:C

D:D
Q.no 44. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 45. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 46.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 47. Transition function of NFA machine is given by

A:

B:

C:

D:
Q.no 48. For two regular languages
L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 49. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 50. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:

Q.no 51. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*
Q.no 52. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 53. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 54. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*
B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 55. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 56. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 57. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 58. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 59. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:

C:
D:

Q.no 60. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)
Answer for Question No 1. is c

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is a

Answer for Question No 7. is d

Answer for Question No 8. is b

Answer for Question No 9. is c

Answer for Question No 10. is b

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is d

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is d

Answer for Question No 18. is d

Answer for Question No 19. is d

Answer for Question No 20. is b

Answer for Question No 21. is b

Answer for Question No 22. is a

Answer for Question No 23. is b

Answer for Question No 24. is b

Answer for Question No 25. is c

Answer for Question No 26. is d

Answer for Question No 27. is b

Answer for Question No 28. is c

Answer for Question No 29. is c

Answer for Question No 30. is b

Answer for Question No 31. is b

Answer for Question No 32. is b

Answer for Question No 33. is d

Answer for Question No 34. is d

Answer for Question No 35. is c

Answer for Question No 36. is a

Answer for Question No 37. is d

Answer for Question No 38. is d

Answer for Question No 39. is a

Answer for Question No 40. is d

Answer for Question No 41. is d

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is d

Answer for Question No 48. is d

Answer for Question No 49. is c

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is c

Answer for Question No 53. is d

Answer for Question No 54. is a

Answer for Question No 55. is d

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is b

Answer for Question No 59. is c

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 2. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA

D : accepted by Turing machine

Q.no 3. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 4. In given Transition function of TM which head movement of tape is shown

(q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 5. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 6. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 7. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}

D : {y}

Q.no 8. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 9. Which of the following does not belong to the language if input alphabet
set is a,b

A:a

B:b

C : epsilon

D:c

Q.no 10. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*

D:

Q.no 11.

A : L*

B:

C:L

D:

Q.no 12. Which one of the following languages over the alphabet {0, 1} is
described by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 13. The push down automata indicate the acceptance of input string in terms
of

A : final state

B : empty stack

C : final state and empty stack

D : start state

Q.no 14.

A:

B:

C:L

D : L*

Q.no 15. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 16. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 17. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 18. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 19. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 20. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 21. Let the class of language accepted by finite state machine be L1 and the
class of languages represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2
Q.no 22. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 23. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 24. Pushdown automata behaves like Turing machine when it has the
number of auxiliary memory

A : one or more

B : two or more

C : zero

D : one

Q.no 25. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 26. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 27. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is
an independent set iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 28.

A:

B:

C:

D : {0, 1}

Q.no 29. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 30. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 31. Given a Grammar G:
S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 32. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 33. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 34. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 35. Number of states required to accept strings ending with 10 are

A:3
B:2

C:1

D : can’t be represented.

Q.no 36. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 37. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 38. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 39. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 40. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?
A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 41. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 42. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:
B:

C:

D:

Q.no 43. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 44. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5
Q.no 45. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 46. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 47. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 48. The output of Moore machine can be defined as

A:

B:

C:
D : state and its input

Q.no 49. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 50. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 51. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 52.
A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 53. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 54. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 55. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 56. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.
A:

B:

C:
D:

Q.no 57. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 58. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 59. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?
A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 60. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard
Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is a

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is c

Answer for Question No 13. is c

Answer for Question No 14. is c

Answer for Question No 15. is d

Answer for Question No 16. is b

Answer for Question No 17. is a

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is c

Answer for Question No 21. is d

Answer for Question No 22. is a

Answer for Question No 23. is c

Answer for Question No 24. is b

Answer for Question No 25. is c

Answer for Question No 26. is d

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is b

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is d

Answer for Question No 34. is d

Answer for Question No 35. is a

Answer for Question No 36. is d

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is d

Answer for Question No 40. is d

Answer for Question No 41. is b

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is d

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is a

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is b

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is c

Answer for Question No 56. is a

Answer for Question No 57. is d

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 2. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 3. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 4. Finite state machine can recognize

A : any grammar

B : only context-free grammar

C : context free grammar and regualr grammar

D : only regular grammar

Q.no 5. If the PDA does not stop on an accepting state and the stack is not empty,
the string is

A : rejected

B : goes into loop forever

C : rejected and goes into loop forever

D : accepted

Q.no 6. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 7. A->aA| a| b
The number of steps to generate aab are

A:2

B:3

C:4

D:5
Q.no 8. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 9. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 10. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 11. Minimal finite automata need _____________ no. of final states

A:1

B:2

C:3

D : Depends on problem

Q.no 12. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational
D : Computable

Q.no 13. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted

Q.no 14. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 15. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 16. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 17. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*
D:

Q.no 18. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 19. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 20. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 21. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:
Q.no 22. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 23. Which of the functions are not performed by the Turing machine after
reading a symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 24. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 25. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 26. Which of the following statement(s) are correct? (a) All languages can be
generated by CFG, (b) Any regular language has an equivalent CFG, (c) Some non
regular languages cannot be generated by CFG.

A : only (a)
B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 27. Let the class of language accepted by finite state machine be L1 and the
class of languages represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 28. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory

machine.

Q.no 29. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 30. What does it mean when we say that an algorithm X is asymptotically
more efficient than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 31. The operations of PDA never work on elements other than top of the
stack.

A : false

B : true

C : may be

D : cannot say

Q.no 32. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice
versa.

A : true

B : false

C : maybe

D : probably

Q.no 33.

A : {w | w is a string of odd length}

B : {w | w is a string of length multiple of 3}

C : {w | w is a string of length 3}

D : {w | w is an empty string}

Q.no 34. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 35. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent

deterministic Turing machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 36. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite
automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 37. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 38. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 39. Construct a regular expression for the language that contains strings that
start with either ‘01’ or ‘10’ over {0, 1}.

A : (01 + 10)*

B : (1+0)* (01 + 10) (1+0)*

C : (01 + 10) (1+0)*

D : (1+0)*

Q.no 40. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 41. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 42. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 43. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:

Q.no 44. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*
B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 45. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:
C:

D:

Q.no 46. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 47. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 48. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 49. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 50. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.
A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 51. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 52. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 53. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa
C : abbbaabb

D : abbaabbaa

Q.no 54. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 55. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III
C : Only I and II

D : Only I and III

Q.no 56. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 57. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 58. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 59. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of
non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:

B:

C:
D:

Q.no 60. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)
Answer for Question No 1. is c

Answer for Question No 2. is c

Answer for Question No 3. is b

Answer for Question No 4. is d

Answer for Question No 5. is a

Answer for Question No 6. is b

Answer for Question No 7. is b

Answer for Question No 8. is d

Answer for Question No 9. is c

Answer for Question No 10. is a

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is c

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is c

Answer for Question No 20. is b

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is d

Answer for Question No 24. is c

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is d

Answer for Question No 28. is d

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is b

Answer for Question No 32. is a

Answer for Question No 33. is b

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is d

Answer for Question No 37. is b

Answer for Question No 38. is d

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is a

Answer for Question No 44. is a

Answer for Question No 45. is c

Answer for Question No 46. is b

Answer for Question No 47. is a

Answer for Question No 48. is c

Answer for Question No 49. is c

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is c

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is d

Answer for Question No 56. is d

Answer for Question No 57. is c

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 2. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language
Q.no 3. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.

A : true

B : false

C : Cannot say

D : May be

Q.no 4. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 5. Which of the following are the examples of finite state machine system?
(a) Control Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 6. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 7. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable
C : decision

D : complete

Q.no 8. Turing Machine also behaves like General purpose computer and that TM
is known as _______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 9. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 10. Which of the following regular expressions represents the set of strings
which do not contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 11. Are the given two patterns equivalent?

(1) gray | grey (2) gr(a|e)y

A : yes

B : no

C : may be

D : cannot say

Q.no 12. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states
B : initial state

C : Final state

D : Non-final states

Q.no 13. In given Transition function of TM which head movement of tape is

shown (q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 14. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 15. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 16. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 17. To simplify a grammar we can eliminate

A : Useful symbols
B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 18. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2

D : type 3

Q.no 19. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 20. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 21. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 22. Which among the following is the LEAF of the parse tree?

A : Production P
B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 23. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*

B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 24. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 25. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree

C : Parse tree

D : Forest

Q.no 26. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 27. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent

deterministic Turing machine.
B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 28. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 29. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively

enumerable.

D : The complement of a context-free language is context-free.

Q.no 30. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 31. The power of non-deterministic pushdown automata and deterministic

pushdown automata is not same.

A : true

B : false

C : maybe

D : cannot say

Q.no 32. PDA is useful in

A : lexical analysis

B : syntax analysis

C : semantic analysis

D : code generation

Q.no 33. Which among the following is equivalent to the given regular expression
01*+1

A : (01)*+1

B : 0((1)*+1)

C : (0(1)*)+1

D : ((0*1)1*)*

Q.no 34. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 35. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 36. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control
D : All of these

Q.no 37. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 38. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 39. Recursively enumerable languages are …….. , whereas recursive

languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 40. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 41. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 42. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 43. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 44. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 45. The output of Moore machine can be defined as

A:

B:

C:
D : state and its input

Q.no 46. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 47. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 48. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement
D : Union

Q.no 49. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 50. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?
A:

B:

C:

D:
Q.no 51. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 52. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 53. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 54. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD
C:CD

D:DA

Q.no 55. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 56. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 57. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2
Q.no 58. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 59.

A:A
B:B

C:C

D:D

Q.no 60. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab
Answer for Question No 1. is c

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is d

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is a

Answer for Question No 14. is b

Answer for Question No 15. is d

Answer for Question No 16. is a

Answer for Question No 17. is b

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is d

Answer for Question No 21. is c

Answer for Question No 22. is c

Answer for Question No 23. is b

Answer for Question No 24. is c

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is d

Answer for Question No 29. is a

Answer for Question No 30. is d

Answer for Question No 31. is a

Answer for Question No 32. is b

Answer for Question No 33. is c

Answer for Question No 34. is a

Answer for Question No 35. is c

Answer for Question No 36. is d

Answer for Question No 37. is b

Answer for Question No 38. is b

Answer for Question No 39. is b

Answer for Question No 40. is b

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is d

Answer for Question No 47. is c

Answer for Question No 48. is c

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is d

Answer for Question No 52. is c

Answer for Question No 53. is c

Answer for Question No 54. is c

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 2. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 3. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 4. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational

D : Computable

Q.no 5. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 6. Construct a regular expression for the language that contains strings
having at least one pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*

C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

Q.no 7. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted

Q.no 8. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 9. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 10. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 11. In Parse Tree, Root represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 12. RR* can be expressed in which of the forms:

A : R+

B : R-

C : R+ U R-

D:R

Q.no 13. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 14. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 15. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 16. Which of the following correctly recognize the symbol ‘|-‘ in context to
PDA?

A : moves

B : transition function

C : or symbol

D : not symbol

Q.no 17. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 18. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 19. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 20. What is the Regular Expression Matching Zero or More Specific
Characters

A:x

B:#

C:*

D:&

Q.no 21. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 22. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 23. Number of external states of a UTM should be atleast

A:1

B:2

C:3

D:4

Q.no 24. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 25. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 26. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 27. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L
(G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 28. Which of the following is the restricted model of Turing machines (a)
Turing machine with semi-infinite tape, (b) Multi stack machine, (c) Offline
Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 29. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 30. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 31. Is the language preserved in all the steps while eliminating epsilon
transitions from a NFA?

A : yes

B : no

C : may be

D : cannot say
Q.no 32. The complement of a language will only be defined when and only when
the __________ over the language is defined.

A : String

B : Word

C : Alphabet

D : Grammar

Q.no 33. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 34. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 35. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 36. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple
C : Triple

D : None of the mentioned

Q.no 37. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 38. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 39. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 40. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 41. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?
A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 42. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 43. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 44. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 45.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 46. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 47. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 48. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 49. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 50. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?
A : 10

B : 11

C : 12

D : 15

Q.no 51. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 52. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 53. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0
Q.no 54. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 55. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 56. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct
Q.no 57.

A:A

B:B

C:C

D:D

Q.no 58. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 59. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV
Q.no 60. Context free grammar having the following production
X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Answer for Question No 1. is d

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is c

Answer for Question No 5. is a

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is a

Answer for Question No 12. is d

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is a

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is b

Answer for Question No 23. is d

Answer for Question No 24. is a

Answer for Question No 25. is d

Answer for Question No 26. is c

Answer for Question No 27. is c

Answer for Question No 28. is a

Answer for Question No 29. is b

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is a

Answer for Question No 33. is c

Answer for Question No 34. is a

Answer for Question No 35. is c

Answer for Question No 36. is b

Answer for Question No 37. is d

Answer for Question No 38. is b

Answer for Question No 39. is b

Answer for Question No 40. is d

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is c

Answer for Question No 44. is a

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is c

Answer for Question No 48. is a

Answer for Question No 49. is a

Answer for Question No 50. is b

Answer for Question No 51. is b

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is b

Answer for Question No 55. is a

Answer for Question No 56. is b

Answer for Question No 57. is c

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 2. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 3. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 4. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 5. Which of the production rule can be accepted by Chomsky grammar. (i) A-
>BC, (ii) A->a

A : only i

B : only ii

C : both i and ii

D : neither i nor ii

Q.no 6. Those problems that require large amount of computational resources

that are practically not feasible to solve, these problems are known as _________

A : Decidable

B : Undecidable

C : Tractable

D : Intractable

Q.no 7. A Language for which no DFA exist is a________

A : Regular Language
B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 8. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 9. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 10. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 11. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 12. Which of the following correctly recognize the symbol ‘|-‘ in context to
PDA?

A : moves
B : transition function

C : or symbol

D : not symbol

Q.no 13. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 14. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 15. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 16. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 17. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 18. A language L is said to be ____________ if there is a turing machine M such

that L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 19. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5

Q.no 20. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 21. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 22. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite
automata

B : Every language defined by finite automata can also be defined by regular

expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 23. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 24. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 25. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb

Q.no 26. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively
enumerable.

D : The complement of a context-free language is context-free.

Q.no 27. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 28. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k

instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 29. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 30. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:
C:

D:

Q.no 31. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 32. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 33. An NFA’s transition function returns

A : Boolean value

B : A state

C : A set of states

D : An edge

Q.no 34. Which productions will generate even length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb
D : S-> aSb|bSa|a|b

Q.no 35. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 36. Recursively enumerable languages are …….. , whereas recursive

languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 37. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 38. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 39. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 40. The maximum number of transitions which can be performed over a
state in a DFA having alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 41. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 42. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 43. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 44. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 45. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 46. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar
D : Phrase grammar

Q.no 47. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 48. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 49. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 50. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 51. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 52. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 53. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 54. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)
D : (a), (b) and (c)

Q.no 55. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 56. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 57. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 58. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.
A:

B:

C:
D:

Q.no 59. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 60. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Answer for Question No 1. is a

Answer for Question No 2. is b

Answer for Question No 3. is d

Answer for Question No 4. is d

Answer for Question No 5. is d

Answer for Question No 6. is d

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is c

Answer for Question No 10. is a

Answer for Question No 11. is b

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is b

Answer for Question No 15. is b

Answer for Question No 16. is d

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is b

Answer for Question No 20. is a

Answer for Question No 21. is d

Answer for Question No 22. is d

Answer for Question No 23. is d

Answer for Question No 24. is c

Answer for Question No 25. is c

Answer for Question No 26. is a

Answer for Question No 27. is d

Answer for Question No 28. is a

Answer for Question No 29. is a

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is c

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is b

Answer for Question No 37. is b

Answer for Question No 38. is c

Answer for Question No 39. is a

Answer for Question No 40. is c

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is d

Answer for Question No 45. is b

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is a

Answer for Question No 50. is d

Answer for Question No 51. is b

Answer for Question No 52. is b

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is d

Answer for Question No 56. is d

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 2. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 3. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 4. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 5. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 6. Given the expression, is there some assignment of true and false values to the
variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 7. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 8. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 9. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 10. The transition a Push down automaton makes is additionally dependent upon
the:

A : Current State

B : input tape

C : stack

D : terminals

Q.no 11. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 12. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete
Q.no 13.

A:R

B:

C : R*

D:

Q.no 14. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 15.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 16.

A:

B:

C:L

D : L*

Q.no 17. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 18. In given Transition function of TM which head movement of tape is shown
(q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 19. Which of the following does not belong to the language if input alphabet set is
a,b

A:a

B:b

C : epsilon

D:c

Q.no 20. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 21. Which of the regular expressions corresponds to the given problem statement
over the alphabet = {a, b}, All strings in which any occurrence of the symbol b, is in
groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*
Q.no 22. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 23. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 24. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.

A : true

B : false

C : maybe

D : probably

Q.no 25. If there exists a TM which when applied to any problem in the class,
terminates, if correct answer is yes and may or may not terminate otherwise is called

A : Stable

B : Unsolvable

C : Partially solvable

D : Unstable

Q.no 26. Number of external states of a UTM should be atleast

A:1

B:2

C:3

D:4

Q.no 27. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 28. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 29. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 30. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 31. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 32. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 33. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L (G1) =

L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 34. The worst case complexity of a deterministic problem to find the satisfiability
of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 35. Recursively enumerable languages are …….. , whereas recursive languages are
…....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 36. Unrestricted grammar is also called_______ Grammar

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 37. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple
C : Triple

D : None of the mentioned

Q.no 38. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 39. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 40. Which of the following is the restricted model of Turing machines (a) Turing
machine with semi-infinite tape, (b) Multi stack machine, (c) Offline Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 41. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 42. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them
are ambiguous.
B : An unambiguous context free grammar always has a unique parse tree for each string of
the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 43.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 44. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 45. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-
blank symbols does not contain any blank symbols B in between. Consider Alphabet
{a,b}.

A:
B:

C:

D:

Q.no 46. Transition function of Epsilon-NFA machine is given by

A:

B:

C:
D:

Q.no 47. Choose the correct option for the given statement: The DFA shown represents
all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 48. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 49. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 50. The set of all strings over alphabet ={a,b} in which a single a followed by any
number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*
C : a*b + b*a

D : (a+b)(a+b)*

Q.no 51. John is asked to make an automaton which accepts a given string for all the
occurrence of ‘1001’ in it. How many number of transitions would John use such that,
the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 52. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 53. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 54. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 55.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 56. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 57.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 58. In conversion from the following CFG to CNF, the number of nonterminals to
be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3
C:4

D:5

Q.no 59. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 60. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is a

Answer for Question No 7. is a

Answer for Question No 8. is d

Answer for Question No 9. is b

Answer for Question No 10. is c

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is b

Answer for Question No 14. is d

Answer for Question No 15. is c

Answer for Question No 16. is c

Answer for Question No 17. is a

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is c

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is d

Answer for Question No 28. is c

Answer for Question No 29. is d

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is c

Answer for Question No 33. is d

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is d

Answer for Question No 37. is b

Answer for Question No 38. is b

Answer for Question No 39. is c

Answer for Question No 40. is d

Answer for Question No 41. is a

Answer for Question No 42. is c

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is c

Answer for Question No 47. is b

Answer for Question No 48. is c

Answer for Question No 49. is d

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is a

Answer for Question No 53. is d

Answer for Question No 54. is d

Answer for Question No 55. is b

Answer for Question No 56. is c

Answer for Question No 57. is a

Answer for Question No 58. is d

Answer for Question No 59. is c

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 2. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 3. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 4. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 5. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 6. A two-way infinite tape Turing machine is ________ superior than the basic
model of the Turing machine in terms of power.

A : More

B : Less

C : No way

D : Very Much

Q.no 7. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5
Q.no 8.

A : L*

B:

C:L

D:

Q.no 9. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 10. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 11. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 12. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 13. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 14. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 15. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 16. A boolean formula is said to be in Conjuctive Normal Form (CNF) if it can
represented as

A : e1 V e2 V e3

B : e1 Ʌ e2 V e3

C : e1 V e2 Ʌ e3

D : e1 Ʌ e2 Ʌ e3

Q.no 17. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.
A : true

B : false

C : Cannot say

D : May be

Q.no 18. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 19. Given the expression, is there some assignment of true and false values
to the variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 20. A->aA| a| b

The number of steps to generate aab are

A:2

B:3

C:4

D:5

Q.no 21. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language
Q.no 22. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 23. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb

Q.no 24. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L

(G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 25. Unrestricted grammar is also called_______ Grammar

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 26. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite
automata

B : Every language defined by finite automata can also be defined by regular

expression
C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 27. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is
an independent set iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 28. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 29. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 30. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 31. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}
B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 32. A non-deterministic pushdown automaton can be converted into an

equivalent deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 33. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 34. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice
versa.

A : true

B : false

C : maybe

D : probably

Q.no 35. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 36. The set of all strings over alphabet = {a,b} in which all strings having
bbbb as substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 37. Let the class of language accepted by finite state machine be L1 and the
class of languages represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 38. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 39. The complement of a language will only be defined when and only when
the __________ over the language is defined.

A : String

B : Word

C : Alphabet

D : Grammar

Q.no 40. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))

B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 41. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 42. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 43. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 44. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*
C : (1+0)

D : (00+0111+10)*

Q.no 45. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 46. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 47. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)
Q.no 48. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 49. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 50.
A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 51. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 52. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 53. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 54. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete
B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 55. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 56. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 57. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 58. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 59. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 60. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Answer for Question No 1. is d

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is d

Answer for Question No 5. is d

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is b

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is a

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is b

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is b

Answer for Question No 32. is b

Answer for Question No 33. is d

Answer for Question No 34. is a

Answer for Question No 35. is c

Answer for Question No 36. is a

Answer for Question No 37. is d

Answer for Question No 38. is c

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is d

Answer for Question No 42. is c

Answer for Question No 43. is c

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is c

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is b

Answer for Question No 53. is c

Answer for Question No 54. is b

Answer for Question No 55. is d

Answer for Question No 56. is a

Answer for Question No 57. is c

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following are the examples of finite state machine system?
(a) Control Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 2. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet
Q.no 3. Turing Machine also behaves like General purpose computer and that TM
is known as _______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 4. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 5. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 6. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 7. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 8.

A:

B:

C:0

D:1

Q.no 9. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}

D : {y}

Q.no 10. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 11.

A:

B:

C:L

D : L*

Q.no 12. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 13. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 14. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 15. In given Transition function of TM which head movement of tape is

shown (q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 16. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 17. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 18. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 19. An algorithm is called efficient if it runs in ____________ time on a serial

computer.

A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 20. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 21. An NFA’s transition function returns

A : Boolean value

B : A state

C : A set of states

D : An edge
Q.no 22. X is a simple mathematical model of a computer. X has unrestricted and
unlimited memory. X is a FA with R/W head. X can have an infinite tape divided
into cells, each cell holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 23.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the
right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform
the right movement.

Q.no 24. PDA works as Finite Automata when the number of auxiliary memory it
has is

A:3

B:2

C:1

D:0

Q.no 25. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k
instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 26. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 27. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 28. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 29. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 30. Which of the following is not a Non deterministic Turing machine?
A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 31. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 32. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined

Q.no 33. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 34. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4
Q.no 35. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 36. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 37. A non-deterministic pushdown automaton can be converted into an

equivalent deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 38. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L

(G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 39. The total number of states and transitions required to form a Moore
machine that processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4
D : 2 and 5

Q.no 40. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 41. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 42. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 43. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 44. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 45. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 46. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 47. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 48. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:

C:
D:

Q.no 49. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 50. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab
Q.no 51. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 52. What does the following transition graph shows

A : Copies a symbol
B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 53. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 54. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:
D:

Q.no 55. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 56. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 57. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 58. The output of Moore machine can be defined as

A:
B:

C:

D : state and its input

Q.no 59. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 60. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2
Answer for Question No 1. is d

Answer for Question No 2. is d

Answer for Question No 3. is c

Answer for Question No 4. is d

Answer for Question No 5. is a

Answer for Question No 6. is b

Answer for Question No 7. is b

Answer for Question No 8. is a

Answer for Question No 9. is a

Answer for Question No 10. is c

Answer for Question No 11. is c

Answer for Question No 12. is d

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is b

Answer for Question No 17. is a

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is c

Answer for Question No 22. is c

Answer for Question No 23. is a

Answer for Question No 24. is d

Answer for Question No 25. is a

Answer for Question No 26. is d

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is b

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is b

Answer for Question No 34. is a

Answer for Question No 35. is a

Answer for Question No 36. is a

Answer for Question No 37. is b

Answer for Question No 38. is d

Answer for Question No 39. is a

Answer for Question No 40. is b

Answer for Question No 41. is b

Answer for Question No 42. is d

Answer for Question No 43. is a

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is c

Answer for Question No 48. is c

Answer for Question No 49. is a

Answer for Question No 50. is d

Answer for Question No 51. is b

Answer for Question No 52. is c

Answer for Question No 53. is d

Answer for Question No 54. is b

Answer for Question No 55. is b

Answer for Question No 56. is d

Answer for Question No 57. is c

Answer for Question No 58. is a

Answer for Question No 59. is c

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 2. Which one of the following languages over the alphabet {0, 1} is described
by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 3. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 4. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 5. _________ is the class of decision problems that can be solved by non-
deterministic polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 6. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 7. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 8. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 9. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 10. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 11. The Grammar can be defined as: G= (V, T, P, S) In the given definition,
what does S represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 12. Transition function of DFA machine maps.

A:

B:

C:
D:

Q.no 13. The minimum number of states required to recognize an octal number
divisible by 3 is

A:1

B:3

C:5

D:7

Q.no 14. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 15. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 16. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 17.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 18. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 19. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 20. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 21. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 22. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a
D : abc

Q.no 23. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 24. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 25. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which the total number of a’s is
divisible by 2.

A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 26.

A:

B:

C:

D : {0, 1}
Q.no 27. The shown language is recognized by (a) Turing machine, (b) Pushdown
automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 28. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 29. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 30. Construct a regular expression for the language that contains strings
having even number of 0’s followed by odd number of 1’s over {0, 1}.

A : (00)* 1 (11)*

B : ((0+1)(0+1))*

C : (0+1)*

D : (001)*

Q.no 31. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 32. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L

(G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 33. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 34. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 35. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 36. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree
C : Parse tree

D : Forest

Q.no 37. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 38. Which of the following statement is false?

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 39. Construct a regular expression for the language that contains strings
having no pair of consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 40. Which is a wrong satatement?

A : A regular language is produced by union of two regular languages

B : The concatenation of two regular languages is regular

C : The Kleene closure of a regular language is regular

D : The complement of a regular language is also a regular language

Q.no 41. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*
B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 42. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 43. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 44. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 45. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3
C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 46. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 47. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 48. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 49. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 50. For two regular languages
L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 51.

A:A

B:B

C:C

D:D

Q.no 52. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 53. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 54. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?
A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 55. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 56. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 57. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 58. Transition function of NFA machine is given by

A:

B:

C:

D:
Q.no 59. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 60. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable
Answer for Question No 1. is b

Answer for Question No 2. is c

Answer for Question No 3. is b

Answer for Question No 4. is d

Answer for Question No 5. is a

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is b

Answer for Question No 14. is c

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is c

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is a

Answer for Question No 21. is a

Answer for Question No 22. is c

Answer for Question No 23. is b

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is a

Answer for Question No 27. is d

Answer for Question No 28. is d

Answer for Question No 29. is c

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is d

Answer for Question No 33. is c

Answer for Question No 34. is b

Answer for Question No 35. is d

Answer for Question No 36. is c

Answer for Question No 37. is d

Answer for Question No 38. is c

Answer for Question No 39. is b

Answer for Question No 40. is d

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is d

Answer for Question No 47. is a

Answer for Question No 48. is c

Answer for Question No 49. is b

Answer for Question No 50. is d

Answer for Question No 51. is b

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is b

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is c

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 2. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 3. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 4. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 5. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 6. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 7. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete
Q.no 8. A two-way infinite tape Turing machine is ________ superior than the basic
model of the Turing machine in terms of power.

A : More

B : Less

C : No way

D : Very Much

Q.no 9. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 10. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 11. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 12. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)
Q.no 13. Which of the following regular expressions represents the set of strings
which do not contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 14. Which of the following is false for a grammar G in Chomsky Normal
Form:

A : G has no useless symbols

B : G has no unit productions

C : G has no epsilon productions

D : G must have useless symbols

Q.no 15. RR* can be expressed in which of the forms:

A : R+

B : R-

C : R+ U R-

D:R

Q.no 16. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 17. Which among the following are incorrect regular identities?

A:
B:

C:

D:

Q.no 18. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 19. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 20. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 21. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb
Q.no 22. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 23. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 24. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 25. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine
Q.no 26. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 27. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 28. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown

automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing

Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 29. Which of the following statement is false?

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 30. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 31. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 32. A non-deterministic pushdown automaton can be converted into an

equivalent deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 33. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 34. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 35. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T
D : Starting symbol S

Q.no 36. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 37. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 38.

A:

B:

C:

D : {0, 1}

Q.no 39. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 40. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 41. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 42. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 43. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?
A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 44. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 45. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 46. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard
Q.no 47.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 48. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 49. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 50. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 51. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 52. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 53. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 54. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?
A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 55. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 56. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 57. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:
Q.no 58.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 59. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 60. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac
Answer for Question No 1. is b

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is b

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is b

Answer for Question No 10. is d

Answer for Question No 11. is b

Answer for Question No 12. is a

Answer for Question No 13. is d

Answer for Question No 14. is d

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is d

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is c

Answer for Question No 22. is a

Answer for Question No 23. is c

Answer for Question No 24. is b

Answer for Question No 25. is c

Answer for Question No 26. is d

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is c

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is b

Answer for Question No 33. is b

Answer for Question No 34. is c

Answer for Question No 35. is c

Answer for Question No 36. is d

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is d

Answer for Question No 40. is a

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is d

Answer for Question No 45. is b

Answer for Question No 46. is b

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is d

Answer for Question No 50. is d

Answer for Question No 51. is a

Answer for Question No 52. is c

Answer for Question No 53. is c

Answer for Question No 54. is c

Answer for Question No 55. is d

Answer for Question No 56. is a

Answer for Question No 57. is c

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 2. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol
Q.no 3. Which one of the following languages over the alphabet {0, 1} is described
by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 4. Which of the production rule can be accepted by Chomsky grammar. (i) A-
>BC, (ii) A->a

A : only i

B : only ii

C : both i and ii

D : neither i nor ii

Q.no 5. The decision problem is the function from string to ______________

A : char

B :  int

C :  boolean

D : float

Q.no 6. For alphabet = {a,b}, the regular expression r = (aa)*(bb)*b denotes

A : Set of strings with 2 a’s and 2 b’s

B : Set of strings with 2 a’s 2 b’s followed by b

C : Set of strings with 2 a’s followed by b’s which is a multiple of 3

D : Set of strings with even number of a’s followed by odd number of b’s

Q.no 7. Which of the following pair of regular expressions are not equivalent?

A : 1(01)* and (10)*1

B : x(xx)* and (xx)*x

C : (ab)* and a*b*

D : x+ and x*x+

Q.no 8. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 9. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 10. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 11. A grammar that produces more than one parse tree for some sentence is
called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 12. Finite state machine is ___________tuple machine.

A:4

B:5

C:6
D : unlimitted

Q.no 13. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 14. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 15. The transition a Push down automaton makes is additionally dependent
upon the:

A : Current State

B : input tape

C : stack

D : terminals

Q.no 16. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 17. The minimum number of states required to recognize an octal number
divisible by 3 is

A:1

B:3
C:5

D:7

Q.no 18. Identify the problem: Given a graph G = <V, E>, and a starting node a,
does it have a tour cost less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 19. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 20. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 21. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 22. Which productions will generate even length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b
B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 23. Construct a regular expression for the language that contains strings
that start with either ‘01’ or ‘10’ over {0, 1}.

A : (01 + 10)*

B : (1+0)* (01 + 10) (1+0)*

C : (01 + 10) (1+0)*

D : (1+0)*

Q.no 24. Let the class of language accepted by finite state machine be L1 and the
class of languages represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 25. The complexity class P consist of all the decision problems that can be
solved by ___________using polynomial amount of computation time.

A : Push Down automata

B : DFA

C : NDFA

D : Deterministic Turing machine

Q.no 26. PDA is useful in

A : lexical analysis

B : syntax analysis

C : semantic analysis

D : code generation

Q.no 27. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 28. It is less complex to prove the closure properties over regular languages
using

A : NFA

B : DFA

C : PDA

D : Canot be said

Q.no 29. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 30. Which of the regular expressions correspond to the given problem
statement: Express the identifiers in C Programming language where l=letters
d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 31. Which of the following does not obey pumping lemma for context free
languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages
D : Restricted languages

Q.no 32. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 33. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 34. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 35. According to the given language, which among the following expressions
does it corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 36. Can a DFA recognize a palindrome number?

A : Yes

B : No
C : May be

D : Cannot be determined

Q.no 37. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 38. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 39. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 40. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 41. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac
A:2

B:3

C:4

D:5

Q.no 42. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 43. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 44. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 45. The output of Moore machine can be defined as

A:

B:
C:

D : state and its input

Q.no 46. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 47. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 48. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)
A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 49. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 50. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:
Q.no 51.

A:A

B:B

C:C

D:D

Q.no 52. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 53. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 54. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?
A:

B:

C:

D:

Q.no 55. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 56. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 57. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 58. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0
Q.no 59. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 60. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Answer for Question No 1. is a

Answer for Question No 2. is d

Answer for Question No 3. is c

Answer for Question No 4. is d

Answer for Question No 5. is c

Answer for Question No 6. is d

Answer for Question No 7. is c

Answer for Question No 8. is c

Answer for Question No 9. is a

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is b

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is c

Answer for Question No 16. is c

Answer for Question No 17. is b

Answer for Question No 18. is d

Answer for Question No 19. is b

Answer for Question No 20. is d

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is d

Answer for Question No 26. is b

Answer for Question No 27. is a

Answer for Question No 28. is a

Answer for Question No 29. is d

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is a

Answer for Question No 33. is c

Answer for Question No 34. is c

Answer for Question No 35. is d

Answer for Question No 36. is b

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is a

Answer for Question No 40. is a

Answer for Question No 41. is d

Answer for Question No 42. is c

Answer for Question No 43. is a

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is d

Answer for Question No 50. is c

Answer for Question No 51. is b

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is a

Answer for Question No 55. is b

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is a

Answer for Question No 59. is c

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 2. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational

D : Computable

Q.no 3. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 4. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 5. Turing Machine also behaves like General purpose computer and that TM
is known as _______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 6. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 7. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input
Q.no 8. What is the Regular Expression Matching Zero or More Specific
Characters

A:x

B:#

C:*

D:&

Q.no 9. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 10. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 11. An algorithm is called efficient if it runs in ____________ time on a serial

computer.

A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 12. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 13. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 14. Which of the following regular expressions represents the set of strings
which do not contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 15. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 16. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 17. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols
D : Non Unit productions

Q.no 18. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 19. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 20. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 21. Is the language preserved in all the steps while eliminating epsilon
transitions from a NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 22. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 23. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 24. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))

B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 25. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 26.

A:

B:
C:

D : {0, 1}

Q.no 27. The total number of states and transitions required to form a Moore
machine that processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 28. The minimum number of 1’s to be used in a regular expression of the
given language of all strings containing exactly 2 zeroes.

A:2

B:3

C:0

D:1

Q.no 29. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 30. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 31. The ability for a system of instructions to simulate a Turing Machine is
called _________
A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 32. Which of the following statement(s) are correct? (a) All languages can be
generated by CFG, (b) Any regular language has an equivalent CFG, (c) Some non
regular languages cannot be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 33. A non-deterministic pushdown automaton can be converted into an

equivalent deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 34. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 35. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb
D : (a+b)+ bb

Q.no 36. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 37. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k

instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 38. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 39. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 40. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine
D : Finite state machine

Q.no 41. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 42. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 43. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 44.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 45. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 46. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 47. Transition function of NFA machine is given by

A:
B:

C:

D:

Q.no 48. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 49. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 50. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 51. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 52. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 53. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:
C:

D:

Q.no 54. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*
Q.no 55. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 56. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 57. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb
D : abbaabbaa

Q.no 58. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 59. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 60. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a
Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is d

Answer for Question No 4. is b

Answer for Question No 5. is c

Answer for Question No 6. is a

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is b

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is d

Answer for Question No 13. is c

Answer for Question No 14. is d

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is b

Answer for Question No 18. is a

Answer for Question No 19. is b

Answer for Question No 20. is d

Answer for Question No 21. is a

Answer for Question No 22. is c

Answer for Question No 23. is a

Answer for Question No 24. is a

Answer for Question No 25. is d

Answer for Question No 26. is a

Answer for Question No 27. is a

Answer for Question No 28. is b

Answer for Question No 29. is d

Answer for Question No 30. is c

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is b

Answer for Question No 34. is c

Answer for Question No 35. is c

Answer for Question No 36. is b

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is c

Answer for Question No 40. is c

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is d

Answer for Question No 48. is d

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is d

Answer for Question No 52. is a

Answer for Question No 53. is c

Answer for Question No 54. is a

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is a

Answer for Question No 58. is b

Answer for Question No 59. is d

Answer for Question No 60. is d

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 2. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 3. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 4. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*

D:

Q.no 5. Which of the following pair of regular expressions are not equivalent?

A : 1(01)* and (10)*1

B : x(xx)* and (xx)*x

C : (ab)* and a*b*

D : x+ and x*x+

Q.no 6. Given the expression, is there some assignment of true and false values to
the variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 7. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted
Q.no 8. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 9. Identify the problem: Given a graph G = <V, E>, and a starting node a, does
it have a tour cost less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 10. Which one of the following languages over the alphabet {0, 1} is
described by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 11. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 12. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 13. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 14. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 15. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 16. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 17. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 18. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 19. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 20. For alphabet = {a,b}, the regular expression r = (aa)*(bb)*b denotes

A : Set of strings with 2 a’s and 2 b’s

B : Set of strings with 2 a’s 2 b’s followed by b

C : Set of strings with 2 a’s followed by b’s which is a multiple of 3

D : Set of strings with even number of a’s followed by odd number of b’s

Q.no 21. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L

(G1) = L (G2).
D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 22. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent

deterministic Turing machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 23. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 24. Which of the regular expressions correspond to the given problem
statement: Express the identifiers in C Programming language where l=letters
d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 25. A PDA machine configuration (p, w, y) can be correctly represented as

A : unprocessed input, stack content, current state

B : current state, unprocessed input, stack content

C : current state, stack content, unprocessed input

D : stack content, current state, unprocessed input

Q.no 26. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals
B : Start symbol

C : Set of terminals

D : Production

Q.no 27. Which is a wrong satatement?

A : A regular language is produced by union of two regular languages

B : The concatenation of two regular languages is regular

C : The Kleene closure of a regular language is regular

D : The complement of a regular language is also a regular language

Q.no 28. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 29. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 30. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 31. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa
B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 32. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 33. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 34. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 35.

A:

B:
C:

D : {0, 1}

Q.no 36. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 37. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 38. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 39. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which any occurrence of the
symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*
D : a* b* (bb)* a*

Q.no 40. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 41. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 42. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 43. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2
Q.no 44.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 45. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 46. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 47. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 48. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?
A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 49. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 50. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa
Q.no 51.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 52. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 53. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 54. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 55. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 56. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 57. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 58. Construct the regular expressions for the following DFAs:
A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 59. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 60. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*
Answer for Question No 1. is d

Answer for Question No 2. is c

Answer for Question No 3. is c

Answer for Question No 4. is b

Answer for Question No 5. is c

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is c

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is b

Answer for Question No 17. is d

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is a

Answer for Question No 24. is c

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is d

Answer for Question No 28. is c

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is c

Answer for Question No 34. is d

Answer for Question No 35. is a

Answer for Question No 36. is a

Answer for Question No 37. is b

Answer for Question No 38. is c

Answer for Question No 39. is b

Answer for Question No 40. is b

Answer for Question No 41. is b

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is b

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is a

Answer for Question No 48. is a

Answer for Question No 49. is b

Answer for Question No 50. is a

Answer for Question No 51. is b

Answer for Question No 52. is c

Answer for Question No 53. is b

Answer for Question No 54. is d

Answer for Question No 55. is d

Answer for Question No 56. is d

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is c

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 2. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these
Q.no 3. If T1 and T2 are two Turing machines, the composite can be represented
using the expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 4. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 5. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 6. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 7. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states
Q.no 8. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 9. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 10. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 11. A boolean formula is said to be in Conjuctive Normal Form (CNF) if it can
represented as

A : e1 V e2 V e3

B : e1 Ʌ e2 V e3

C : e1 V e2 Ʌ e3

D : e1 Ʌ e2 Ʌ e3

Q.no 12. Those problems that require large amount of computational resources
that are practically not feasible to solve, these problems are known as _________

A : Decidable

B : Undecidable

C : Tractable
D : Intractable

Q.no 13. Identify the problem: Given a graph G = <V, E>, and a starting node a,
does it have a tour cost less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 14. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 15. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 16. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack
Q.no 17. Which of the following are the examples of finite state machine system?
(a) Control Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 18. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 19. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 20. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 21. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine
D : finite state machine

Q.no 22. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 23. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which the total number of a’s is
divisible by 2.

A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 24. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 25. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined

Q.no 26. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 27. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 28. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 29. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 30. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 31. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 32. Which of the following is the restricted model of Turing machines (a)
Turing machine with semi-infinite tape, (b) Multi stack machine, (c) Offline
Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 33. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 34. PDA works as Finite Automata when the number of auxiliary memory it
has is

A:3

B:2

C:1

D:0

Q.no 35. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which any occurrence of the
symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*
D : a* b* (bb)* a*

Q.no 36. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice
versa.

A : true

B : false

C : maybe

D : probably

Q.no 37. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))

B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 38. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 39. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 40. X is a simple mathematical model of a computer. X has unrestricted and

unlimited memory. X is a FA with R/W head. X can have an infinite tape divided
into cells, each cell holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 41. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 42. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 43. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 44. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 45. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 46. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:

Q.no 47. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.
A:

B:

C:
D:

Q.no 48. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 49. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 50. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*
Q.no 51. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 52. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 53. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 54.

A:A

B:B

C:C

D:D

Q.no 55. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 56. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 57. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 58. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 59. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 60. If all the production rules have single nonterminal symbol on the left
side then grammar is called as
A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar
Answer for Question No 1. is a

Answer for Question No 2. is d

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is b

Answer for Question No 7. is a

Answer for Question No 8. is d

Answer for Question No 9. is c

Answer for Question No 10. is a

Answer for Question No 11. is d

Answer for Question No 12. is d

Answer for Question No 13. is d

Answer for Question No 14. is d

Answer for Question No 15. is b

Answer for Question No 16. is d

Answer for Question No 17. is d

Answer for Question No 18. is c

Answer for Question No 19. is b

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is c

Answer for Question No 24. is a

Answer for Question No 25. is b

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is a

Answer for Question No 29. is a

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is d

Answer for Question No 33. is c

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is a

Answer for Question No 40. is c

Answer for Question No 41. is d

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is a

Answer for Question No 45. is c

Answer for Question No 46. is a

Answer for Question No 47. is a

Answer for Question No 48. is d

Answer for Question No 49. is b

Answer for Question No 50. is d

Answer for Question No 51. is d

Answer for Question No 52. is a

Answer for Question No 53. is b

Answer for Question No 54. is b

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is c

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 2. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 3. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 4. The decision problem is the function from string to ______________

A : char

B :  int

C :  boolean

D : float

Q.no 5.

A : L*

B:

C:L

D:

Q.no 6. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 7. The push down automata indicate the acceptance of input string in terms
of

A : final state

B : empty stack

C : final state and empty stack

D : start state

Q.no 8. What is the Regular Expression Matching Zero or More Specific

Characters

A:x

B:#

C:*

D:&

Q.no 9. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 10. The Grammar can be defined as: G= (V, T, P, S) In the given definition,
what does S represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 11. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*

D:

Q.no 12.

A:
B:

C:L

D : L*

Q.no 13. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 14. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 15. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 16. In given Transition function of TM which head movement of tape is

shown (q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 17. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 18. The recognizing capability of NDFAand DFA

A : must be the same

B : may be different

C : must be different

D : cannot say

Q.no 19. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2

D : type 3

Q.no 20. The finite automata  is called NFA when there exists____________ for a
specific input from current state to next state

A : Single path

B : Multiple paths

C : Only two paths

D : Three paths

Q.no 21. Which of the following statement is false?

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 22. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 23. How many strings of length less than 4 contain the language described by
the regular expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 24. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 25. Unrestricted grammar is also called_______ Grammar

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 26. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa
Q.no 27. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 28. Which of the following does not obey pumping lemma for context free
languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

Q.no 29. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)

B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 30. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 31. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 32. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 33. Let the class of language accepted by finite state machine be L1 and the
class of languages represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 34. PDA works as Finite Automata when the number of auxiliary memory it
has is

A:3

B:2

C:1

D:0

Q.no 35. The power of non-deterministic pushdown automata and deterministic

pushdown automata is not same.

A : true

B : false

C : maybe

D : cannot say

Q.no 36. Recursively enumerable languages are …….. , whereas recursive

languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 37. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 38. The set of all strings over alphabet = {a,b} in which all strings having
bbbb as substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 39. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D :  Unrestricted

Q.no 40. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 41. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 42. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 43. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 44. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*
C : (0+010)*

D : (0+1)*

Q.no 45. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 46. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 47. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 48. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 49. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 50. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 51. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 52. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 53. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 54. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 55.

A:A

B:B

C:C

D:D

Q.no 56.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 57.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 58. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 59. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 60. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".
A:

B:

C:

D:
Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is c

Answer for Question No 5. is b

Answer for Question No 6. is c

Answer for Question No 7. is c

Answer for Question No 8. is c

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is c

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is c

Answer for Question No 18. is a

Answer for Question No 19. is c

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is a

Answer for Question No 23. is c

Answer for Question No 24. is b

Answer for Question No 25. is d

Answer for Question No 26. is a

Answer for Question No 27. is a

Answer for Question No 28. is c

Answer for Question No 29. is d

Answer for Question No 30. is a

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is d

Answer for Question No 34. is d

Answer for Question No 35. is a

Answer for Question No 36. is b

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is b

Answer for Question No 40. is d

Answer for Question No 41. is d

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is a

Answer for Question No 45. is c

Answer for Question No 46. is b

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is c

Answer for Question No 50. is d

Answer for Question No 51. is a

Answer for Question No 52. is d

Answer for Question No 53. is b

Answer for Question No 54. is d

Answer for Question No 55. is b

Answer for Question No 56. is b

Answer for Question No 57. is a

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 2. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 3. If P, Q, R are three regular expressions and if P does not contain epsilon,
then the equation R = Q + RP has a unique solution given by

A : R = QP*

B : R = P*Q

C : R = RP

D : R = QP

Q.no 4. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 5. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 6. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 7. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 8. Given the expression, is there some assignment of true and false values to
the variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 9. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 10. Which of the following are the examples of finite state machine system?
(a) Control Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 11. The transition a Push down automaton makes is additionally dependent
upon the:

A : Current State

B : input tape

C : stack

D : terminals

Q.no 12. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable
C : Context free

D : Context sensitive

Q.no 13. The push down automata indicate the acceptance of input string in terms
of

A : final state

B : empty stack

C : final state and empty stack

D : start state

Q.no 14. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 15. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 16. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 17. Transition function of DFA machine maps.

A:
B:

C:

D:

Q.no 18. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 19. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 20. An algorithm is called efficient if it runs in ____________ time on a serial

computer.

A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 21.

A : {w | w is a string of odd length}

B : {w | w is a string of length multiple of 3}

C : {w | w is a string of length 3}

D : {w | w is an empty string}
Q.no 22.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the
right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform
the right movement.

Q.no 23. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))

B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 24. What does it mean when we say that an algorithm X is asymptotically
more efficient than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 25. Which among the following is equivalent to the given regular expression
01*+1

A : (01)*+1

B : 0((1)*+1)

C : (0(1)*)+1
D : ((0*1)1*)*

Q.no 26. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which any occurrence of the
symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*

Q.no 27. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 28. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 29. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D :  Unrestricted

Q.no 30. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers
C : Text Search

D : Image processing

Q.no 31. The complexity class P consist of all the decision problems that can be
solved by ___________using polynomial amount of computation time.

A : Push Down automata

B : DFA

C : NDFA

D : Deterministic Turing machine

Q.no 32. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 33. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 34. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*
D:

Q.no 35. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 36. PDA can be represented with the help of

A : Instantaneous description

B : input symbols

C : start state

D : final state

Q.no 37. If there exists a TM which when applied to any problem in the class,
terminates, if correct answer is yes and may or may not terminate otherwise is
called

A : Stable

B : Unsolvable

C : Partially solvable

D : Unstable

Q.no 38. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 39. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which the total number of a’s is
divisible by 2.
A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 40. The operations of PDA never work on elements other than top of the
stack.

A : false

B : true

C : may be

D : cannot say

Q.no 41. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 42. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 43. From the options given below the statement, which is not necessarily true
if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:
B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 44. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 45. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of
non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:
B:

C:

D:

Q.no 46. If all the production rules have single nonterminal symbol on the left side
then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 47. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 48. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 49. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".
A:

B:

C:

D:

Q.no 50. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 51. The output of Moore machine can be defined as

A:

B:
C:

D : state and its input

Q.no 52. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 53. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 54. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 55. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 56. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 57. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV
Q.no 58. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 59.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 60. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)
Answer for Question No 1. is d

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is d

Answer for Question No 7. is c

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is c

Answer for Question No 12. is b

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is d

Answer for Question No 16. is a

Answer for Question No 17. is d

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is a

Answer for Question No 23. is a

Answer for Question No 24. is b

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is d

Answer for Question No 29. is b

Answer for Question No 30. is d

Answer for Question No 31. is d

Answer for Question No 32. is d

Answer for Question No 33. is a

Answer for Question No 34. is a

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is c

Answer for Question No 38. is c

Answer for Question No 39. is c

Answer for Question No 40. is b

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is b

Answer for Question No 50. is d

Answer for Question No 51. is a

Answer for Question No 52. is b

Answer for Question No 53. is c

Answer for Question No 54. is d

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 2. In given Transition function of TM which head movement of tape is shown

(q0,a)->(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement
Q.no 3. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 4. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 5. Identify the problem: Given a graph G = <V, E>, and a starting node a, does
it have a tour cost less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 6. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 7. What is the Regular Expression Matching Zero or More Specific

Characters

A:x

B:#

C:*
D:&

Q.no 8. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 9. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 10. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 11. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 12. Which of the following are the actions that operates on stack top?

A : only push

B : only pop
C : only push and pop

D : push, pop and replace

Q.no 13. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.

A : true

B : false

C : Cannot say

D : May be

Q.no 14. Which of the following is false for a grammar G in Chomsky Normal
Form:

A : G has no useless symbols

B : G has no unit productions

C : G has no epsilon productions

D : G must have useless symbols

Q.no 15. Given the expression, is there some assignment of true and false values
to the variables that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 16. An algorithm is called efficient if it runs in ____________ time on a serial

computer.

A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 17. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 18. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 19. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 20. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 21. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 22. According to Chomsky hierarchy, which of the following is recognized by
Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 23. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 24. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 25. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 26. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol
C : Set of terminals

D : Production

Q.no 27. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 28. Recursively enumerable languages are …….. , whereas recursive

languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 29. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 30. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 31. The RE that gives none or many instances of an x or y is

A : (x+y)
B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 32. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 33. Which of the following does not obey pumping lemma for context free
languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

Q.no 34. X is a simple mathematical model of a computer. X has unrestricted and

unlimited memory. X is a FA with R/W head. X can have an infinite tape divided
into cells, each cell holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 35. The minimum number of productions required to produce a language

consisting of palindrome strings over T={a,b} is

A:3

B:7

C:5

D:6
Q.no 36. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 37. The total number of states and transitions required to form a Moore
machine that processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 38. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 39. Which of the following is the restricted model of Turing machines (a)
Turing machine with semi-infinite tape, (b) Multi stack machine, (c) Offline
Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 40. The shown language is recognized by (a) Turing machine, (b) Pushdown

automata, (c) Finite automata

A : Only (a)
B : Only (b)

C : Only (c)

D : Only (a) and (b)

Q.no 41. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 42. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 43.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 44. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)
B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 45. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 46.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 47.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 48. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 49. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 50. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 51. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 52. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 53. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 54. Construct the regular expressions for the following DFAs:
A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 55. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 56. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 57. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 58. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*
C:

D : (0+1)* 011

Q.no 59. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 60. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:
D:
Answer for Question No 1. is d

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is c

Answer for Question No 5. is d

Answer for Question No 6. is c

Answer for Question No 7. is c

Answer for Question No 8. is b

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is a

Answer for Question No 14. is d

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is d

Answer for Question No 18. is b

Answer for Question No 19. is b

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is c

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is c

Answer for Question No 30. is a

Answer for Question No 31. is b

Answer for Question No 32. is c

Answer for Question No 33. is c

Answer for Question No 34. is c

Answer for Question No 35. is c

Answer for Question No 36. is c

Answer for Question No 37. is a

Answer for Question No 38. is d

Answer for Question No 39. is d

Answer for Question No 40. is d

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is b

Answer for Question No 44. is b

Answer for Question No 45. is d

Answer for Question No 46. is b

Answer for Question No 47. is a

Answer for Question No 48. is b

Answer for Question No 49. is b

Answer for Question No 50. is c

Answer for Question No 51. is b

Answer for Question No 52. is d

Answer for Question No 53. is a

Answer for Question No 54. is a

Answer for Question No 55. is b

Answer for Question No 56. is c

Answer for Question No 57. is b

Answer for Question No 58. is c

Answer for Question No 59. is a

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 2.

A:R

B:

C : R*
D:

Q.no 3. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 4. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 5. A deterministic Turing machine is

A : Ambiguous Turing Machine

B : Unambiguous Turing Machine

C : Non-Deterministic Finite Automata

D : Deterministic Finite Automata

Q.no 6. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 7. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language
D : Context Sensitive language

Q.no 8. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}

D : {y}

Q.no 9. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 10. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 11. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 12. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 13. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 14. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 15. The finite automata  is called NFA when there exists____________ for a
specific input from current state to next state

A : Single path

B : Multiple paths

C : Only two paths

D : Three paths

Q.no 16. Transition function of Turing Machine is

A:

B:

C:

D:
Q.no 17. A language L is said to be ____________ if there is a turing machine M such
that L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 18. Which one of the following languages over the alphabet {0, 1} is
described by the regular expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 19. A grammar G=(V, T, P, S) is __________ if every production taken one of the
two forms: B->aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 20. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 21. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k
instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 22. The set of all strings over alphabet = {a,b} in which all strings having
bbbb as substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 23. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 24. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 25. The problem of finding a path in a graph that visits every vertex exactly
once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 26. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))
B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 27. The minimum number of 1’s to be used in a regular expression of the
given language of all strings containing exactly 2 zeroes.

A:2

B:3

C:0

D:1

Q.no 28. Construct a regular expression for the language that contains strings
having no pair of consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 29. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:

C:

D:
Q.no 30. Which productions will generate even length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 31. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 32. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 33. The maximum number of transitions which can be performed over a
state in a DFA having alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 34. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol
C : Set of terminals

D : Production

Q.no 35. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 36. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*

B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 37. PDA works as Finite Automata when the number of auxiliary memory it
has is

A:3

B:2

C:1

D:0

Q.no 38. Which productions will generate odd length palindromes for terminals
'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b
Q.no 39. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is
an independent set iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 40. A context free language is called ambiguous if (a) It has two or more
leftmost derivations for the same string. (b) It has two or more rightmost
derivations for the same string. (c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 41. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 42. The regular expression denotes a language comprising all possible
strings of even length over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 43. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.
A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 44.

A:A

B:B

C:C

D:D

Q.no 45. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)
Q.no 46. Consider the following statements.
I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 47. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 48. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 49. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is
A:3

B:5

C:7

D:2

Q.no 50.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 51. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.

A:
B:

C:

D:

Q.no 52. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*
C : a*b + b*a

D : (a+b)(a+b)*

Q.no 53. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 54. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 55. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 56. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union
Q.no 57. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 58. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable
Q.no 59. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 60. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011
Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is b

Answer for Question No 7. is c

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is b

Answer for Question No 12. is b

Answer for Question No 13. is d

Answer for Question No 14. is c

Answer for Question No 15. is b

Answer for Question No 16. is a

Answer for Question No 17. is b

Answer for Question No 18. is c

Answer for Question No 19. is b

Answer for Question No 20. is a

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is a

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is d

Answer for Question No 32. is b

Answer for Question No 33. is c

Answer for Question No 34. is a

Answer for Question No 35. is a

Answer for Question No 36. is b

Answer for Question No 37. is d

Answer for Question No 38. is a

Answer for Question No 39. is b

Answer for Question No 40. is c

Answer for Question No 41. is d

Answer for Question No 42. is d

Answer for Question No 43. is b

Answer for Question No 44. is b

Answer for Question No 45. is b

Answer for Question No 46. is d

Answer for Question No 47. is c

Answer for Question No 48. is a

Answer for Question No 49. is b

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is c

Answer for Question No 57. is a

Answer for Question No 58. is d

Answer for Question No 59. is c

Answer for Question No 60. is c

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what
does S represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 2. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted
Q.no 3. An algorithm is called efficient if it runs in ____________ time on a serial
computer.

A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 4. If P, Q, R are three regular expressions and if P does not contain epsilon,
then the equation R = Q + RP has a unique solution given by

A : R = QP*

B : R = P*Q

C : R = RP

D : R = QP

Q.no 5. Which of the following a Turing machine does not consist of?

A : Input tape

B : Head

C : State register

D : Stack

Q.no 6. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 7. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 8. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 9. In Mealy machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 10. Construct a regular expression for the language that contains strings
having at least one pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*

C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

Q.no 11. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 12. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 13. In Parse Tree, Root represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 14. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

Q.no 15. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 16. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 17. To which of the following class does a CNF-satisfiability problem belong?
A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 18. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 19. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 20. For alphabet = {a,b}, the regular expression r = (aa)*(bb)*b denotes

A : Set of strings with 2 a’s and 2 b’s

B : Set of strings with 2 a’s 2 b’s followed by b

C : Set of strings with 2 a’s followed by b’s which is a multiple of 3

D : Set of strings with even number of a’s followed by odd number of b’s

Q.no 21. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

C : may be

D : cannot say

Q.no 22. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 23. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 24. Construct a regular expression for the language that contains strings
having no pair of consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 25. An NFA’s transition function returns

A : Boolean value

B : A state

C : A set of states

D : An edge

Q.no 26. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 27. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 28. The set of all strings over {a,b} in which strings consisting a’s and b’s and
ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb

Q.no 29.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the
right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the
Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform
the right movement.

Q.no 30. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable
Q.no 31. Construct a regular expression for the language that contains strings
that start with either ‘01’ or ‘10’ over {0, 1}.

A : (01 + 10)*

B : (1+0)* (01 + 10) (1+0)*

C : (01 + 10) (1+0)*

D : (1+0)*

Q.no 32. The regular expression with all strings of 0′s and 1′s with at least two
consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 33. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 34. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:

C:
D:

Q.no 35. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 36. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 37. Which of the following statement(s) are correct? (a) All languages can be
generated by CFG, (b) Any regular language has an equivalent CFG, (c) Some non
regular languages cannot be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 38. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*
B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 39. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 40. The difference between number of states in FA for regular expression (a
+ b) and (a + b) * is:

A:1

B:2

C:3

D:0

Q.no 41. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 42. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence
of non-blank symbols does not contain any blank symbols B in between. Consider
Alphabet {a,b}.
A:

B:

C:
D:

Q.no 43. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 44. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 45. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 46. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 47.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 48. Choose the correct option for the given statement: The DFA shown
represents all strings which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct
Q.no 49. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 50. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 51. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 52. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:

Q.no 53. The regular expression for all strings of 0′s and 1′s with no two
consecutive 0′s is

A : (0+1)

B : (0+1)*
C:

D : (0+1)* 011

Q.no 54. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 55. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:

B:
C:

D:

Q.no 56. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 57. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.
C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 58. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 59. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 60. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is d

Answer for Question No 7. is d

Answer for Question No 8. is b

Answer for Question No 9. is b

Answer for Question No 10. is c

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is c

Answer for Question No 14. is c

Answer for Question No 15. is b

Answer for Question No 16. is c

Answer for Question No 17. is c

Answer for Question No 18. is c

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is b

Answer for Question No 22. is b

Answer for Question No 23. is c

Answer for Question No 24. is b

Answer for Question No 25. is c

Answer for Question No 26. is d

Answer for Question No 27. is a

Answer for Question No 28. is c

Answer for Question No 29. is a

Answer for Question No 30. is b

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is c

Answer for Question No 34. is a

Answer for Question No 35. is a

Answer for Question No 36. is b

Answer for Question No 37. is d

Answer for Question No 38. is b

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is a

Answer for Question No 48. is b

Answer for Question No 49. is a

Answer for Question No 50. is c

Answer for Question No 51. is d

Answer for Question No 52. is c

Answer for Question No 53. is c

Answer for Question No 54. is d

Answer for Question No 55. is a

Answer for Question No 56. is c

Answer for Question No 57. is c

Answer for Question No 58. is a

Answer for Question No 59. is d

Answer for Question No 60. is c

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 2. Turing Machine can update symbols on its tape, whereas the FA cannot
update symbols on tape.

A : true

B : false

C : Cannot say

D : May be
Q.no 3. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 4. In regular expressions, the operator ‘*’ stands for

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 5. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 6. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 7. An algorithm is called efficient if it runs in ____________ time on a serial

computer.
A : Polynomial

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 8. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 9. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 10. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 11. Which of the following statement is true? (a) Turing machine was
developed by Alan Turing, (b) PDA is less powerful than Turing machine, (c) FA is
more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)
Q.no 12. A->aA| a| b
The number of steps to generate aab are

A:2

B:3

C:4

D:5

Q.no 13. If T1 and T2 are two Turing machines, the composite can be represented
using the expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 14. Decidable can be taken as a synonym to:

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 15. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 16. Can we convert PDA to equivalent CFG?

A : yes

B : no

C : maybe
D : never

Q.no 17. In Moore machine, if input is of length n, then length of output string will
be

A:n

B : n+1

C : n+n

D : n-1

Q.no 18. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 19. A language L is said to be ____________ if there is a turing machine M such

that L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 20. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 21. Is the language preserved in all the steps while eliminating epsilon
transitions from a NFA?

A : yes

B : no
C : may be

D : cannot say

Q.no 22. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 23. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:

C:

D:

Q.no 24. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 25. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 26. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 27. Pushdown automata behaves like Turing machine when it has the
number of auxiliary memory

A : one or more

B : two or more

C : zero

D : one

Q.no 28. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 29. Which among the following is equivalent to the given regular expression
01*+1

A : (01)*+1

B : 0((1)*+1)

C : (0(1)*)+1

D : ((0*1)1*)*
Q.no 30. The worst case complexity of a deterministic problem to find the
satisfiability of a given formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 31. The RE in which any number of 0′s is followed by any number of 1′s
followed by any number of 2′s is

A : (0+1+2)*

B : 0*1*2*

C : 0* + 1 + 2

D : (0+1)*2*

Q.no 32. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 33. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 34. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 35. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 36. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 37. Turing machine (TM) is more powerful than FSM (Finite State Machine)
because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 38. It is less complex to prove the closure properties over regular languages
using

A : NFA

B : DFA

C : PDA

D : Canot be said
Q.no 39. Which of the functions are not performed by the Turing machine after
reading a symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 40. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined

Q.no 41. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 42. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 43. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3
B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 44. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:

B:
C:

D:

Q.no 45. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 46. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".
A:

B:

C:

D:

Q.no 47. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 48. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 49. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 50. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?

A:
B:

C:

D:

Q.no 51. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV
Q.no 52. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 53. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 54. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 55. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable
D : X1 – X3 is recursively enumerable

Q.no 56. The minimum number of productions required to produce a language

consisting of palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 57. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 58. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 59. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 60. The language A-> tB|t generated by which of the following grammar?

A : Type 3
B : Type 2

C : Type 1

D : Type 0
Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is d

Answer for Question No 4. is c

Answer for Question No 5. is a

Answer for Question No 6. is c

Answer for Question No 7. is a

Answer for Question No 8. is c

Answer for Question No 9. is d

Answer for Question No 10. is a

Answer for Question No 11. is c

Answer for Question No 12. is b

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is d

Answer for Question No 16. is a

Answer for Question No 17. is b

Answer for Question No 18. is d

Answer for Question No 19. is b

Answer for Question No 20. is d

Answer for Question No 21. is a

Answer for Question No 22. is b

Answer for Question No 23. is a

Answer for Question No 24. is a

Answer for Question No 25. is c

Answer for Question No 26. is c

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is c

Answer for Question No 30. is d

Answer for Question No 31. is b

Answer for Question No 32. is a

Answer for Question No 33. is d

Answer for Question No 34. is d

Answer for Question No 35. is d

Answer for Question No 36. is c

Answer for Question No 37. is c

Answer for Question No 38. is a

Answer for Question No 39. is d

Answer for Question No 40. is b

Answer for Question No 41. is d

Answer for Question No 42. is b

Answer for Question No 43. is a

Answer for Question No 44. is c

Answer for Question No 45. is c

Answer for Question No 46. is b

Answer for Question No 47. is a

Answer for Question No 48. is a

Answer for Question No 49. is a

Answer for Question No 50. is a

Answer for Question No 51. is b

Answer for Question No 52. is d

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is d

Answer for Question No 56. is b

Answer for Question No 57. is a

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is a

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Turing machine is more powerful than (a) Finite automata, (b) Push down
automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Neither (a) nor (b)

Q.no 2. Transition function of Turing Machine is

A:

B:

C:
D:

Q.no 3. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 4. The recognizing capability of NDFAand DFA

A : must be the same

B : may be different

C : must be different

D : cannot say

Q.no 5. The push down automata indicate the acceptance of input string in terms
of

A : final state

B : empty stack

C : final state and empty stack

D : start state

Q.no 6. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 7. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive
B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 8.

A:

B:

C:0

D:1

Q.no 9. Given the language L = {ab, aa, baa}, which of the following strings are in
L*? 1) abaabaaabaa 2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 10. A deterministic Turing machine is

A : Ambiguous Turing Machine

B : Unambiguous Turing Machine

C : Non-Deterministic Finite Automata

D : Deterministic Finite Automata

Q.no 11. For alphabet = {a,b}, the regular expression r = (aa)*(bb)*b denotes

A : Set of strings with 2 a’s and 2 b’s

B : Set of strings with 2 a’s 2 b’s followed by b

C : Set of strings with 2 a’s followed by b’s which is a multiple of 3

D : Set of strings with even number of a’s followed by odd number of b’s

Q.no 12. Can we convert PDA to equivalent CFG?

A : yes

B : no

C : maybe

D : never

Q.no 13. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 14. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 15. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 16. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)
D : CLR(K)

Q.no 17. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 18. A boolean formula is said to be in Conjuctive Normal Form (CNF) if it can
represented as

A : e1 V e2 V e3

B : e1 Ʌ e2 V e3

C : e1 V e2 Ʌ e3

D : e1 Ʌ e2 Ʌ e3

Q.no 19. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 20. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 21. The minimum number of productions required to produce a language

consisting of palindrome strings over T={a,b} is

A:3

B:7
C:5

D:6

Q.no 22. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 23. For a DFA accepting binary numbers whose decimal equivalent is
divisible by 4, what are all the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 24.

A:

B:

C:

D:

Q.no 25. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 26. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 27. Which of the regular expressions corresponds to the given problem
statement over the alphabet = {a, b}, All strings in which any occurrence of the
symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*

Q.no 28. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 29. Which of the following represents a language which has no pair of
consecutive 1’s if alphabet = {0,1}?

A:

B:

C:

D:
Q.no 30. PDA works as Finite Automata when the number of auxiliary memory it
has is

A:3

B:2

C:1

D:0

Q.no 31. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 32. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 33. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 34. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory
machine.

Q.no 35. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 36. X is a simple mathematical model of a computer. X has unrestricted and

unlimited memory. X is a FA with R/W head. X can have an infinite tape divided
into cells, each cell holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 37. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be
performed by standard TM.

D : Tape is only in one direction.

Q.no 38. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 39. Given grammar G:
(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 40. What does it mean when we say that an algorithm X is asymptotically
more efficient than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 41. John is asked to make an automaton which accepts a given string for all
the occurrence of ‘1001’ in it. How many number of transitions would John use
such that, the string processing application works?

A : 10

B : 11

C : 12

D : 15

Q.no 42. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 43. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)
B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 44. The set of all strings over alphabet ={a,b} in which a single a followed by
any number of b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 45. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:
D:

Q.no 46.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 47. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 48. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 49. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 50. Transition function of Epsilon-NFA machine is given by

A:

B:
C:

D:

Q.no 51.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 52. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 53. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 54. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.
A:

B:

C:
D:

Q.no 55. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 56. Consider three decision problems P1, P2 and P3. It is known that P1 is
decidable and P2 is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 57. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union
Q.no 58. The context free languages are closed under (a) union, (b) concatenation,
(c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 59. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 60.

A:A

B:B
C:C

D:D
Answer for Question No 1. is c

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is c

Answer for Question No 6. is a

Answer for Question No 7. is b

Answer for Question No 8. is a

Answer for Question No 9. is c

Answer for Question No 10. is b

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is b

Answer for Question No 14. is c

Answer for Question No 15. is a

Answer for Question No 16. is a

Answer for Question No 17. is b

Answer for Question No 18. is d

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is c

Answer for Question No 22. is b

Answer for Question No 23. is d

Answer for Question No 24. is d

Answer for Question No 25. is d

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is c

Answer for Question No 29. is a

Answer for Question No 30. is d

Answer for Question No 31. is d

Answer for Question No 32. is a

Answer for Question No 33. is a

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is d

Answer for Question No 38. is d

Answer for Question No 39. is a

Answer for Question No 40. is b

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is b

Answer for Question No 44. is a

Answer for Question No 45. is b

Answer for Question No 46. is b

Answer for Question No 47. is c

Answer for Question No 48. is b

Answer for Question No 49. is d

Answer for Question No 50. is c

Answer for Question No 51. is b

Answer for Question No 52. is d

Answer for Question No 53. is d

Answer for Question No 54. is c

Answer for Question No 55. is b

Answer for Question No 56. is c

Answer for Question No 57. is c

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is b

 Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Turing machine is more powerful than (a) Finite automata, (b) Push down
automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Neither (a) nor (b)

Q.no 2. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input
Q.no 3. Construct a regular expression for the language that contains strings
having at least one pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*

C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

Q.no 4. Linear Bounded Automaton is a

A : Finite Automaton

B : Turing Machine

C : Push down Automaton

D : Deterministic Finite Automata

Q.no 5. If P, Q, R are three regular expressions and if P does not contain epsilon,
then the equation R = Q + RP has a unique solution given by

A : R = QP*

B : R = P*Q

C : R = RP

D : R = QP

Q.no 6. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 7. A boolean formula is said to be in Conjuctive Normal Form (CNF) if it can

represented as

A : e1 V e2 V e3

B : e1 Ʌ e2 V e3

C : e1 V e2 Ʌ e3
D : e1 Ʌ e2 Ʌ e3

Q.no 8. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 9. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 10. Turing machine was invented by

A : Alan Turing

B : Turing man

C : Turing taring

D : Turling Bake

Q.no 11. Choose the correct option for the statement: Unambiguity is the ideal
structure of a language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 12. The decision problem is the function from string to ______________
A : char

B :  int

C :  boolean

D : float

Q.no 13. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5

Q.no 14. If there exists a language L, for which there exists a TM, T, that accepts
every word in L and either rejects or loops for every word that is not in L, is
called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 15. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing

Q.no 16. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union
Q.no 17. A grammar G=(V, T, P, S) is __________ if every production taken one of the
two forms: B->aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 18. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 19. A two-way infinite tape Turing machine is ________ superior than the basic
model of the Turing machine in terms of power.

A : More

B : Less

C : No way

D : Very Much

Q.no 20. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 21. Construct a regular expression for the language that contains strings
that start with either ‘01’ or ‘10’ over {0, 1}.

A : (01 + 10)*

B : (1+0)* (01 + 10) (1+0)*

C : (01 + 10) (1+0)*

D : (1+0)*

Q.no 22. A non-deterministic pushdown automaton can be converted into an

equivalent deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 23. According to Chomsky hierarchy, which of the following is recognized by

Recursively Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 24. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 25. The total number of states and transitions required to form a Moore
machine that processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 26. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory

machine.

Q.no 27. The ability for a system of instructions to simulate a Turing Machine is
called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 28. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 29. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 30. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined
Q.no 31. The automaton which allows transformation to a new state without
consuming any input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 32. Construct a regular expression for the language that contains strings
having no pair of consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 33. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is
an independent set iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 34. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 35. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree
C : Parse tree

D : Forest

Q.no 36. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down

Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 37. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 38. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 39. The minimum number of productions required to produce a language

consisting of palindrome strings over T={a,b} is

A:3

B:7

C:5

D:6

Q.no 40. Number of states required to accept strings ending with 10 are

A:3
B:2

C:1

D : can’t be represented.

Q.no 41. Out of the three problems S, Q and R, S is an NP-complete problem and Q
and R are the two other problems not known to be in NP. Which one of the
following statements is true if Q is polynomial time reducible to S and S is the
polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 42. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii)
((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 43. Examine the following DFA: If input is 011100101, which edge is NOT

traversed?

A:AB

B:BD

C:CD

D:DA
Q.no 44. In conversion from the following CFG to CNF, the number of
nonterminals to be introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 45. Which grammar accepts the language of {a, b} having strings ending with
'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 46. If all the production rules have single nonterminal symbol on the left
side then grammar is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 47. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 48. Which Transition table of Turing Machine is correct for the following
problem
"Design a TM to find 2's complement of a binary number".
A:

B:

C:

D:

Q.no 49. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 50. The lexical analysis for a modern computer language such as Java needs
the power of which one of the following machine models in a necessary and
sufficient sense?
A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 51. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 52. Construct a Turing machine which accepts a string with ‘aba’ as its
substring.

A:
B:

C:

D:

Q.no 53. From the options given below the statement, which is not necessarily
true if X1 is the recursive language and X2 and X3 are the languages that are
recursively enumerable but not recursive.
A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 54. The problems which have no algorithm, regardless of whether or not
they are accepted by a turing machine that fails to halt on some input are
referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 55. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 56. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating
them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each
string of the language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.
D : Finite set of strings from one alphabet is always a regular language.

Q.no 57. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 58. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 59. Let S be an NP-complete problem and Q and R be two other problems not
known to be in NP. Q is polynomial time reducible to S and S is polynomial-time
reducible to R. Which one of the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 60. Which Transition table of Turing Machine is correct to check well
formedness of parentheses?
A:

B:

C:

D:
Answer for Question No 1. is c

Answer for Question No 2. is a

Answer for Question No 3. is c

Answer for Question No 4. is b

Answer for Question No 5. is a

Answer for Question No 6. is b

Answer for Question No 7. is d

Answer for Question No 8. is b

Answer for Question No 9. is a

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is c

Answer for Question No 13. is b

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is d

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is c

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is b

Answer for Question No 23. is d

Answer for Question No 24. is c

Answer for Question No 25. is a

Answer for Question No 26. is d

Answer for Question No 27. is a

Answer for Question No 28. is d

Answer for Question No 29. is d

Answer for Question No 30. is b

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is b

Answer for Question No 34. is a

Answer for Question No 35. is c

Answer for Question No 36. is b

Answer for Question No 37. is c

Answer for Question No 38. is b

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is b

Answer for Question No 42. is d

Answer for Question No 43. is c

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is c

Answer for Question No 48. is b

Answer for Question No 49. is d

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is c

Answer for Question No 53. is d

Answer for Question No 54. is b

Answer for Question No 55. is d

Answer for Question No 56. is c

Answer for Question No 57. is c

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is a

12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 2. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 3. Halting states are of two types. They are:

A : accept and reject

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : reject and allow

C : start and reject

D : start and accept

Q.no 4. In Moore machine, if input is of length n, then length of output string will be

A:n

B : n+1

C : n+n

D : n-1

Q.no 5. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 6. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 7. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 8. If P, Q, R are three regular expressions and if P does not contain epsilon, then the
equation R = Q + RP has a unique solution given by

A : R = QP*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : R = P*Q

C : R = RP

D : R = QP

Q.no 9. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}

D : {y}

Q.no 10. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 11. If T1 and T2 are two Turing machines, the composite can be represented using the
expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 12.

A:

B:

C:0

D:1

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 13. The decision problem is the function from string to ______________

A : char

B : int

C : boolean

D : float

Q.no 14. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 15. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 16. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 17. Construct a regular expression for the language that contains strings having at least one
pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*

C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 18. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 19. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 20. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 21. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

D : Type 2 grammar is CFG

Q.no 22. According to the given language, which among the following expressions does it
corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 23. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory machine.

Q.no 24. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 25.

A:

B:

C:

D : {0, 1}

Q.no 26. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 27. Number of states required to accept strings ending with 10 are

A:3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:2

C:1

D : can’t be represented.

Q.no 28. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 29. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 30. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 31. Which productions will generate odd length palindromes for terminals 'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 32. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 33. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 34. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*

B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 35. Which productions will generate even length palindromes for terminals 'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 36. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 37. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : may be

D : cannot say

Q.no 38. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent deterministic Turing
machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 39. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 40. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively enumerable.

D : The complement of a context-free language is context-free.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 41. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 42. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 43. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 44.

A:A

B:B

C:C

D:D

Q.no 45. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 46. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 47. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 48. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 49.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 50. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 51. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are
the two other problems not known to be in NP. Which one of the following statements is true if Q
is polynomial time reducible to S and S is the polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Q is NP-hard

D : R is NP-hard

Q.no 52. The set of all strings over alphabet ={a,b} in which a single a followed by any number of
b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 53. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 54. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 55. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : II and III

D : II and IV

Q.no 56. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 57. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 58. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 59. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 60. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/16
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is b

Answer for Question No 5. is a

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is a

Answer for Question No 9. is a

Answer for Question No 10. is b

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is d

Answer for Question No 15. is b

Answer for Question No 16. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is c

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is d

Answer for Question No 24. is d

Answer for Question No 25. is a

Answer for Question No 26. is d

Answer for Question No 27. is a

Answer for Question No 28. is b

Answer for Question No 29. is b

Answer for Question No 30. is c

Answer for Question No 31. is a

Answer for Question No 32. is a

Answer for Question No 33. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is b

Answer for Question No 37. is b

Answer for Question No 38. is b

Answer for Question No 39. is d

Answer for Question No 40. is a

Answer for Question No 41. is c

Answer for Question No 42. is c

Answer for Question No 43. is c

Answer for Question No 44. is b

Answer for Question No 45. is d

Answer for Question No 46. is c

Answer for Question No 47. is c

Answer for Question No 48. is d

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is b

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is b

Answer for Question No 56. is b

Answer for Question No 57. is d

Answer for Question No 58. is d

Answer for Question No 59. is b

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 2. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 3. Universal TM influenced the concept of

A : Stored program computers

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 4. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 5. In one move the Turing machine___

A : May change its state

B : Write a symbol on the cell being scanned.

C : Move the head one position left or right

D : All of the above

Q.no 6. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 7. Which of the following statement is true? (a) Turing machine was developed by Alan
Turing, (b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 8. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 9. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 10. A grammar G=(V, T, P, S) is __________ if every production taken one of the two forms:
B->aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 11. Which of the following are the examples of finite state machine system? (a) Control
Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 12. Which among the following are incorrect regular identities?

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 13. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 14. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 15.

A:

B:

C:0

D:1

Q.no 16. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 17. Identify the problem: Given a graph G = <V, E>, and a starting node a, does it have a
tour cost less than k?

A : Satisfiability
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 18. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 19. Minimal finite automata need _____________ no. of final states

A:1

B:2

C:3

D : Depends on problem

Q.no 20. Turing Machine also behaves like General purpose computer and that TM is known as
_______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 21. The difference between number of states in FA for regular expression (a + b) and (a + b)
* is:

A:1

B:2

C:3

D:0

Q.no 22. Which of the following is a false statement?

A : Moore machine has no accepting states

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 23. The operations of PDA never work on elements other than top of the stack.

A : false

B : true

C : may be

D : cannot say

Q.no 24. A non-deterministic pushdown automaton can be converted into an equivalent

deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 25. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 26. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 27. Which of the following statement is false?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : For non deterministic PDA, equivalence is undecidable.

B : For deterministic PDA, equivalence is decidable.

C : For deterministic PDA, equivalence is undecidable.

D : For non deterministic PDA, equivalence is decidable.

Q.no 28. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

Q.no 29. Turing machine (TM) is more powerful than FSM (Finite State Machine) because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 30. The production of the form A->B , where A and B are non terminals is called

A : Null production

B : Greibach Normal Form

C : Unit production

D : Chomsky Normal Form

Q.no 31. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 32. The string (a)|((b)*(c)) is equivalent to

A : Empty
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : abcabc

C : b*c|a

D : abc

Q.no 33. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 34. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 35. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 36. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 37. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 38. Is the language preserved in all the steps while eliminating epsilon transitions from a
NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 39. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 40. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 41. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 42. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 43. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 44. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are
the two other problems not known to be in NP. Which one of the following statements is true if Q
is polynomial time reducible to S and S is the polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 45. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 46. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 47. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 48. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 49. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 50. Construct a Turing machine which accepts a string with ‘aba’ as its substring.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 51. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 52. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 53. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 54. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 55. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 56. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : 10

B : 11

C : 12

D : 15

Q.no 57. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 58. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 59.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 60.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is d

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is d

Answer for Question No 9. is a

Answer for Question No 10. is b

Answer for Question No 11. is d

Answer for Question No 12. is d

Answer for Question No 13. is a

Answer for Question No 14. is c

Answer for Question No 15. is a

Answer for Question No 16. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is d

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is c

Answer for Question No 21. is a

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is b

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is a

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is b

Answer for Question No 32. is c

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is d

Answer for Question No 35. is c

Answer for Question No 36. is d

Answer for Question No 37. is c

Answer for Question No 38. is a

Answer for Question No 39. is c

Answer for Question No 40. is d

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is c

Answer for Question No 47. is d

Answer for Question No 48. is c

Answer for Question No 49. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is c

Answer for Question No 51. is d

Answer for Question No 52. is d

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is d

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2

D : type 3

Q.no 2. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 3. Given the language L = {ab, aa, baa}, which of the following strings are in L*? 1) abaabaaabaa
2) aaaabaaaa
3) baaaaabaaaab 4) baaaaabaa

A : 1, 2 and 3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : 2, 3 and 4

C : 1, 2 and 4

D : 1, 3 and 4

Q.no 4. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 5.

A:

B:

C:0

D:1

Q.no 6.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 7. Can we convert PDA to equivalent CFG?

A : yes

B : no

C : maybe

D : never

Q.no 8. The decision problem is the function from string to ______________

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : char

B : int

C : boolean

D : float

Q.no 9. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 10. Which of the following is false for a grammar G in Chomsky Normal Form:

A : G has no useless symbols

B : G has no unit productions

C : G has no epsilon productions

D : G must have useless symbols

Q.no 11. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 12. Transition function of Turing Machine is

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 13. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted

Q.no 14. _________ is the class of decision problems that can be solved by non-deterministic polynomial
algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 15. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 16. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 17. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Context sensitive

Q.no 18. Which of the following statement is true? (a) Turing machine was developed by Alan Turing,
(b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 19. Identify the problem: Given a graph G = <V, E>, and a starting node a, does it have a tour cost
less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 20. Which of the following does not belong to the language if input alphabet set is a,b

A:a

B:b

C : epsilon

D:c

Q.no 21. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 22. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata (NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 23. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings in which the total number of a’s is divisible by 2.

A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 24. For a DFA accepting binary numbers whose decimal equivalent is divisible by 4, what are all
the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 25. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 26. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 27. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:3

Q.no 28. Which of the following automata takes stack as auxiliary storage

A : finite automata

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 29. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 30.

A:

B:

C:

D : {0, 1}

Q.no 31. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 32. The maximum number of transitions which can be performed over a state in a DFA having
alphabet set a,b,c are

A:1

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:2

C:3

D:4

Q.no 33.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform the right movement.

Q.no 34. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 35. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 36. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 37. Let the class of language accepted by finite state machine be L1 and the class of languages
represented by regular expressions be L2 then

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 38. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 39. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 40. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree

C : Parse tree

D : Forest

Q.no 41. John is asked to make an automaton which accepts a given string for all the occurrence of
‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

C : 12

D : 15

Q.no 42. The problems which have no algorithm, regardless of whether or not they are accepted by a
turing machine that fails to halt on some input are referred as:

A : Decidable

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Undecidable

C : Computable

D : Recognizable

Q.no 43. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 44.

A:A

B:B

C:C

D:D

Q.no 45. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is
undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 46. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 47. The regular expression denotes a language comprising all possible strings of even length over
the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 48. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 49. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 50. Which Transition table of Turing Machine is correct to check well formedness of parentheses?

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

Q.no 51. The lexical analysis for a modern computer language such as Java needs the power of which
one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 52. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 53. Let S be an NP-complete problem and Q and R be two other problems not known to be in NP.
Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the given
statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 54. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 55. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 56. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 57. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are the two
other problems not known to be in NP. Which one of the following statements is true if Q is polynomial
time reducible to S and S is the polynomial time reducible to R?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 58. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 59. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 60.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is c

Answer for Question No 2. is b

Answer for Question No 3. is c

Answer for Question No 4. is b

Answer for Question No 5. is a

Answer for Question No 6. is c

Answer for Question No 7. is a

Answer for Question No 8. is c

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is b

Answer for Question No 12. is a

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is c

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is d

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is c

Answer for Question No 28. is b

Answer for Question No 29. is b

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is c

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is a

Answer for Question No 35. is a

Answer for Question No 36. is c

Answer for Question No 37. is d

Answer for Question No 38. is a

Answer for Question No 39. is c

Answer for Question No 40. is c

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is b

Answer for Question No 45. is c

Answer for Question No 46. is c

Answer for Question No 47. is d

Answer for Question No 48. is b

Answer for Question No 49. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is d

Answer for Question No 53. is b

Answer for Question No 54. is b

Answer for Question No 55. is d

Answer for Question No 56. is c

Answer for Question No 57. is b

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 2. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 3. In CFG, notation of VARIABLE representation is

A : Captal Letters
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 4. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 5. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 6. RR* can be expressed in which of the forms:

A : R+

B : R-

C : R+ U R-

D:R

Q.no 7. What is the Regular Expression Matching Zero or More Specific Characters

A:x

B:#

C:*

D:&

Q.no 8. If P, Q, R are three regular expressions and if P does not contain epsilon, then the
equation R = Q + RP has a unique solution given by

A : R = QP*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : R = P*Q

C : R = RP

D : R = QP

Q.no 9. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 10. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what does S
represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 11. (a+b)* is equivalent to

A : b*a*

B : (a*b*)*

C : a*b*

D:

Q.no 12. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 13. Which of the following are the actions that operates on stack top?

A : only push
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 14.

A:

B:

C:0

D:1

Q.no 15. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 16. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 17. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 18. What is the value of n if Turing machine is defined using n-tuples?
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:6

B:7

C:8

D:5

Q.no 19. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 20. Finite state machine can recognize

A : any grammar

B : only context-free grammar

C : context free grammar and regualr grammar

D : only regular grammar

Q.no 21.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the right
movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the right
movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the Left
movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform the right
movement.

Q.no 22. Number of states required to accept strings ending with 10 are

A:3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:2

C:1

D : can’t be represented.

Q.no 23. Which of the following represents a language which has no pair of consecutive 1’s if
alphabet = {0,1}?

A:

B:

C:

D:

Q.no 24. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 25. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 26. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 27. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 28. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 29.

A:

B:

C:

D:

Q.no 30. The power of non-deterministic pushdown automata and deterministic pushdown
automata is not same.

A : true

B : false

C : maybe

D : cannot say
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 31. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 32. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 33. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 34. Is the language preserved in all the steps while eliminating epsilon transitions from a
NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 35. A non-deterministic pushdown automaton can be converted into an equivalent

deterministic pushdown automaton.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : never

B : not always

C : always

D : maybe

Q.no 36. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 37. According to the given language, which among the following expressions does it
corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 38. Pushdown automata behaves like Turing machine when it has the number of auxiliary
memory

A : one or more

B : two or more

C : zero

D : one

Q.no 39. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 40. Which of the following is the restricted model of Turing machines (a) Turing machine
with semi-infinite tape, (b) Multi stack machine, (c) Offline Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 41. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 42. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

C : 12

D : 15

Q.no 43. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 44. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 45. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 46. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:4

D:5

Q.no 47. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 48. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 49. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 50. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 51. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 52. Transition function of NFA machine is given by

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 53. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 54. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 55. From the options given below the statement, which is not necessarily true if X1 is the
recursive language and X2 and X3 are the languages that are recursively enumerable but not
recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 56. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Turing machine

Q.no 57. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 58. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 59. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 60. Construct a Turing machine which accepts a string with ‘aba’ as its substring.
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is c

Answer for Question No 2. is d

Answer for Question No 3. is a

Answer for Question No 4. is c

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is a

Answer for Question No 9. is a

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is d

Answer for Question No 13. is d

Answer for Question No 14. is a

Answer for Question No 15. is c

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is c

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is a

Answer for Question No 24. is a

Answer for Question No 25. is d

Answer for Question No 26. is a

Answer for Question No 27. is c

Answer for Question No 28. is b

Answer for Question No 29. is d

Answer for Question No 30. is a

Answer for Question No 31. is b

Answer for Question No 32. is d

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is a

Answer for Question No 35. is b

Answer for Question No 36. is d

Answer for Question No 37. is d

Answer for Question No 38. is b

Answer for Question No 39. is a

Answer for Question No 40. is d

Answer for Question No 41. is c

Answer for Question No 42. is a

Answer for Question No 43. is c

Answer for Question No 44. is a

Answer for Question No 45. is a

Answer for Question No 46. is d

Answer for Question No 47. is b

Answer for Question No 48. is c

Answer for Question No 49. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is b

Answer for Question No 51. is d

Answer for Question No 52. is d

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is d

Answer for Question No 56. is a

Answer for Question No 57. is c

Answer for Question No 58. is c

Answer for Question No 59. is c

Answer for Question No 60. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 2. Linear Bounded Automaton is a

A : Finite Automaton

B : Turing Machine

C : Push down Automaton

D : Deterministic Finite Automata

Q.no 3. Transition function of Turing Machine is

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 4. Construct a regular expression for the language that contains strings having at least one
pair of consecutive zeros over {0, 1}.

A : (100)*

B : 1* (00)* 1*

C : [ (1 + 0 )* (00) (1 + 0 )*] +

D : ((0+1)(0+1))*

Q.no 5. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 6. Are the given two patterns equivalent?

(1) gray | grey (2) gr(a|e)y

A : yes

B : no

C : may be

D : cannot say

Q.no 7. Turing machine is more powerful than (a) Finite automata, (b) Push down automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Neither (a) nor (b)

Q.no 8. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 9. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 10. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 11. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 12. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:+,.,*

Q.no 13. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 14. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 15. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 16. The recognizing capability of NDFAand DFA

A : must be the same

B : may be different

C : must be different

D : cannot say

Q.no 17. Given the expression, is there some assignment of true and false values to the variables
that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Traveling Salesman Problem

Q.no 18. Which of the following case does not exist in complexity theory?

A : Best case

B : Worst case

C : Average case

D : Null case

Q.no 19. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 20. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 21. An NFA’s transition function returns

A : Boolean value

B : A state

C : A set of states

D : An edge

Q.no 22. According to the given language, which among the following expressions does it
corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : (0+1+ε)^4

Q.no 23. The regular expression with all strings of 0′s and 1′s with at least two consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 24. The set of all strings over alphabet = {a,b} in which all strings having bbbb as substring
is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 25. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 26. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent deterministic Turing
machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 27. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata
(NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 28. A context free language is called ambiguous if (a) It has two or more leftmost
derivations for the same string. (b) It has two or more rightmost derivations for the same string.
(c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 29. The automaton which allows transformation to a new state without consuming any
input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 30. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 31. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : regular and context free

Q.no 32. The RE that gives none or many instances of an x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 33. Recursively enumerable languages are …….. , whereas recursive languages are …....

A : completely-solvable, semi solvable

B : semi-solvable, completely solvable

C : not solvable, completely solvable

D : semi-solvable, not solvable

Q.no 34. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 35. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively enumerable.

D : The complement of a context-free language is context-free.

Q.no 36. The minimum number of 1’s to be used in a regular expression of the given language of
all strings containing exactly 2 zeroes.

A:2

B:3

C:0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:1

Q.no 37. The operations of PDA never work on elements other than top of the stack.

A : false

B : true

C : may be

D : cannot say

Q.no 38. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 39.

A:

B:

C:

D:

Q.no 40. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 41. Any string of terminals that can be generated by the following CFG
S-> XY ,

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 42. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 43.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 44. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

B : R is NP-hard

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Q is NP-complete

D : Q is NP-hard

Q.no 45. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 46. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 47. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 48. Construct a Turing machine which accepts a string with ‘aba’ as its substring.

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 49.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 50. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 51. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 52. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Computable

D : Recognizable

Q.no 53. From the options given below the statement, which is not necessarily true if X1 is the
recursive language and X2 and X3 are the languages that are recursively enumerable but not
recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 54. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 55. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 56. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 57. Which of following can be accepted by DPDA

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 58. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 59. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 60. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is d

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is c

Answer for Question No 5. is d

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is b

Answer for Question No 9. is b

Answer for Question No 10. is d

Answer for Question No 11. is d

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is b

Answer for Question No 15. is c

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is a

Answer for Question No 18. is d

Answer for Question No 19. is b

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is b

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is c

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is d

Answer for Question No 32. is b

Answer for Question No 33. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is b

Answer for Question No 35. is a

Answer for Question No 36. is b

Answer for Question No 37. is b

Answer for Question No 38. is d

Answer for Question No 39. is d

Answer for Question No 40. is c

Answer for Question No 41. is d

Answer for Question No 42. is d

Answer for Question No 43. is a

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is c

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is c

Answer for Question No 52. is b

Answer for Question No 53. is d

Answer for Question No 54. is a

Answer for Question No 55. is a

Answer for Question No 56. is d

Answer for Question No 57. is d

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. _________ is the class of decision problems that can be solved by non-deterministic
polynomial algorithms?

A : NP

B:P

C : Hard

D : Complete

Q.no 2. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 3. Finite state machine is ___________tuple machine.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:4

B:5

C:6

D : unlimitted

Q.no 4. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 5. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 6. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 7. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 8. The major difference between Mealy and Moore machine is about:

A : Output Variations

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Input Variations

C : Both

D : Transitions

Q.no 9. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational

D : Computable

Q.no 10. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 11. If there exists a language L, for which there exists a TM, T, that accepts every word in L
and either rejects or loops for every word that is not in L, is called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 12. Which of the following correctly recognize the symbol ‘|-‘ in context to PDA?

A : moves

B : transition function

C : or symbol

D : not symbol

Q.no 13. Which one of the following languages over the alphabet {0, 1} is described by the regular
expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 14. The recognizing capability of NDFAand DFA

A : must be the same

B : may be different

C : must be different

D : cannot say

Q.no 15. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA

D : accepted by Turing machine

Q.no 16. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 17. Which of the following statement is true? (a) Turing machine was developed by Alan
Turing, (b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 18. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2

D : type 3

Q.no 19. Which of the following is false for a grammar G in Chomsky Normal Form:

A : G has no useless symbols

B : G has no unit productions

C : G has no epsilon productions

D : G must have useless symbols

Q.no 20. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 21. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is an
independent set iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 22. The regular expression with all strings of 0′s and 1′s with at least two consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 23. Which of the following is a false statement?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 24. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 25. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 26. Under which of the following operation, NFA is not closed?

A : Negation

B : Kleene

C : Concatenation

D : complement

Q.no 27. Which is a wrong satatement?

A : A regular language is produced by union of two regular languages

B : The concatenation of two regular languages is regular

C : The Kleene closure of a regular language is regular

D : The complement of a regular language is also a regular language

Q.no 28. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 29. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 30. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 31. It is less complex to prove the closure properties over regular languages using

A : NFA

B : DFA

C : PDA

D : Canot be said

Q.no 32. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 33. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 34. The difference between Turing Machine and Two Way FA is in:

A : Input Tape

B : Read Write Head

C : Finite Control

D : All of these

Q.no 35. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D : Unrestricted

Q.no 36. Which of the following does not obey pumping lemma for context free languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

Q.no 37. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 38. PDA works as Finite Automata when the number of auxiliary memory it has is

A:3

B:2

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:1

D:0

Q.no 39. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 40.

A : {w | w is a string of odd length}

B : {w | w is a string of length multiple of 3}

C : {w | w is a string of length 3}

D : {w | w is an empty string}

Q.no 41. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 42. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 43. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 44. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 45. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 46. Construct the regular expressions for the following DFAs:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 47. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 48.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 49. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 50. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 51. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 52. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 53.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 54. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:5

Q.no 55. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 56. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

C : 12

D : 15

Q.no 57. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 58. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 59. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 60. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is a

Answer for Question No 2. is b

Answer for Question No 3. is b

Answer for Question No 4. is b

Answer for Question No 5. is c

Answer for Question No 6. is b

Answer for Question No 7. is a

Answer for Question No 8. is a

Answer for Question No 9. is a

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is a

Answer for Question No 16. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is c

Answer for Question No 18. is c

Answer for Question No 19. is d

Answer for Question No 20. is d

Answer for Question No 21. is b

Answer for Question No 22. is b

Answer for Question No 23. is d

Answer for Question No 24. is d

Answer for Question No 25. is a

Answer for Question No 26. is d

Answer for Question No 27. is d

Answer for Question No 28. is c

Answer for Question No 29. is b

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is d

Answer for Question No 33. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is c

Answer for Question No 38. is d

Answer for Question No 39. is b

Answer for Question No 40. is b

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is d

Answer for Question No 44. is c

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is d

Answer for Question No 48. is b

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is a

Answer for Question No 51. is b

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is b

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted

Q.no 2. If T1 and T2 are two Turing machines, the composite can be represented using the
expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 3.

A:

B:

C:0

D:1

Q.no 4. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 5. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 6. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 7. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Unrestricted

Q.no 8. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 9. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 10. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 11. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 12. A grammar that produces more than one parse tree for some sentence is called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 13. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 14. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 15. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 16. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 17. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}

D : {y}

Q.no 18. Which of the following statement is true?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 19. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 20. Which of the following regular expressions represents the set of strings which do not
contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 21. The worst-case efficiency of solving a problem in polynomial time is?

A : O(p(n))

B : O(p( n log n))

C:

D : O(p(m log n))

Q.no 22. Is the language preserved in all the steps while eliminating epsilon transitions from a
NFA?

A : yes

B : no

C : may be

D : cannot say

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 23.

A:

B:

C:

D : {0, 1}

Q.no 24. A context free language is called ambiguous if (a) It has two or more leftmost
derivations for the same string. (b) It has two or more rightmost derivations for the same string.
(c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 25. X is a simple mathematical model of a computer. X has unrestricted and unlimited
memory. X is a FA with R/W head. X can have an infinite tape divided into cells, each cell
holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 26. What does it mean when we say that an algorithm X is asymptotically more efficient
than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : X will always be a better choice for all inputs

Q.no 27. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is undecidable.
The statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3

Q.no 28. Which of the following statements is false?

A : For every non-deterministic Turing machine, there exists an equivalent deterministic Turing
machine.

B : Turing recognizable languages are closed under union and complement.

C : Turing decidable languages are closed under intersection

and complement.

D : Turing recognizable languages are closed under union and intersection.

Q.no 29. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 30. The set of all strings over {a,b} in which strings consisting a’s and b’s and ending with
bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb

Q.no 31. A string derived by a grammar is graphically represented using ……...

A : Binary tree

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Sparse tree

C : Parse tree

D : Forest

Q.no 32. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 33. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 34. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 35. The regular expression with all strings of 0′s and 1′s with at least two consecutive 0′s is:

A : 1 + (10)*

B : (0+1)*00(0+1)*

C : (0+1)*011

D : 0*1*2*

Q.no 36. Language is accepted by PDA if it is

A : regular language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : context free language

C : unrestricted

D : regular and context free

Q.no 37. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 38. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 39. The power of non-deterministic pushdown automata and deterministic pushdown
automata is not same.

A : true

B : false

C : maybe

D : cannot say

Q.no 40. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively enumerable.

D : The complement of a context-free language is context-free.

Q.no 41. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:5

C:7

D:2

Q.no 42. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 43. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : 12

D : 15

Q.no 44. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 45. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 46. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 47. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 48. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 49. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 50. From the options given below the statement, which is not necessarily true if X1 is the
recursive language and X2 and X3 are the languages that are recursively enumerable but not
recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 51. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:4

D:5

Q.no 52. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 53. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 54. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 55. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 56. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 57. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 58. The set of all strings over alphabet ={a,b} in which a single a followed by any number of
b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 59.

A:A

B:B

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:C

D:D

Q.no 60. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is a

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is d

Answer for Question No 21. is a

Answer for Question No 22. is a

Answer for Question No 23. is a

Answer for Question No 24. is c

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is d

Answer for Question No 28. is b

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is d

Answer for Question No 33. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is d

Answer for Question No 37. is a

Answer for Question No 38. is a

Answer for Question No 39. is a

Answer for Question No 40. is a

Answer for Question No 41. is b

Answer for Question No 42. is b

Answer for Question No 43. is a

Answer for Question No 44. is d

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is c

Answer for Question No 48. is b

Answer for Question No 49. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is d

Answer for Question No 52. is c

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is d

Answer for Question No 56. is d

Answer for Question No 57. is d

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. A language L is said to be ____________ if there is a turing machine M such that L(M)=L
and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 2. Which of the following does not belong to the language if input alphabet set is a,b

A:a

B:b

C : epsilon

D:c

Q.no 3. Every grammar in Chomsky Normal Form is:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 4. Which of the following is false for a grammar G in Chomsky Normal Form:

A : G has no useless symbols

B : G has no unit productions

C : G has no epsilon productions

D : G must have useless symbols

Q.no 5. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 6. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 7. In Moore machine, if input is of length n, then length of output string will be

A:n

B : n+1

C : n+n

D : n-1

Q.no 8. Finite state machine is ___________tuple machine.

A:4
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:5

C:6

D : unlimitted

Q.no 9. A two-way infinite tape Turing machine is ________ superior than the basic model of the
Turing machine in terms of power.

A : More

B : Less

C : No way

D : Very Much

Q.no 10. A problem is called __________ if it has an efficient algorithm for itself.

A : Tractable

B : Intractable

C : Computational

D : Computable

Q.no 11. A grammar that produces more than one parse tree for some sentence is called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 12. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 13. A formal language is recursive if :

A : A turing machine exists

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 14. Turing machine is more powerful than (a) Finite automata, (b) Push down automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Neither (a) nor (b)

Q.no 15. Which of the following statement is true? (a) Turing machine was developed by Alan
Turing, (b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 16. Turing Machine also behaves like General purpose computer and that TM is known as
_______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 17. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 18. A push down automaton employs which data structure?

A : queue

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : linked list

C : hash table

D : stack

Q.no 19. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 20.

A : L*

B:

C:L

D:

Q.no 21. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 22. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 23. Limitation of PDA can be overcome by

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 24. According to the given language, which among the following expressions does it
corresponds to Language L={xϵ{0,1}|x is of length 4 or less}

A : (0+1+0+1+0+1+0+1)^4

B : (0+1)^4

C : (01)^4

D : (0+1+ε)^4

Q.no 25. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D : Unrestricted

Q.no 26. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings in which the total number of a’s is divisible by 2.

A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 27. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 28. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 29. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 30. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.

A : true

B : false

C : maybe

D : probably

Q.no 31. The power of non-deterministic pushdown automata and deterministic pushdown
automata is not same.

A : true

B : false

C : maybe

D : cannot say

Q.no 32. The maximum number of transitions which can be performed over a state in a DFA
having alphabet set a,b,c are

A:1

B:2

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:3

D:4

Q.no 33.

A:

B:

C:

D:

Q.no 34. The total number of states and transitions required to form a Moore machine that
processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 35. Which of the following statement(s) are correct? (a) All languages can be generated by
CFG, (b) Any regular language has an equivalent CFG, (c) Some non regular languages cannot
be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 36. Construct a regular expression for the language that contains strings having even
number of 0’s followed by odd number of 1’s over {0, 1}.

A : (00)* 1 (11)*

B : ((0+1)(0+1))*

C : (0+1)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : (001)*

Q.no 37. The minimum number of 1’s to be used in a regular expression of the given language of
all strings containing exactly 2 zeroes.

A:2

B:3

C:0

D:1

Q.no 38. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 39. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree

C : Parse tree

D : Forest

Q.no 40. In multi head Turing machine there are

A : More than one heads of the Turing machine

B : More than one input tapes of Turing machine

C : Similar to the basic model of Turing machine

D : More than one input symbols of Turing machine

Q.no 41. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : (111*)* and (111+11*)*

Q.no 42. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 43. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 44. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 45. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 46. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 47. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 48. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 49. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 50. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 51. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

C : 12

D : 15

Q.no 52. The language generated by

S-> aSa|bSb|a|b
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 53. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 54. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 55. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 56. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 57. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 58. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 59. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 60. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/16
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is d

Answer for Question No 3. is c

Answer for Question No 4. is d

Answer for Question No 5. is b

Answer for Question No 6. is b

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is c

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is c

Answer for Question No 13. is d

Answer for Question No 14. is c

Answer for Question No 15. is c

Answer for Question No 16. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is d

Answer for Question No 18. is d

Answer for Question No 19. is a

Answer for Question No 20. is b

Answer for Question No 21. is d

Answer for Question No 22. is d

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is b

Answer for Question No 26. is c

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is c

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is c

Answer for Question No 33. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is a

Answer for Question No 35. is d

Answer for Question No 36. is a

Answer for Question No 37. is b

Answer for Question No 38. is c

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is c

Answer for Question No 42. is b

Answer for Question No 43. is d

Answer for Question No 44. is b

Answer for Question No 45. is b

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is a

Answer for Question No 49. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is c

Answer for Question No 53. is d

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is c

Answer for Question No 57. is b

Answer for Question No 58. is c

Answer for Question No 59. is d

Answer for Question No 60. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Why Palindromes cannot be recognized by any FSM ?

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 2. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 3. Which one of the following is the most powerful method?

A : LL(1)
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : SLR

C : CLR

D : LALR

Q.no 4. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 5. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 6. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing

Q.no 7. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 8. Halting problem is an example for

A : decidable problem

B : undecidable problem

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : complete problem

D : trackable problem

Q.no 9.

A:R

B:

C : R*

D:

Q.no 10. Which of the following are the examples of finite state machine system? (a) Control
Mechanism of an elevator (b) Traffic Lights (c) Combinational Locks

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 11. What is the Regular Expression Matching Zero or More Specific Characters

A:x

B:#

C:*

D:&

Q.no 12. The recognizing capability of NDFAand DFA

A : must be the same

B : may be different

C : must be different

D : cannot say

Q.no 13. What is the value of n if Turing machine is defined using n-tuples?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:6

B:7

C:8

D:5

Q.no 14. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 15. A language L is said to be ____________ if there is a turing machine M such that
L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 16. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 17. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Cannot be said

Q.no 18. Which of the following statement is true? (a) Turing machine was developed by Alan
Turing, (b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 19. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 20. Given the expression, is there some assignment of true and false values to the variables
that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 21. Which of the following statement is false?

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 22. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 23. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 24. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 25. Which of the given problems are NP-complete?

A : (a) Traveling Salesman Problem

B : (b) Satisfiability Problem

C : Both (a) and (b)

D : Turing Machine

Q.no 26. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 27. A context free language is called ambiguous if (a) It has two or more leftmost derivations
for the same string. (b) It has two or more rightmost derivations for the same string. (c) It has
Only single derivation tree.

A : Only (a)

B : Only (b)
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Both (a) and (b)

D : Only (c)

Q.no 28. The worst case complexity of a deterministic problem to find the satisfiability of a given
formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 29. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 30. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree

C : Parse tree

D : Forest

Q.no 31. Construct a regular expression for the language that contains strings having no pair of
consecutive zeros over {0, 1}.

A : (1+0)*

B:

C : ((0+1)(0+1))*

D : (01 + 10)*

Q.no 32. Unrestricted grammar is also called_______ Grammar

A : Type 3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Type 2

C : Type 1

D : Type 0

Q.no 33. The ability for a system of instructions to simulate a Turing Machine is called _________

A : Turing Completeness

B : Simulation

C : Turing Halting

D : Computability

Q.no 34. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 35.

A : {w | w is a string of odd length}

B : {w | w is a string of length multiple of 3}

C : {w | w is a string of length 3}

D : {w | w is an empty string}

Q.no 36. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 37. Which of the following does not obey pumping lemma for context free languages ?

A : Finite languages

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

Q.no 38. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 39. The total number of states and transitions required to form a Moore machine that
processes a binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 40. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 41. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 42. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 43. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 44. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 45. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 46. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 47. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 48. From the options given below the statement, which is not necessarily true if X1 is the
recursive language and X2 and X3 are the languages that are recursively enumerable but not
recursive.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 49. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 50. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 51. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

A : (0+1)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : (0+1)*

C:

D : (0+1)* 011

Q.no 52. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 53. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 54. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 55. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Strings starting and ending with different character

Q.no 56. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 57. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 58. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 59. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 60. Find the pair of regular expressions that are equivalent
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is a

Answer for Question No 2. is b

Answer for Question No 3. is c

Answer for Question No 4. is b

Answer for Question No 5. is d

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is b

Answer for Question No 9. is b

Answer for Question No 10. is d

Answer for Question No 11. is c

Answer for Question No 12. is a

Answer for Question No 13. is b

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is c

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is d

Answer for Question No 22. is d

Answer for Question No 23. is c

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is a

Answer for Question No 27. is c

Answer for Question No 28. is d

Answer for Question No 29. is d

Answer for Question No 30. is c

Answer for Question No 31. is b

Answer for Question No 32. is d

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is c

Answer for Question No 35. is b

Answer for Question No 36. is a

Answer for Question No 37. is c

Answer for Question No 38. is c

Answer for Question No 39. is a

Answer for Question No 40. is a

Answer for Question No 41. is a

Answer for Question No 42. is d

Answer for Question No 43. is c

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is d

Answer for Question No 47. is c

Answer for Question No 48. is d

Answer for Question No 49. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is b

Answer for Question No 51. is c

Answer for Question No 52. is c

Answer for Question No 53. is b

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is a

Answer for Question No 58. is b

Answer for Question No 59. is b

Answer for Question No 60. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 2. In given Transition function of TM which head movement of tape is shown (q0,a)->
(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 3. A push down automata is different than finite automata by

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 4. Which among the following is the format of unit production?

A : A->B

B : A->b

C : B->Aa

D : B->aA

Q.no 5. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 6. Bottom-up parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : operator precedence parsing

D : LL1 Parsing

Q.no 7. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 8. If the PDA does not stop on an accepting state and the stack is not empty, the string is

A : rejected
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : goes into loop forever

C : rejected and goes into loop forever

D : accepted

Q.no 9. Which of these does not belong to CFG?

A : Terminal Symbol

B : Non Terminal Symbol

C : Start symbol

D : End symbol

Q.no 10. The major difference between a moore and mealy machine is that

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 11. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 12. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 13. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 14. A push down automaton employs which data structure?

A : queue

B : linked list

C : hash table

D : stack

Q.no 15. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 16. Turing machine is more powerful than (a) Finite automata, (b) Push down automata

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Neither (a) nor (b)

Q.no 17. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 18. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 19. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 20. NFA, in its name has Non-deterministic words because

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 21. Construct a regular expression for the language that contains strings that start with
either ‘01’ or ‘10’ over {0, 1}.

A : (01 + 10)*

B : (1+0)* (01 + 10) (1+0)*

C : (01 + 10) (1+0)*

D : (1+0)*

Q.no 22. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 23. For a DFA accepting binary numbers whose decimal equivalent is divisible by 4, what
are all the possible remainders?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 24. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 25. Given a Grammar G:

S->aA
A->a | A
B->B
The number of productions to be removed immediately as Unit productions are

A:0

B:1

C:2

D:3

Q.no 26. Turing machine (TM) is more powerful than FSM (Finite State Machine) because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 27. According to Chomsky hierarchy, which of the following is recognized by Recursively
Enumerable language?

A : Type 3

B : Type 2

C : Type 1

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Type 0

Q.no 28. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D : Unrestricted

Q.no 29. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 30. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 31. What does it mean when we say that an algorithm X is asymptotically more efficient
than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 32. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Type 2 grammar is CFG

Q.no 33. How many strings of length less than 4 contain the language described by the regular
expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 34. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 35. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 36. Which of the functions are not performed by the Turing machine after reading a
symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 37. The set of all strings over {a,b} in which strings consisting a’s and b’s and ending with
bb is

A : ab

B : a*bbb

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : (a+b)* bb

D : (a+b)+ bb

Q.no 38. Which one of the following is FALSE?

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to an equivalent DFA.

C : Every Epsilon NFA can be converted to an equivalent DFA.

D : Every Mealy can be converted to an equivalent Moore machine.

Q.no 39. Which of the following is not a regular expression?

A : [(a+b)*(aa+bb)]*

B : [(0+1)-(0b+a1)*(a+]*

C : (01+11+10)*

D : (1+2+0)*(1+2)*

Q.no 40. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 41. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 42. John is asked to make an automaton which accepts a given string for all the occurrence
of ‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : 10

B : 11

C : 12

D : 15

Q.no 43. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 44. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 45. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 46. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 47. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 48. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 49. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : abbaabbaa

Q.no 50. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 51. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 52. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 53.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : X is undecidable and not even partially decidable.

Q.no 54.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 55. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 56. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are
the two other problems not known to be in NP. Which one of the following statements is true if Q
is polynomial time reducible to S and S is the polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 57. Construct the regular expressions for the following DFAs:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 58. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 59. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 60. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is d

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is a

Answer for Question No 7. is b

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is b

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is d

Answer for Question No 14. is d

Answer for Question No 15. is d

Answer for Question No 16. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is b

Answer for Question No 20. is b

Answer for Question No 21. is c

Answer for Question No 22. is d

Answer for Question No 23. is d

Answer for Question No 24. is c

Answer for Question No 25. is c

Answer for Question No 26. is c

Answer for Question No 27. is d

Answer for Question No 28. is b

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is b

Answer for Question No 32. is b

Answer for Question No 33. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is a

Answer for Question No 35. is d

Answer for Question No 36. is d

Answer for Question No 37. is c

Answer for Question No 38. is a

Answer for Question No 39. is b

Answer for Question No 40. is a

Answer for Question No 41. is a

Answer for Question No 42. is a

Answer for Question No 43. is d

Answer for Question No 44. is a

Answer for Question No 45. is d

Answer for Question No 46. is c

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is b

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is a

Answer for Question No 56. is b

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is a

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 2.

A : L*

B:

C:L

D:
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 3. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 4. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 5. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 6. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 7. A Turing machine operates over

A : Finite memory tape

B : Infinite memory tape

C : Depends on the algorithm

D : Depends on the input

Q.no 8. In Parse Tree, Intermediate Node represents

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 9. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 10. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 11. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 12. Are the given two patterns equivalent?

(1) gray | grey (2) gr(a|e)y

A : yes

B : no

C : may be

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : cannot say

Q.no 13. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 14. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 15. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 16. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 17.

A:R

B:

C : R*

D:

Q.no 18. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 19. The finite automata is called NFA when there exists____________ for a specific input
from current state to next state

A : Single path

B : Multiple paths

C : Only two paths

D : Three paths

Q.no 20. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 21. PDA works as Finite Automata when the number of auxiliary memory it has is

A:3

B:2
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:1

D:0

Q.no 22. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 23. The difference between number of states in FA for regular expression (a + b) and (a + b)
* is:

A:1

B:2

C:3

D:0

Q.no 24. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 25. The maximum number of transitions which can be performed over a state in a DFA
having alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 26. An NFA’s transition function returns

A : Boolean value

B : A state

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : A set of states

D : An edge

Q.no 27. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 28. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 29. If there exists a TM which when applied to any problem in the class, terminates, if
correct answer is yes and may or may not terminate otherwise is called

A : Stable

B : Unsolvable

C : Partially solvable

D : Unstable

Q.no 30. What does it mean when we say that an algorithm X is asymptotically more efficient
than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 31. The subset construction shows that every NFA accepts a ……..

A : String

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Function

C : Regular language

D : Context-free language

Q.no 32.

A:

B:

C:

D : {0, 1}

Q.no 33. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 34. Which among the following is not true for 2-way infinte TM?

A : Tape in both directions

B : Leftmost square not distinguished

C : Any computation that can be performed by 2-way infinite tape can also be performed by standard
TM.

D : Tape is only in one direction.

Q.no 35. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 36. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 37. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 38. Which productions will generate odd length palindromes for terminals 'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 39. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 40. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 41. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 42. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 43. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 44. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 45. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 46. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 47. Transition function of NFA machine is given by

A:
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

Q.no 48. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 49. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 50. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 51. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

A : (0+1)

B : (0+1)*

C:
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : (0+1)* 011

Q.no 52. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 53. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 54. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Insert a symbol

D : Push the symbol

Q.no 55. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 56. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 57. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 58. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 59. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 60. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/16
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is d

Answer for Question No 6. is a

Answer for Question No 7. is b

Answer for Question No 8. is b

Answer for Question No 9. is a

Answer for Question No 10. is a

Answer for Question No 11. is b

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is d

Answer for Question No 15. is c

Answer for Question No 16. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is b

Answer for Question No 20. is a

Answer for Question No 21. is d

Answer for Question No 22. is a

Answer for Question No 23. is a

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is c

Answer for Question No 27. is b

Answer for Question No 28. is a

Answer for Question No 29. is c

Answer for Question No 30. is b

Answer for Question No 31. is c

Answer for Question No 32. is a

Answer for Question No 33. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is d

Answer for Question No 35. is b

Answer for Question No 36. is b

Answer for Question No 37. is b

Answer for Question No 38. is a

Answer for Question No 39. is c

Answer for Question No 40. is d

Answer for Question No 41. is d

Answer for Question No 42. is d

Answer for Question No 43. is b

Answer for Question No 44. is a

Answer for Question No 45. is d

Answer for Question No 46. is b

Answer for Question No 47. is d

Answer for Question No 48. is d

Answer for Question No 49. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is c

Answer for Question No 51. is c

Answer for Question No 52. is d

Answer for Question No 53. is a

Answer for Question No 54. is b

Answer for Question No 55. is b

Answer for Question No 56. is c

Answer for Question No 57. is a

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Which of the following regular expressions represents the set of strings which do not
contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 2. The format: A->aB refers to which of the following?

A : Chomsky Normal Form

B : Greibach Normal Form

C : Backus Naur Form

D : Sentential form

Q.no 3. In regular expressions, the operator ‘*’ stands for

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Concatenation

B : Selection

C : Iteration

D : Addition

Q.no 4. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 5. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 6. Turing Machine also behaves like General purpose computer and that TM is known as
_______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 7. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 8. Decidable can be taken as a synonym to:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Recursive

B : Non Recursive

C : Recognizable

D : Non Recognizable

Q.no 9. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 10. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 11. Which of the following are the actions that operates on stack top?

A : only push

B : only pop

C : only push and pop

D : push, pop and replace

Q.no 12. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

D : tape symbol

Q.no 13. For alphabet = {a,b}, the regular expression r = (aa)*(bb)*b denotes

A : Set of strings with 2 a’s and 2 b’s

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Set of strings with 2 a’s 2 b’s followed by b

C : Set of strings with 2 a’s followed by b’s which is a multiple of 3

D : Set of strings with even number of a’s followed by odd number of b’s

Q.no 14. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 15. A DPDA is a PDA in which:

A : No state p has two outgoing transitions

B : More than one state can have two or more outgoing transitions

C : At least one state has more than one transitions

D : At most one state has more than one transitions

Q.no 16. Given the expression, is there some assignment of true and false values to the variables
that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 17. Transition function of DFA machine maps.

A:

B:

C:

D:

Q.no 18. If there exists a language L, for which there exists a TM, T, that accepts every word in L
and either rejects or loops for every word that is not in L, is called
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 19. A grammar that produces more than one parse tree for some sentence is called

A : ambiguous

B : unambiguous

C : regular

D : context free grammar

Q.no 20. Choose the correct option for the statement: Unambiguity is the ideal structure of a
language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 21. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

Q.no 22. Which of the functions are not performed by the Turing machine after reading a
symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 23. Which of the following statements is false ?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L (G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 24. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 25. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 26. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 27. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 28. The worst case complexity of a deterministic problem to find the satisfiability of a given
formula of n variables is

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 29. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 30. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

D : The language of all strings which does not end with 10

Q.no 31. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 32. X is a simple mathematical model of a computer. X has unrestricted and unlimited
memory. X is a FA with R/W head. X can have an infinite tape divided into cells, each cell
holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 33. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 34. Regular expression (x|y)(x|y) denotes the set

A : {xy,xy}

B : {xx,xy,yx,yy}

C : {x,y}

D : {x,y,xy}

Q.no 35. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 36. Which of the following is the restricted model of Turing machines (a) Turing machine
with semi-infinite tape, (b) Multi stack machine, (c) Offline Turing machine

A : Only (a)

B : Only (b)

C : Only (c)

D : Both (a) and (b)

Q.no 37. The minimum number of productions required to produce a language consisting of
palindrome strings over T={a,b} is

A:3

B:7

C:5

D:6

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 38. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 39. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 40. A context free language is called ambiguous if (a) It has two or more leftmost
derivations for the same string. (b) It has two or more rightmost derivations for the same string.
(c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 41. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 42. Transition function of Epsilon-NFA machine is given by

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 43. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 44. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 45. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 46. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 47. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 48. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 49. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 50.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 51. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 52. The output of Moore machine can be defined as

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : state and its input

Q.no 53. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 54. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 55. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 56. Which of the following will not be accepted by the following DFA?

A : ababaabaa

B : abbbaa

C : abbbaabb

D : abbaabbaa

Q.no 57. Construct a Turing machine which accepts a string with ‘aba’ as its substring.

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

Q.no 58. Let S be an NP-complete problem and Q and R be two other problems not known to be
in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the given statements is true?

A : R is NP-complete

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : R is NP-hard

C : Q is NP-complete

D : Q is NP-hard

Q.no 59.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 60. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is d

Answer for Question No 2. is b

Answer for Question No 3. is c

Answer for Question No 4. is b

Answer for Question No 5. is c

Answer for Question No 6. is c

Answer for Question No 7. is d

Answer for Question No 8. is a

Answer for Question No 9. is a

Answer for Question No 10. is a

Answer for Question No 11. is d

Answer for Question No 12. is b

Answer for Question No 13. is d

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is d

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is d

Answer for Question No 22. is d

Answer for Question No 23. is d

Answer for Question No 24. is b

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is d

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is d

Answer for Question No 32. is c

Answer for Question No 33. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is d

Answer for Question No 37. is c

Answer for Question No 38. is d

Answer for Question No 39. is a

Answer for Question No 40. is c

Answer for Question No 41. is b

Answer for Question No 42. is c

Answer for Question No 43. is b

Answer for Question No 44. is a

Answer for Question No 45. is b

Answer for Question No 46. is d

Answer for Question No 47. is c

Answer for Question No 48. is d

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is b

Answer for Question No 51. is a

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is a

Answer for Question No 55. is d

Answer for Question No 56. is a

Answer for Question No 57. is c

Answer for Question No 58. is b

Answer for Question No 59. is a

Answer for Question No 60. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Turing Machine can update symbols on its tape, whereas the FA cannot update symbols
on tape.

A : true

B : false

C : Cannot say

D : May be

Q.no 2. The push down automata indicate the acceptance of input string in terms of

A : final state

B : empty stack

C : final state and empty stack

D : start state

Q.no 3. NFA, in its name has Non-deterministic words because

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : The result is undetermined

B : The choice of path is non-deterministic

C : The state to be transited next is non-deterministic

D : More number of final states

Q.no 4. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 5. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 6. In given Transition function of TM which head movement of tape is shown (q0,a)->
(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 7. Which of the following is true?

A : (01)*0 = 0(10)0*

B : (0+1)*0(0+1)*1(0+1) = (0+1)*01(0+1)*

C : (0+1)*01(0+1)*+1*0* = (0+1)*0

D : (01)*01 = 0(10)0*1

Q.no 8. Why Palindromes cannot be recognized by any FSM ?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : an FSM cannot deterministically fix the mid-point

B : an FSM can remember arbitrarily large amount of information

C : FSM has finite memory

D : FSM has only 5 tuples

Q.no 9. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 10. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 11. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

C : Universal Turing machine

D : Complete Turing machine

Q.no 12. Halting states are of two types. They are:

A : accept and reject

B : reject and allow

C : start and reject

D : start and accept

Q.no 13. To which of the following class does a CNF-satisfiability problem belong?

A : NP class
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : P class

C : NP complete

D : NP hard

Q.no 14. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 15. The transition a Push down automaton makes is additionally dependent upon the:

A : Current State

B : input tape

C : stack

D : terminals

Q.no 16. Which of the following regular expressions represents the set of strings which do not
contain a substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 17. Top-down parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 18. An algorithm is called efficient if it runs in ____________ time on a serial computer.

A : Polynomial

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Non polynomial

C : Logarithmic

D : Non Logarithmic

Q.no 19. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 20. PDA accepts languages generated by which grammar

A : type 0

B : type 1

C : type 2

D : type 3

Q.no 21. Which of the following statement(s) are correct? (a) All languages can be generated by
CFG, (b) Any regular language has an equivalent CFG, (c) Some non regular languages cannot
be generated by CFG.

A : only (a)

B : Only (b)

C : Only (c)

D : Both (b) and (c)

Q.no 22. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 23. The power of non-deterministic pushdown automata and deterministic pushdown
automata is not same.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : true

B : false

C : maybe

D : cannot say

Q.no 24. If there exists a TM which when applied to any problem in the class, terminates, if
correct answer is yes and may or may not terminate otherwise is called

A : Stable

B : Unsolvable

C : Partially solvable

D : Unstable

Q.no 25. Every grammar in Chomsky Normal Form is:

A : Regular

B : Context free

C : Context sensitive

D : Unrestricted

Q.no 26. The difference between number of states in FA for regular expression (a + b) and (a + b)
* is:

A:1

B:2

C:3

D:0

Q.no 27. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 28. Which of the following statement is false?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Context free language is the subset of context sensitive language

B : Regular language is the subset of context sensitive language

C : Recursively ennumerable language is the super set of regular language

D : Context sensitive language is a subset of context free language

Q.no 29. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata
(NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 30. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 31.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the right
movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the right
movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the Left
movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform the right
movement.

Q.no 32. The maximum number of transitions which can be performed over a state in a DFA
having alphabet set a,b,c are

A:1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:2

C:3

D:4

Q.no 33. Is the language preserved in all the steps while eliminating epsilon transitions from a
NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 34. A PDA machine configuration (p, w, y) can be correctly represented as

A : unprocessed input, stack content, current state

B : current state, unprocessed input, stack content

C : current state, stack content, unprocessed input

D : stack content, current state, unprocessed input

Q.no 35. Which of the following is true?

A : The complement of a recursive language is recursive.

B : The complement of a recursively enumerable language is recursively enumerable.

C : The complement of a recursive language is either recursive or recursively enumerable.

D : The complement of a context-free language is context-free.

Q.no 36. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 37. What does it mean when we say that an algorithm X is asymptotically more efficient
than Y?

A : X will always be a better choice for small inputs

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 38.

A:

B:

C:

D:

Q.no 39. The operations of PDA never work on elements other than top of the stack.

A : false

B : true

C : may be

D : cannot say

Q.no 40. CFGs are more powerful than (a) DFA, (b) NDFA, (c) Mealy Machine

A : Only (a)

B : Only (b) and (c)

C : Only (a) and (c)

D : (a), (b) and (c)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 41. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 42. The set of all strings over alphabet ={a,b} in which a single a followed by any number of
b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 43. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Center Recursive Grammar

Q.no 44. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 45. If all the production rules have single nonterminal symbol on the left side then grammar
is called as

A : Context free grammar

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 46. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 47. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 48. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 49. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 50. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

Q.no 51. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 52. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 53. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 54. CFG is not closed under

A : Kleene closure

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Concatenation

C : Complement

D : Union

Q.no 55. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 56.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 57. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 58. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 59.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 60. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is a

Answer for Question No 2. is c

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is b

Answer for Question No 8. is a

Answer for Question No 9. is b

Answer for Question No 10. is a

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is c

Answer for Question No 14. is c

Answer for Question No 15. is c

Answer for Question No 16. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is a

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is c

Answer for Question No 21. is d

Answer for Question No 22. is d

Answer for Question No 23. is a

Answer for Question No 24. is c

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is b

Answer for Question No 28. is d

Answer for Question No 29. is b

Answer for Question No 30. is b

Answer for Question No 31. is a

Answer for Question No 32. is c

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is b

Answer for Question No 35. is a

Answer for Question No 36. is a

Answer for Question No 37. is b

Answer for Question No 38. is d

Answer for Question No 39. is b

Answer for Question No 40. is d

Answer for Question No 41. is b

Answer for Question No 42. is a

Answer for Question No 43. is a

Answer for Question No 44. is b

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is b

Answer for Question No 48. is c

Answer for Question No 49. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is a

Answer for Question No 52. is d

Answer for Question No 53. is c

Answer for Question No 54. is c

Answer for Question No 55. is d

Answer for Question No 56. is b

Answer for Question No 57. is c

Answer for Question No 58. is c

Answer for Question No 59. is b

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 2.

A:

B:

C:0

D:1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 3. A->aA| a| b
The number of steps to generate aab are

A:2

B:3

C:4

D:5

Q.no 4. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5

Q.no 5. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 6. If T1 and T2 are two Turing machines, the composite can be represented using the
expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 7. Kruskal's algorithm is used to find

A : whether there is cycle in the graph

B : spanning tree of the graph

C : minimum spanning tree in the graph

D : whether there is spanning tree in the graph

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 8. In given Transition function of TM which head movement of tape is shown (q0,a)->
(q1,X,L)

A : Left Movement

B : Right Movement

C : Top Movement

D : Bottom Movement

Q.no 9. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 10. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 11. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 12. The minimum number of states required to recognize an octal number divisible by 3 is

A:1

B:3

C:5

D:7

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 13. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 14. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 15. Minimal finite automata need _____________ no. of final states

A:1

B:2

C:3

D : Depends on problem

Q.no 16. Choose the correct option for the statement: Unambiguity is the ideal structure of a
language.

A : true

B : Partially True

C : false

D : Cannot be said

Q.no 17. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 18. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 19. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 20. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 21. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings in which any occurrence of the symbol b, is in groups of odd
numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*

Q.no 22. Which of the following does not obey pumping lemma for context free languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 23. The worst case complexity of a deterministic problem to find the satisfiability of a given
formula of n variables is

A : O(n)

B : O(n^2)

C : O(n^3)

D : O(2^n)

Q.no 24. The travelling salesman problem can be solved using _________

A : A spanning tree

B : A minimum spanning tree

C : Bellman – Ford algorithm

D : DFS traversal

Q.no 25. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 26. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 27. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 28. Which of the following problems is solvable ?

A : Writing a universal Turing machine

B : Determining of an arbitrary Turing machine is an universal Turing machine

C : Determining of a universal Turing machine can be written for fewer than k instructions for some k

D : Determining of a universal Turing machine and some input will halt

Q.no 29. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 30. Turing machine (TM) is more powerful than FSM (Finite State Machine) because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 31. How many strings of length less than 4 contain the language described by the regular
expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 32. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 33. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory machine.

Q.no 34. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

D : Context-free language

Q.no 35. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 36. The operations of PDA never work on elements other than top of the stack.

A : false

B : true

C : may be

D : cannot say

Q.no 37. Language is accepted by PDA if it is

A : regular language

B : context free language

C : unrestricted

D : regular and context free

Q.no 38. Which of the following pairs have different expressive power
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata
(NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 39. Which of the regular expressions correspond to the given problem statement: Express
the identifiers in C Programming language where l=letters d=digits

A : (l+_)(d+_)*

B : (l+d+_)*

C : (l+_)(l+d+_)*

D : (_+d)(l+d+_)*

Q.no 40. For a DFA accepting binary numbers whose decimal equivalent is divisible by 4, what
are all the possible remainders?

A:0

B:2

C : 0,2,4

D : 0,1,2,3

Q.no 41. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 42. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 43. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 44. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 45. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 46. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 47. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 48. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 49. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

III. Whether two push-down automata accept the same language

IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

Q.no 50. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 51. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 52. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 53.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 54. The set of all strings over alphabet ={a,b} in which a single a followed by any number of
b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

Q.no 55.

A:A

B:B

C:C

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:D

Q.no 56. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 57. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 58. From the options given below the statement, which is not necessarily true if X1 is the
recursive language and X2 and X3 are the languages that are recursively enumerable but not
recursive.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 59. In conversion from the following CFG to CNF, the number of nonterminals to be
introduced for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 60. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is b

Answer for Question No 4. is b

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is c

Answer for Question No 8. is a

Answer for Question No 9. is b

Answer for Question No 10. is a

Answer for Question No 11. is c

Answer for Question No 12. is b

Answer for Question No 13. is d

Answer for Question No 14. is b

Answer for Question No 15. is d

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is c

Answer for Question No 23. is d

Answer for Question No 24. is b

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is a

Answer for Question No 28. is a

Answer for Question No 29. is c

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is a

Answer for Question No 33. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is c

Answer for Question No 35. is a

Answer for Question No 36. is b

Answer for Question No 37. is d

Answer for Question No 38. is b

Answer for Question No 39. is c

Answer for Question No 40. is d

Answer for Question No 41. is c

Answer for Question No 42. is c

Answer for Question No 43. is d

Answer for Question No 44. is c

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is b

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is a

Answer for Question No 51. is a

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is a

Answer for Question No 55. is b

Answer for Question No 56. is b

Answer for Question No 57. is d

Answer for Question No 58. is d

Answer for Question No 59. is d

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Precedence of regular expression in decreasing order is

A:*,.,+

B:.,*,+

C:.,+,*

D:+,.,*

Q.no 2. In Moore machine the output depends on

A : Only present state

B : Present state and present input

C : Nothing

D : Type of input

Q.no 3. Are the given two patterns equivalent?

(1) gray | grey (2) gr(a|e)y

A : yes

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : no

C : may be

D : cannot say

Q.no 4. Which among the following are incorrect regular identities?

A:

B:

C:

D:

Q.no 5. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 6. PDA always works on top element of stack

A : true

B : false

C : maybe

D : cannot say

Q.no 7. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 8. The transition a Push down automaton makes is additionally dependent upon the:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Current State

B : input tape

C : stack

D : terminals

Q.no 9. Those problems that are solvable in polynomial time belong to __

A : NP

B:P

C : Hard

D : Complete

Q.no 10. To simplify a grammar we can eliminate

A : Useful symbols

B : epsilon productions

C : Reachable symbols

D : Non Unit productions

Q.no 11. The minimum number of states required to recognize an octal number divisible by 3 is

A:1

B:3

C:5

D:7

Q.no 12. Turing Machine also behaves like General purpose computer and that TM is known as
_______

A : Multi-tape Turing Machine

B : Poly-tape Turing Machine

C : Universal Turing Machine

D : Deterministic Finite Automata

Q.no 13. A Turing machine with several tapes in known as

A : Multi-tape Turing machine

B : Poly-tape Turing maching

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : Universal Turing machine

D : Complete Turing machine

Q.no 14. Transition function of Turing Machine is

A:

B:

C:

D:

Q.no 15.

A:R

B:

C : R*

D:

Q.no 16. Finite state machine is ___________tuple machine.

A:4

B:5

C:6

D : unlimitted

Q.no 17. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 18. Which of the following case does not exist in complexity theory?

A : Best case

B : Worst case

C : Average case

D : Null case

Q.no 19.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 20. If the PDA does not stop on an accepting state and the stack is not empty, the string is

A : rejected

B : goes into loop forever

C : rejected and goes into loop forever

D : accepted

Q.no 21. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is an independent set
iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 22. Out of the three decision problems P1, P2 and P3, P1 is decidable and P2 is undecidable. The
statement that holds true is

A : P3 is decidable if P3 is reducible to compliment of P2

B : P3 is decidable if P1 is reducible to P3

C : P3 is undecidable if P1 is reducible to P3

D : P3 is undecidable if P2 is reducible to P3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 23. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 24. The maximum number of transitions which can be performed over a state in a DFA having
alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 25. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 26. The instantaneous description is PDA shows

A : present state, string to be processed and stack symbol

B : present state and stack symbol

C : present state and string to be processed

D : stack symbol and string to be processed

Q.no 27. Limitation of PDA can be overcome by

A : Mealy machine

B : Moore machine

C : Turing machine

D : Finite state machine

Q.no 28. Which of the following automata takes stack as auxiliary storage

A : finite automata

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : pushdown automata

C : Turing machine

D : finite state machine

Q.no 29. Which of the functions are not performed by the Turing machine after reading a symbol?

A : Writes the symbol

B : Moves the tape one cell left/right

C : Proceeds with next instruction or halts

D : Push the input in stack

Q.no 30. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 31. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 32. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

C : b*c|a

D : abc

Q.no 33. Construct a regular expression for the language that contains strings having even number of
0’s followed by odd number of 1’s over {0, 1}.

A : (00)* 1 (11)*

B : ((0+1)(0+1))*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : (0+1)*

D : (001)*

Q.no 34. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 35. Recursive languages are ………… of recursively enumerable languages.

A : subset

B : proper subset

C : not subset

D : not proper subset

Q.no 36. A context free language is called ambiguous if (a) It has two or more leftmost derivations for
the same string. (b) It has two or more rightmost derivations for the same string. (c) It has Only single
derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 37. How many strings of length less than 4 contain the language described by the regular
expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 38. Which regular language corresponds to 1+(1+0)*0+(0+1)*11

A : The language of all strings that end with 11 or 00

B : The language of all strings that end with 0 or 1

C : The language of all strings which does not end with 01

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : The language of all strings which does not end with 10

Q.no 39. An instantaneous description of Turing machine consists of

A : Present state and input to be processed

B : Present state and entire input to be processed

C : Present input only

D : Present state only

Q.no 40. The set of all strings over {a,b} in which strings consisting a’s and b’s and ending with bb is

A : ab

B : a*bbb

C : (a+b)* bb

D : (a+b)+ bb

Q.no 41. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 42.

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 43. Context free grammar having the following production

X->Xa

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 44. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 45.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 46. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 47. From the options given below the statement, which is not necessarily true if X1 is the recursive
language and X2 and X3 are the languages that are recursively enumerable but not recursive.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 48. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank symbols
does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 49. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 50. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

Q.no 51. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 52. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 53. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 54. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 55. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

A : (0+1)

B : (0+1)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D : (0+1)* 011

Q.no 56. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 57.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 58. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 59. In conversion from the following CFG to CNF, the number of nonterminals to be introduced
for the terminals are:
S->Aba , A->aab , B->Ac
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:2

B:3

C:4

D:5

Q.no 60. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is a

Answer for Question No 2. is a

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is c

Answer for Question No 6. is a

Answer for Question No 7. is a

Answer for Question No 8. is c

Answer for Question No 9. is b

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is c

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is c

Answer for Question No 18. is d

Answer for Question No 19. is c

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is d

Answer for Question No 23. is b

Answer for Question No 24. is c

Answer for Question No 25. is b

Answer for Question No 26. is a

Answer for Question No 27. is c

Answer for Question No 28. is b

Answer for Question No 29. is d

Answer for Question No 30. is c

Answer for Question No 31. is d

Answer for Question No 32. is c

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is c

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is c

Answer for Question No 38. is c

Answer for Question No 39. is b

Answer for Question No 40. is c

Answer for Question No 41. is d

Answer for Question No 42. is b

Answer for Question No 43. is a

Answer for Question No 44. is c

Answer for Question No 45. is a

Answer for Question No 46. is b

Answer for Question No 47. is d

Answer for Question No 48. is a

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is d

Answer for Question No 52. is d

Answer for Question No 53. is c

Answer for Question No 54. is a

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is b

Answer for Question No 58. is a

Answer for Question No 59. is d

Answer for Question No 60. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. If there exists a language L, for which there exists a TM, T, that accepts every word in L and
either rejects or loops for every word that is not in L, is called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 2.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 3. The major difference between a moore and mealy machine is that

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Output of the former depends on the present state and present input

B : output of the former depends only on the present state

C : output of the former depends only on the present input

D : output of the former depends on the present input and next state

Q.no 4. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 5. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 6. Number of states required to accept strings ending with 101

A:3

B:4

C:2

D : cannot be represented.

Q.no 7. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 8. A grammar that produces more than one parse tree for some sentence is called

A : ambiguous

B : unambiguous

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : regular

D : context free grammar

Q.no 9. Which of the production rule can be accepted by Chomsky grammar. (i) A->BC, (ii) A->a

A : only i

B : only ii

C : both i and ii

D : neither i nor ii

Q.no 10. Which of the following is not a part of 5-tuple finite automata?

A : Input alphabet

B : Transition function

C : Initial State

D : Output alphabet

Q.no 11. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 12. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 13. Minimal finite automata need _____________ no. of final states

A:1

B:2

C:3

D : Depends on problem

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 14. Which of the following does not belong to the language if input alphabet set is a,b

A:a

B:b

C : epsilon

D:c

Q.no 15. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 16. A grammar G=(V, T, P, S) is __________ if every production taken one of the two forms: B-
>aC , B->a

A : Ambiguous

B : Regular

C : Non Regular

D : Context sensitive

Q.no 17. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what does S
represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 18. A problem which is both _______ and _________ is said to be NP complete.

A : P, NP

B : NP, NP hard

C : P, P complete

D : NP Hard,P

Q.no 19. Transition function of Turing Machine is

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 20. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 21. It is less complex to prove the closure properties over regular languages using

A : NFA

B : DFA

C : PDA

D : Canot be said

Q.no 22. Which of the following statements is incorrect?

A : A Turing Machine cannot solve Halting problem

B : Set of recursively enumerated languages is closed under union

C : A FSM with 3 stacks is more powerful than FSM with 2 stacks

D : Context sensitive grammar can be recognized by a linearly bounded memory machine.

Q.no 23. According to Chomsky hierarchy, which of the following is recognized by Recursively
Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 24. X is a simple mathematical model of a computer. X has unrestricted and unlimited memory. X
is a FA with R/W head. X can have an infinite tape divided into cells, each cell holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

Q.no 25. Let the class of language accepted by finite state machine be L1 and the class of languages
represented by regular expressions be L2 then

A : L1<L2

B : L1>=L2

C : L1!=L2

D : L1=L2

Q.no 26. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 27. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 28. How many strings of length less than 4 contain the language described by the regular
expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 29. The minimum number of 1’s to be used in a regular expression of the given language of all
strings containing exactly 2 zeroes.

A:2

B:3

C:0

D:1

Q.no 30. Pushdown automata behaves like Turing machine when it has the number of auxiliary
memory

A : one or more

B : two or more

C : zero

D : one

Q.no 31. The automaton which allows transformation to a new state without consuming any input
symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 32. The RE in which any number of 0′s is followed by any number of 1′s followed by any number
of 2′s is

A : (0+1+2)*

B : 0*1*2*

C : 0* + 1 + 2

D : (0+1)*2*

Q.no 33. If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by

A : (r1)(r2)

B : (r1 + r2)

C : (r2)(r1)

D : (r1)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 34. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 35. Which among the following is the LEAF of the parse tree?

A : Production P

B : Nonterminal V

C : Terminal T

D : Starting symbol S

Q.no 36. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 37. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 38. PDA is useful in

A : lexical analysis

B : syntax analysis

C : semantic analysis

D : code generation

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 39. Which of the following represents a language which has no pair of consecutive 1’s if alphabet =
{0,1}?

A:

B:

C:

D:

Q.no 40. The maximum number of transitions which can be performed over a state in a DFA having
alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 41. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 42. In conversion from the following CFG to CNF, the number of nonterminals to be introduced
for the terminals are:
S->Aba , A->aab , B->Ac

A:2

B:3

C:4

D:5

Q.no 43. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 44. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : (0+010)*

D : (0+1)*

Q.no 45. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 46. John is asked to make an automaton which accepts a given string for all the occurrence of
‘1001’ in it. How many number of transitions would John use such that, the string processing
application works?

A : 10

B : 11

C : 12

D : 15

Q.no 47. The lexical analysis for a modern computer language such as Java needs the power of which
one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 48. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 49. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 50. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 51. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is
undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 52. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 53. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 54.

A:A

B:B

C:C

D:D

Q.no 55. Transition function of Epsilon-NFA machine is given by

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

Q.no 56. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 57. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 58. Any string of terminals that can be generated by the following CFG
S-> XY ,
X-> aX | bX | a ,
Y-> Ya | Yb | a

A : has atleast one 'b'

B : should end with 'aa'

C : has no consecutive a's or b's

D : has atleast two a's

Q.no 59. CFG is not closed under

A : Kleene closure

B : Concatenation

C : Complement

D : Union

Q.no 60. The output of Moore machine can be defined as

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D : state and its input

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is c

Answer for Question No 3. is b

Answer for Question No 4. is b

Answer for Question No 5. is b

Answer for Question No 6. is b

Answer for Question No 7. is d

Answer for Question No 8. is a

Answer for Question No 9. is d

Answer for Question No 10. is d

Answer for Question No 11. is c

Answer for Question No 12. is a

Answer for Question No 13. is d

Answer for Question No 14. is d

Answer for Question No 15. is c

Answer for Question No 16. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is a

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is a

Answer for Question No 22. is d

Answer for Question No 23. is d

Answer for Question No 24. is c

Answer for Question No 25. is d

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is c

Answer for Question No 29. is b

Answer for Question No 30. is b

Answer for Question No 31. is c

Answer for Question No 32. is b

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is d

Answer for Question No 35. is c

Answer for Question No 36. is a

Answer for Question No 37. is a

Answer for Question No 38. is b

Answer for Question No 39. is a

Answer for Question No 40. is c

Answer for Question No 41. is b

Answer for Question No 42. is d

Answer for Question No 43. is d

Answer for Question No 44. is a

Answer for Question No 45. is d

Answer for Question No 46. is a

Answer for Question No 47. is a

Answer for Question No 48. is a

Answer for Question No 49. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is c

Answer for Question No 51. is c

Answer for Question No 52. is c

Answer for Question No 53. is d

Answer for Question No 54. is b

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is c

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 2. A Language for which no DFA exist is a________

A : Regular Language

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 3. Pushdown automata accepts

A : regular language

B : context free language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : context sensitive language

D : unrestricted language

Q.no 4. Which of the following can be used to simulate any Turing machine?

A : Finite State Automaton

B : Universal Turing Machine

C : Counter machines

D : Deterministic Finite Automata

Q.no 5. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 6. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 7. Halting problem is an example for

A : decidable problem

B : undecidable problem

C : complete problem

D : trackable problem

Q.no 8.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Starts and end with same symbol

Q.no 9. If two finite state machines are equivalent,

A : they should have the same number of states

B : they should have the same number of edges

C : they should have the same number of states and edges

D : they can have different number of states and edges

Q.no 10. Every grammar in Chomsky Normal Form is:

A : regular

B : context sensitive

C : context free

D : Unrestricted

Q.no 11. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what does S
represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 12. Top-down parsing is also known as

A : shift reduce parsing

B : predictive descent parsing

C : LR parsing

D : SLR parsing

Q.no 13. Finite automata needs minimum _______ number of stacks

A:0

B:1

C:2

D:3

Q.no 14. RR* can be expressed in which of the forms:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : R+

B : R-

C : R+ U R-

D:R

Q.no 15. The regular expression to denote zero or more instances of x or y is

A : (x+y)

B : (x+y)*

C : (x* + y)

D : (xy)*

Q.no 16. Which of the following regular expressions represents the set of strings which do not contain a
substring ‘rt’ if alphabet = {r, t}

A : (rt)*

B : (tr)*

C : (r*t*)

D : (t*r*)

Q.no 17. Which of the following does not belong to the language if input alphabet set is a,b

A:a

B:b

C : epsilon

D:c

Q.no 18. Consider following regular expression

i) (a|b)* ii) (a*|b*)* iii) ((a)*b*)* Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : all are equal

Q.no 19. A push down automata is different than finite automata by

A : Its memory

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : number of states

C : start state

D : input symbols

Q.no 20. If T1 and T2 are two Turing machines, the composite can be represented using the expression

A : T1 T2

B : T2 T1

C : T1 X T2

D : T2 X T1

Q.no 21. An Epsilon-NFA is ___________ in representation.

A : Quadruple

B : Quintuple

C : Triple

D : None of the mentioned

Q.no 22. The total number of states and transitions required to form a Moore machine that processes a
binary input string and will produce residue mod 3.

A : 3 and 6

B : 3 and 5

C : 2 and 4

D : 2 and 5

Q.no 23. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 24. The worst case complexity of a deterministic problem to find the satisfiability of a given
formula of n variables is

A : O(n)

B : O(n^2)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : O(n^3)

D : O(2^n)

Q.no 25. Complement of a DFA can be obtained by

A : making starting state as final state.

B : no trival method.

C : making final states non-final and non-final to final.

D : make final as a starting state.

Q.no 26. 3-SAT and 2-SAT problems are

A : NP-complete and in P respectively

B : Undecidable and NP-complete

C : Both NP-complete

D : Both in P

Q.no 27. In given Transition function of TM

(q1,b)->(q2,Y,R)
Which one is the correct statement?

A : "q1" symbol is changed to "q2"

B : "b" symbol is changed to "q2"

C : "Y" symbol is changed to "b"

D : "b" symbol is changed to "Y"

Q.no 28. Which language is represented by the following grammar G:

G={{S},{0,1},P,S}
where elements of P are:
S --> SS
S--> 0S1
S--> 1S0
S--> Є

A : Regular language

B : Context-free language

C : Context-sensitive language

D : Recursively enumerable language

Q.no 29. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

Q.no 30. A string derived by a grammar is graphically represented using ……...

A : Binary tree

B : Sparse tree

C : Parse tree

D : Forest

Q.no 31. Which of the following does not obey pumping lemma for context free languages ?

A : Finite languages

B : Context free Languages

C : Unrestricted languages

D : Restricted languages

Q.no 32. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 33. Which productions will generate odd length palindromes for terminals 'a' and 'b' ?

A : S-> aSa|bSb|a|b

B : S-> aSa|bSb|aa|bb

C : S-> aSa|bSb

D : S-> aSb|bSa|a|b

Q.no 34. The subset construction shows that every NFA accepts a ……..

A : String

B : Function

C : Regular language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Context-free language

Q.no 35. Which of the following is not a Non deterministic Turing machine?

A : Alternating Turing Machine

B : Probabalistic Turing Machine

C : Read-only Turing Machine

D : Unsolvable

Q.no 36. Production Rule: aAb->agb belongs to which of the following category?

A : Regular Language

B : Context free Language

C : Context Sensitive Language

D : Recursively Ennumerable Language

Q.no 37. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

D : transition function

Q.no 38. Which of the following represents a language which has no pair of consecutive 1’s if alphabet =
{0,1}?

A:

B:

C:

D:

Q.no 39. A non-deterministic pushdown automaton can be converted into an equivalent deterministic
pushdown automaton.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : never

B : not always

C : always

D : maybe

Q.no 40. PDA is useful in

A : lexical analysis

B : syntax analysis

C : semantic analysis

D : code generation

Q.no 41. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 42. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 43.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 44. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 45. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is
undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 46. For two regular languages

L1 = (a + b)* a
and
L2 = b (a + b ) *
the intersection of L1 and L2 is given by

A : (a + b ) * ab

B : ab (a + b ) *

C:a(a+b)*b

D : b (a + b ) * a

Q.no 47. Construct a Turing machine which accepts a string with ‘aba’ as its substring.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 48. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank symbols
does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 49. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 50. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

D : ababbbbbab

Q.no 51. Which Transition table of Turing Machine is correct to check well formedness of parentheses?

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 52. If all the production rules have single nonterminal symbol on the left side then grammar is
called as

A : Context free grammar

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Context sensitive grammar

C : Unrestricted grammar

D : Phrase grammar

Q.no 53. Consider the following regular expressions. i) (a+b)* ii) (a*+b*)* iii) ((ϵ+a)b*)*
Which of the following statements is correct?

A : i,ii are equal and ii,iii are not

B : i,ii are equal and i,iii are not

C : ii,iii are equal and i,ii are not

D : i,ii,iii are equal

Q.no 54. From the options given below the statement, which is not necessarily true if X1 is the recursive
language and X2 and X3 are the languages that are recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

Q.no 55. The regular expression for all strings of 0′s and 1′s with no two consecutive 0′s is

A : (0+1)

B : (0+1)*

C:

D : (0+1)* 011

Q.no 56. Transition function of Epsilon-NFA machine is given by

A:

B:

C:
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 57. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 58. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 59. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 60. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

A : I and II

B : I and IV

C : II and III

D : II and IV

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/16
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is c

Answer for Question No 2. is b

Answer for Question No 3. is b

Answer for Question No 4. is b

Answer for Question No 5. is d

Answer for Question No 6. is c

Answer for Question No 7. is b

Answer for Question No 8. is c

Answer for Question No 9. is d

Answer for Question No 10. is c

Answer for Question No 11. is b

Answer for Question No 12. is b

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is d

Answer for Question No 18. is d

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is a

Answer for Question No 23. is d

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is a

Answer for Question No 27. is d

Answer for Question No 28. is b

Answer for Question No 29. is a

Answer for Question No 30. is c

Answer for Question No 31. is c

Answer for Question No 32. is a

Answer for Question No 33. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is c

Answer for Question No 35. is c

Answer for Question No 36. is c

Answer for Question No 37. is b

Answer for Question No 38. is a

Answer for Question No 39. is b

Answer for Question No 40. is b

Answer for Question No 41. is c

Answer for Question No 42. is a

Answer for Question No 43. is b

Answer for Question No 44. is a

Answer for Question No 45. is c

Answer for Question No 46. is d

Answer for Question No 47. is c

Answer for Question No 48. is a

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is a

Answer for Question No 52. is a

Answer for Question No 53. is d

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is c

Answer for Question No 57. is b

Answer for Question No 58. is a

Answer for Question No 59. is d

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Bottom-up parsers use

A : leftmost derivation

B : rightmost derivation

C : rightmost derivation in reverse order

D : leftmost derivation in reverse order

Q.no 2. Which of the following statement is true? (a) Turing machine was developed by Alan Turing,
(b) PDA is less powerful than Turing machine, (c) FA is more powerful than TM

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 3. A Language for which no DFA exist is a________

A : Regular Language

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : Non-Regular Language

C : May be Regular

D : Cannot be said

Q.no 4. If the PDA does not stop on an accepting state and the stack is not empty, the string is

A : rejected

B : goes into loop forever

C : rejected and goes into loop forever

D : accepted

Q.no 5. Which of the following is true?

A : Every subset of a regular set is regular

B : Every finite subset of non-regular set is regular

C : The union of two non regular set is not regular

D : Infinite union of finite set is regular

Q.no 6. Universal TM influenced the concept of

A : Stored program computers

B : Interpretive implementation of programming languages

C : Computability

D : All of these

Q.no 7. Identify the problem: Given a graph G = <V, E>, and a starting node a, does it have a tour cost
less than k?

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 8. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol

C : output symbol

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : tape symbol

Q.no 9. In CFG, notation of VARIABLE representation is

A : Captal Letters

B : Small Letters

C : Italic Letters

D : Roman Letters

Q.no 10. A formal language is recursive if :

A : A turing machine exists

B : A turing machine that halts for every input

C : Turing machine rejects if the input does not belong to the language

D : All of the mentioned

Q.no 11. To which of the following class does a CNF-satisfiability problem belong?

A : NP class

B : P class

C : NP complete

D : NP hard

Q.no 12. The Grammar can be defined as: G= (V, T, P, S) In the given definition, what does S
represents?

A : Accepting State

B : Starting Variable

C : Sensitive Grammar

D : Final state

Q.no 13. The transition a Push down automaton makes is additionally dependent upon the:

A : Current State

B : input tape

C : stack

D : terminals

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 14.

A : Always starts with b

B : Can have any number of ba and ab

C : Can not have 2 b's together.

D : Starts and end with same symbol

Q.no 15. If P, Q, R are three regular expressions and if P does not contain epsilon, then the equation R =
Q + RP has a unique solution given by

A : R = QP*

B : R = P*Q

C : R = RP

D : R = QP

Q.no 16. A push down automata is different than finite automata by

A : Its memory

B : number of states

C : start state

D : input symbols

Q.no 17. Which one of the following is the most powerful method?

A : LL(1)

B : SLR

C : CLR

D : LALR

Q.no 18. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 19. Which of the production rule can be accepted by Chomsky grammar. (i) A->BC, (ii) A->a
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : only i

B : only ii

C : both i and ii

D : neither i nor ii

Q.no 20. If there exists a language L, for which there exists a TM, T, that accepts every word in L and
either rejects or loops for every word that is not in L, is called

A : Recursive

B : Recursively Enumerable

C : NP-HARD

D : NP Complete

Q.no 21. Which of the following is true for the language?

A : It is not accepted by a Turing Machine

B : It is regular but not context-free

C : It is context-free but not regular

D : It is neither regular nor context-free, but accepted by a Turing machine

Q.no 22. Which of the following pairs have DIFFERENT expressive power?

A : Deterministic finite automata (DFA) and Non-Deterministic finite automata(NFA)

B : Deterministic push down automata (DPDA) and Non-deterministic pushdown automata (NPDA)

C : Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine

D : Single-tape Turing machine and multi-tape Turing machine

Q.no 23. Which of the following represents a language which has no pair of consecutive 1’s if alphabet =
{0,1}?

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 24. Choose the incorrect statement.

A : Moore and Mealy machines are FSM with output capabilities

B : Any given Moore machine has an equivalent Mealy machine

C : Any given Mealy machine has an equivalent Moore machine

D : Moore machine is not an FSM

Q.no 25. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings in which the total number of a’s is divisible by 2.

A : ((a+b)(a+b))*

B : (a + ab)*

C : ( b* a b*ab*)* + b*

D : a* b (aa)*b a*

Q.no 26. A PDA machine configuration (p, w, y) can be correctly represented as

A : unprocessed input, stack content, current state

B : current state, unprocessed input, stack content

C : current state, stack content, unprocessed input

D : stack content, current state, unprocessed input

Q.no 27. The minimum number of 1’s to be used in a regular expression of the given language of all
strings containing exactly 2 zeroes.

A:2

B:3

C:0

D:1

Q.no 28. In definition of PDA M=(Q, Σ,Γ, q0,Z0,A,δ) what Γ represents

A : initial stack symbol

B : stack alphabet

C : finite set of states

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : transition function

Q.no 29. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings in which any occurrence of the symbol b, is in groups of odd numbers.

A : (abbb)*

B : a* b (bb)* a*

C : ((a+b)(a+b)(a+b))*

D : a* b* (bb)* a*

Q.no 30. Given grammar G:

(1)S->AS (2)S->AAS (3)A->SA (4)A->aa
Which of the following productions denies the format of Chomsky Normal Form?

A : 2,4

B : 1,3

C : 1, 2, 3, 4

D : 2, 3, 4

Q.no 31. The set of all strings over alphabet = {a,b} in which all strings having bbbb as substring is

A : (a+b)* bbbb (a+b)*

B : (a+b)* bb (a+b)*bb

C : bbb(a+b)*

D : bb (a+b)*

Q.no 32. Identify the following problem: If G=(V, E) and V' is subset of V, then V' is an independent set
iff no two nodes in V' are connected by an edge in E.

A : Satisfiability

B : Independent set

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 33. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata (NPDA)

C : single tape turing machine and multi tape turing machine

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 34. The maximum number of transitions which can be performed over a state in a DFA having
alphabet set a,b,c are

A:1

B:2

C:3

D:4

Q.no 35. Turing machine (TM) is more powerful than FSM (Finite State Machine) because

A : Tape movement is confined to one direction

B : It has no finite state

C : It has the capability to remember arbitrarily long sequences of input symbols

D : It has tape symbols

Q.no 36. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.

A : true

B : false

C : maybe

D : probably

Q.no 37. Which of the following is in 2-CNF?

A : (e1 Ʌ e2) Ʌ (e1 Ʌ ~e2)

B : (e1 Ʌ e2) Ʌ (e1 V ~e2)

C : (e1 V e2) Ʌ (e1 V ~e2)

D : (e1 V e2) Ʌ (e1 Ʌ ~e2)

Q.no 38. Which of the following statement is false?

A : Every language that is defined by regular expression can also be defined by finite automata

B : Every language defined by finite automata can also be defined by regular expression

C : We can convert regular expressions into finite automata

D : There exists a unique DFA for every regular language

Q.no 39. The production of the form A->B , where A and B are non terminals is called

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Null production

B : Greibach Normal Form

C : Unit production

D : Chomsky Normal Form

Q.no 40.

A : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the right movement.

B : Perform the transition from q0 to q1 by changing "X" symbol to "a" and perform the right movement.

C : Perform the transition from q0 to q1 by changing "a" symbol to "X" and perform the Left movement.

D : Perform the transition from q0 to q1 by changing "q0" symbol to "q1" and perform the right movement.

Q.no 41. Transition function of Epsilon-NFA machine is given by

A:

B:

C:

D:

Q.no 42. Which one of following is false.

A : There is unique minimal DFA for every regular language.

B : Every NFA can be converted to equivalent PDA.

C : Compliment of every CFL is recursive.

D : Every NPDA can be converted to an equivalent DPDA.

Q.no 43.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : X is decidable

B : X is undecidable but partially decidable

C : X is undecidable and not even partially decidable

D : X is not a decision problem

Q.no 44. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 45.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 46. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank symbols
does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

Q.no 47. The regular expression denotes a language comprising all possible strings of even length over
the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 48. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 49. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 50. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 51. From the options given below the statement, which is not necessarily true if X1 is the recursive
language and X2 and X3 are the languages that are recursively enumerable but not recursive.

A:

B:

C : X2 – X1 is recursively enumerable

D : X1 – X3 is recursively enumerable

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 52. The CFG "S-> aS | bS |a|b " is equivalent to regular expression

A : (a + b)

B : (a + b) (a + b)*

C : (a + b) (a + b)

D : (a . b) (a . b)

Q.no 53.

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 54. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the language
generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 55. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 56. Context free grammar having the following production

X->Xa
is termed as

A : Left Recursive Grammar

B : Non Recursive Grammar

C : Right Recursive Grammar

D : Center Recursive Grammar

Q.no 57.

A:A

B:B

C:C

D:D

Q.no 58. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/15
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 59. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*

Q.no 60. The set of all strings over alphabet ={a,b} in which a single a followed by any number of b’s or
a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a

D : (a+b)(a+b)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/15
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is c

Answer for Question No 2. is c

Answer for Question No 3. is b

Answer for Question No 4. is a

Answer for Question No 5. is b

Answer for Question No 6. is d

Answer for Question No 7. is d

Answer for Question No 8. is b

Answer for Question No 9. is a

Answer for Question No 10. is d

Answer for Question No 11. is c

Answer for Question No 12. is b

Answer for Question No 13. is c

Answer for Question No 14. is c

Answer for Question No 15. is a

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is c

Answer for Question No 18. is a

Answer for Question No 19. is d

Answer for Question No 20. is b

Answer for Question No 21. is d

Answer for Question No 22. is b

Answer for Question No 23. is a

Answer for Question No 24. is d

Answer for Question No 25. is c

Answer for Question No 26. is b

Answer for Question No 27. is b

Answer for Question No 28. is b

Answer for Question No 29. is b

Answer for Question No 30. is a

Answer for Question No 31. is a

Answer for Question No 32. is b

Answer for Question No 33. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is c

Answer for Question No 35. is c

Answer for Question No 36. is a

Answer for Question No 37. is c

Answer for Question No 38. is d

Answer for Question No 39. is c

Answer for Question No 40. is a

Answer for Question No 41. is c

Answer for Question No 42. is d

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is a

Answer for Question No 46. is a

Answer for Question No 47. is d

Answer for Question No 48. is d

Answer for Question No 49. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is c

Answer for Question No 51. is d

Answer for Question No 52. is b

Answer for Question No 53. is b

Answer for Question No 54. is c

Answer for Question No 55. is a

Answer for Question No 56. is a

Answer for Question No 57. is b

Answer for Question No 58. is a

Answer for Question No 59. is a

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. Regular expressions are used to represent which language?

A : Recursive language

B : Context free language

C : Regular language

D : Context Sensitive language

Q.no 2. Language of finite automata is generated by

A : Type 0 grammar

B : Type 1 grammar

C : Type 2 grammar

D : Type 3 grammar

Q.no 3. A push down automata is different than finite automata by

A : Its memory
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : number of states

C : start state

D : input symbols

Q.no 4. Epsilon-closure of a state is a combination of self state and ----

A : Epsilon-reachable states

B : initial state

C : Final state

D : Non-final states

Q.no 5. Which of the following correctly recognize the symbol ‘|-‘ in context to PDA?

A : moves

B : transition function

C : or symbol

D : not symbol

Q.no 6. Which of the following statement is true?

A : Mealy machine has no terminating state

B : A Moore machine has terminating state

C : Converting from Mealy into Moore machine and vice versa is not possible

D : More machine is Moore powerful than Mealy machine

Q.no 7. Which of the following case does not exist in complexity theory?

A : Best case

B : Worst case

C : Average case

D : Null case

Q.no 8. The symbol Z0 in formal definition of PDA is used for

A : input symbol

B : stack symbol
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : output symbol

D : tape symbol

Q.no 9. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable

C : decision

D : complete

Q.no 10. Which operation can be applied on stack

A : Push

B : Pop

C : Push and Pop

D : Read

Q.no 11. How many states a Turing machine has?

A : Finite

B : Infinite

C : May be finite

D : One

Q.no 12. Top-down parsers use the grammar

A : LL(K)

B : LR(K)

C : SLR(K)

D : CLR(K)

Q.no 13. Regular expression x + y denotes the set

A : {x,y}

B : {xy}

C : {x}
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : {y}

Q.no 14. A language L is said to be ____________ if there is a turing machine M such that
L(M)=L and M halts at every point.

A : Turing acceptable

B : Decidable

C : Undecidable

D : NP-HARD

Q.no 15. A language is regular if and only if

A : accepted by DFA

B : accepted by PDA

C : accepted by LBA

D : accepted by Turing machine

Q.no 16. What is the pumping length of string of length x?

A : x+1

B:x

C : x-1

D : x2

Q.no 17. Pushdown automata accepts

A : regular language

B : context free language

C : context sensitive language

D : unrestricted language

Q.no 18.

A : L*

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:L

D:

Q.no 19. Recursive languages are also known as:

A : decidable

B : Undecidable

C : sometimes decidable

D : infinite

Q.no 20. NPDA stands for

A : non deterministic pushup automata

B : null pushdown automata

C : nested pushdown automata

D : non deterministic pushdown automata

Q.no 21. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata
(NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 22. The difference between number of states in FA for regular expression (a + b) and (a + b)
* is:

A:1

B:2

C:3

D:0

Q.no 23. Can a DFA recognize a palindrome number?

A : Yes

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : No

C : May be

D : Cannot be determined

Q.no 24. Is the language preserved in all the steps while eliminating epsilon transitions from a
NFA?

A : yes

B : no

C : may be

D : cannot say

Q.no 25. According to Chomsky hierarchy, which of the following is recognized by Recursively
Enumerable language?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 26. A grammar G=(V,T,P,S) in which V represents

A : Set of Nonterminals

B : Start symbol

C : Set of terminals

D : Production

Q.no 27. X is a simple mathematical model of a computer. X has unrestricted and unlimited
memory. X is a FA with R/W head. X can have an infinite tape divided into cells, each cell
holding one symbol.
Name X?

A : Push Down Automata

B : Non deterministic Finite Automata

C : Turing machines

D : Deterministic Finite Automata

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 28. The automaton which allows transformation to a new state without consuming any
input symbols:

A : NFA

B : DFA

C : Epsilon NFA

D : PDA

Q.no 29. Number of external states of a UTM should be atleast

A:1

B:2

C:3

D:4

Q.no 30. The variable which produces

epsilon is called

A : Empty variable

B : Nullable variable

C : Non-empty variable

D : Non-nullable variable

Q.no 31. PDA works as Finite Automata when the number of auxiliary memory it has is

A:3

B:2

C:1

D:0

Q.no 32. The basic limitation of finite automata is that

A : It cannot remember arbitrary large amount of information.

B : It sometimes recognize grammar that are not regular.

C : It sometimes fails to recognize regular grammar.

D : It sometimes fails to recognize regular laguage

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 33. How many strings of length less than 4 contain the language described by the regular
expression (x+y)*y(a+ab)*

A:7

B : 10

C : 12

D : 11

Q.no 34. The operations of PDA never work on elements other than top of the stack.

A : false

B : true

C : may be

D : cannot say

Q.no 35. What does it mean when we say that an algorithm X is asymptotically more efficient
than Y?

A : X will always be a better choice for small inputs

B : X will always be a better choice for large inputs

C : Y will always be a better choice for small inputs

D : X will always be a better choice for all inputs

Q.no 36. A context free language is called ambiguous if (a) It has two or more leftmost
derivations for the same string. (b) It has two or more rightmost derivations for the same string.
(c) It has Only single derivation tree.

A : Only (a)

B : Only (b)

C : Both (a) and (b)

D : Only (c)

Q.no 37. Which of the following statement is not true?

A : Type 0 grammar is called unrestricted grammar

B : Chomsky hierarchy define only one type of grammar

C : Type 3 grammar is recognized by FA

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : Type 2 grammar is CFG

Q.no 38. Which of the following is analogous to the NFA and NPDA ?

A : Regular language and Context Free language

B : Regular language and Context Sensitive language

C : Context free language and Context Sensitive language

D : Unrestricted language

Q.no 39. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 40. Number of states required to accept strings ending with 10 are

A:3

B:2

C:1

D : can’t be represented.

Q.no 41. Construct the regular expressions for the following DFAs:

A : (0 + 11*0)*

B : 0*+010*

C : (0+010)*

D : (0+1)*
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 42. Choose the correct option for the given statement: The DFA shown represents all strings

which have 1 at the second last position.

A : Correct

B : Incorrect, Incomplete DFA

C : Wrong proposition

D : May be correct

Q.no 43. The context free grammar

S->SS|0S1 |1S0|Є
generates :

A : Unequal number of 0’s and 1’s

B : Equal number of 0’s and 1’s

C : Any number of 0’s followed by any number of 1’s

D : 0's followed by 1's

Q.no 44. Examine the following DFA: If input is 011100101, which edge is NOT traversed?

A:AB

B:BD

C:CD

D:DA

Q.no 45. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A:

B:

C:

D:

Q.no 46. Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2
is undecidable. Which one of the following is True?

A : P3 is decidable if P1 is reducible to P3

B : P3 is undecidable if P3 is reducible to P2

C : P3 is undecidable if P2 is reducible to P3

D : P3 is decidable if P3 is reducible to P2’s complement

Q.no 47.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : Decidable and Recursively Enumerable

B : Undecidable but Recursively Enumerable

C : Undecidable and Not Recursively Enumerable

D : Decidable but not Recursively Enumerable

Q.no 48. Construct a Turing machine which accepts a string with ‘aba’ as its substring.

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 49. Which of the following statement is false.

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 50. Which of the following is NOT generated by regular expression

R = (ab + abb)* bbab

A : ababbbbab

B : abbbab

C : ababbabbbab

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : ababbbbbab

Q.no 51. Transition function of NFA machine is given by

A:

B:

C:

D:

Q.no 52. The lexical analysis for a modern computer language such as Java needs the power of
which one of the following machine models in a necessary and sufficient sense?

A : Finite state automata

B : Deterministic pushdown automata

C : Non-Deterministic pushdown automata

D : Turing machine

Q.no 53. The output of Moore machine can be defined as

A:

B:

C:

D : state and its input

Q.no 54. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 55. What does the following transition graph shows

A : Copies a symbol

B : Reverses a string

C : Accepts a palindrome

D : Push the symbol

Q.no 56. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

Q.no 57. The regular expression denotes a language comprising all possible strings of even length
over the alphabet (0, 1)

A : 1 + 0(1+0)*

B : (0+1) (1+0)*

C : (1+0)

D : (00+0111+10)*

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/16
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 58.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

Q.no 59. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 60. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are
the two other problems not known to be in NP. Which one of the following statements is true if Q
is polynomial time reducible to S and S is the polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/16
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is c

Answer for Question No 2. is d

Answer for Question No 3. is a

Answer for Question No 4. is a

Answer for Question No 5. is a

Answer for Question No 6. is a

Answer for Question No 7. is d

Answer for Question No 8. is b

Answer for Question No 9. is b

Answer for Question No 10. is c

Answer for Question No 11. is a

Answer for Question No 12. is a

Answer for Question No 13. is a

Answer for Question No 14. is b

Answer for Question No 15. is a

Answer for Question No 16. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is b

Answer for Question No 18. is b

Answer for Question No 19. is a

Answer for Question No 20. is d

Answer for Question No 21. is b

Answer for Question No 22. is a

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is d

Answer for Question No 26. is a

Answer for Question No 27. is c

Answer for Question No 28. is c

Answer for Question No 29. is b

Answer for Question No 30. is b

Answer for Question No 31. is d

Answer for Question No 32. is a

Answer for Question No 33. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is b

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is b

Answer for Question No 38. is a

Answer for Question No 39. is a

Answer for Question No 40. is a

Answer for Question No 41. is a

Answer for Question No 42. is b

Answer for Question No 43. is b

Answer for Question No 44. is c

Answer for Question No 45. is b

Answer for Question No 46. is c

Answer for Question No 47. is b

Answer for Question No 48. is c

Answer for Question No 49. is c

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is d

Answer for Question No 51. is d

Answer for Question No 52. is a

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is c

Answer for Question No 56. is d

Answer for Question No 57. is d

Answer for Question No 58. is a

Answer for Question No 59. is b

Answer for Question No 60. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Seat No -
Total number of questions : 60

10270_THEORY OF COMPUTATION
Time : 1hr
Max Marks : 50
N.B

1) All questions are Multiple Choice Questions having single correct option.

2) Attempt any 50 questions out of 60.

3) Use of calculator is allowed.

4) Each question carries 1 Mark.

5) Specially abled students are allowed 20 minutes extra for examination.

6) Do not use pencils to darken answer.

7) Use only black/blue ball point pen to darken the appropriate circle.

8) No change will be allowed once the answer is marked on OMR Sheet.

9) Rough work shall not be done on OMR sheet or on question paper.

10) Darken ONLY ONE CIRCLE for each answer.

Q.no 1. The language accepted by a Turing machine is called ………. language.

A : Regular

B : Recursively Enumerable

C : Context free

D : Context sensitive

Q.no 2. What is the value of n if Turing machine is defined using n-tuples?

A:6

B:7

C:8

D:5

Q.no 3. Can we convert PDA to equivalent CFG?

A : yes
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 1/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : no

C : maybe

D : never

Q.no 4. Which of the production rule can be accepted by Chomsky grammar. (i) A->BC, (ii) A->a

A : only i

B : only ii

C : both i and ii

D : neither i nor ii

Q.no 5. There is a linear grammar that generates a context free grammar

A : Always

B : Never

C : Sometimes

D : Everytime

Q.no 6. In Moore machine, if input is of length n, then length of output string will be

A:n

B : n+1

C : n+n

D : n-1

Q.no 7. If the PDA does not stop on an accepting state and the stack is not empty, the string is

A : rejected

B : goes into loop forever

C : rejected and goes into loop forever

D : accepted

Q.no 8. Problems that can be solved in polynomial time are known as

A : intractable

B : tractable
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 2/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : decision

D : complete

Q.no 9. Which one of the following languages over the alphabet {0, 1} is described by the regular
expression: (0+1)*0(0+1)*0(0+1)*

A : The set of all strings containing the substring 00

B : The set of all strings containing at most two 0’s

C : The set of all strings containing at least two 0’s

D : The set of all strings that begin and end with either 0 or 1

Q.no 10. A deterministic Turing machine is

A : Ambiguous Turing Machine

B : Unambiguous Turing Machine

C : Non-Deterministic Finite Automata

D : Deterministic Finite Automata

Q.no 11. PDA is more powerful than

A : Turing Machine

B : Finite Automata

C : Linear Bounded Automata

D : Non Deterministic Turing Machine

Q.no 12.

A : L*

B:

C:L

D:

Q.no 13. The recognizing capability of NDFAand DFA

A : must be the same

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 3/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : may be different

C : must be different

D : cannot say

Q.no 14. The major difference between Mealy and Moore machine is about:

A : Output Variations

B : Input Variations

C : Both

D : Transitions

Q.no 15. In Parse Tree, Intermediate Node represents

A : Terminals

B : Variables

C : Start Symbol

D : Productions

Q.no 16. Which of the following are not quantifiers?

A : Kleene plus +

B : Kleene star *

C : Question mark ?

D : Union

Q.no 17. RR* can be expressed in which of the forms:

A : R+

B : R-

C : R+ U R-

D:R

Q.no 18. Which among the following cannot be accepted by a regular grammar?

A : L is a set of numbers divisible by 2

B : L is a set of binary complement

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 4/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : L is a set of strings with odd number of 0s

D : L is a set of 0^n1^n

Q.no 19. Given the expression, is there some assignment of true and false values to the variables
that will make the entire expression true? This is termed as

A : Satisfiability problem

B : Independent set problem

C : Node-Cover Problem

D : Traveling Salesman Problem

Q.no 20. If P, Q, R are three regular expressions and if P does not contain epsilon, then the
equation R = Q + RP has a unique solution given by

A : R = QP*

B : R = P*Q

C : R = RP

D : R = QP

Q.no 21. Can a DFA recognize a palindrome number?

A : Yes

B : No

C : May be

D : Cannot be determined

Q.no 22. The problem of finding a path in a graph that visits every vertex exactly once is called

A : Hamiltonian path problem

B : Hamiltonian cycle problem

C : Subset sum problem

D : Turnpike reconstruction problem

Q.no 23. Every CFG can be transformed into equivalent NPDA.

A : false

B : true

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 5/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : may be

D : cannot say

Q.no 24. For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.

A : true

B : false

C : maybe

D : probably

Q.no 25. Which of the following statements is false ?

A : Halting problem of Turing machines is undecidable

B : Determining whether a context-free grammar is ambiguous is undecidable

C : Given two arbitrary context-free grammars G1 G2 and it is undecidable whether L (G1) = L (G2).

D : Given two regular grammars G1 G2 and it is undecidable whether L (G1) = L (G2)

Q.no 26.

A:

B:

C:

D:

Q.no 27. Which of the following represents a language which has no pair of consecutive 1’s if
alphabet = {0,1}?

A:

B:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 6/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C:

D:

Q.no 28. If there exists a TM which when applied to any problem in the class, terminates, if
correct answer is yes and may or may not terminate otherwise is called

A : Stable

B : Unsolvable

C : Partially solvable

D : Unstable

Q.no 29. Which of the following pairs have different expressive power

A : Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA)

B : Deterministic Push Down Automata (DPDA) and Non-deterministic Push Down Automata
(NPDA)

C : single tape turing machine and multi tape turing machine

D : deterministic single tape and nondeterministic single tape turing machine

Q.no 30. Which of the regular expressions corresponds to the given problem statement over the
alphabet = {a, b}, All strings without double a?

A:

B : ((a+b)(a+b))*

C : (a + bb)*

D:

Q.no 31. Which of the following is a false statement?

A : Moore machine has no accepting states

B : Mealy machine has no accepting states

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 7/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : We can convert Mealy to Moore and vice versa

D : We can convert Mealy to Moore but not vice versa

Q.no 32. A non-deterministic pushdown automaton can be converted into an equivalent

deterministic pushdown automaton.

A : never

B : not always

C : always

D : maybe

Q.no 33. Which of the following is not an application of Finite Automaton?

A : Compiler Design

B : Grammar Parsers

C : Text Search

D : Image processing

Q.no 34. Which of the following statement is correct?

A : All Regular grammars are context free but not vice versa

B : All context free grammars are regular grammars but not vice versa

C : Regular grammar and context free grammar are the same entity

D : All context sensitive grammar are regular grammar but not vice versa

Q.no 35. A PDA chooses the next move based on

A : current State and input

B : current state, stack and input

C : current state and stack

D : current state

Q.no 36. The string (a)|((b)*(c)) is equivalent to

A : Empty

B : abcabc

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 8/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

C : b*c|a

D : abc

Q.no 37. PDA is useful in

A : lexical analysis

B : syntax analysis

C : semantic analysis

D : code generation

Q.no 38. Construct a regular expression for the language that contains strings having even
number of 0’s followed by odd number of 1’s over {0, 1}.

A : (00)* 1 (11)*

B : ((0+1)(0+1))*

C : (0+1)*

D : (001)*

Q.no 39. Which of the following is a regular language?

A : String whose length is a sequence of prime numbers

B : String with substring wwr in between

C : Palindrome string

D : String with even number of Zeroes

Q.no 40. For a give Moore Machine,

Statement 1: Null string is processed in Moore Machine.
Statement 2: There are more than 5-Tuples in the definition of Moore Machine.
Choose the correct option.

A : Statement 1 is true and Statement 2 is true

B : Statement 1 is true while Statement 2 is false

C : Statement 1 is false while Statement 2 is true

D : Statement 1 is false and Statement 2 is false

Q.no 41. Which of the following statement is false.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 9/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

A : There exist context-free languages such that all context free grammars generating them are
ambiguous.

B : An unambiguous context free grammar always has a unique parse tree for each string of the
language generated by it.

C : Both deterministic and non deterministic PDA always accet same set of languages.

D : Finite set of strings from one alphabet is always a regular language.

Q.no 42. Which Transition table of Turing Machine is correct to check well formedness of
parentheses?

A:

B:

C:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 10/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D:

Q.no 43. The minimum number of productions required to produce a language consisting of
palindrome strings (even and odd length) over T={a,b} is

A:3

B:5

C:7

D:2

Q.no 44. Which of following can be accepted by DPDA

A : any palindrome

B : odd length palindrome

C : even length palindrome

D : palindrome string is not accepted

Q.no 45. Find the pair of regular expressions that are equivalent

A : (0+1)* and (01)*

B : (0+10)* and (0+10*)

C : (0+10)* and (0*+10)*

D : (111*)* and (111+11*)*

Q.no 46. The set of all strings over alphabet ={a,b} in which a single a followed by any number of
b’s or a single b followed by any number of a’s is

A : ab* + ba*

B : ab*ba*

C : a*b + b*a
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 11/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

D : (a+b)(a+b)*

Q.no 47. Which Transition table of Turing Machine is correct for the following problem
"Design a TM to find 2's complement of a binary number".

A:

B:

C:

D:

Q.no 48. The context free languages are closed under (a) union, (b) concatenation, (c) Kleen
closure

A : Only (a)

B : Only (b)

C : Only (c)

D : (a), (b) and (c)

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 12/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 49. The following Turing machine acts like

A : Copies a string

B : Delete a symbol

C : Insert a symbol

D : Push the symbol

Q.no 50. Which Transition Diagram is correct for the following problem
"Design a TM that erases all non blank symbols on the tape, where the sequence of non-blank
symbols does not contain any blank symbols B in between. Consider Alphabet {a,b}.

A:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 13/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B:

C:

D:

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 14/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 51.

A:A

B:B

C:C

D:D

Q.no 52. The language generated by

S-> aSa|bSb|a|b
over the alphabet {a,b} is the set of

A : All length palindrome

B : Even length palindrome

C : Odd length palindrome

D : Strings starting and ending with different character

Q.no 53. The language A-> tB|t generated by which of the following grammar?

A : Type 3

B : Type 2

C : Type 1

D : Type 0

Q.no 54. Which grammar accepts the language of {a, b} having strings ending with 'a'.

A : S->aS | bS

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 15/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

B : S->aS | bS |b

C : S->aS | bS |S

D : S->aS | bS |a

Q.no 55. Out of the three problems S, Q and R, S is an NP-complete problem and Q and R are
the two other problems not known to be in NP. Which one of the following statements is true if Q
is polynomial time reducible to S and S is the polynomial time reducible to R?

A : Q is NP-complete

B : R is NP-complete

C : Q is NP-hard

D : R is NP-hard

Q.no 56. Which of the following is correct for Chomsky hierarchy?

A : CSL < Unrestricted < CF < Regular

B : Regular < CFL < CSL < Unrestricted

C : CFL < CSL < Unrestricted < Regular

D : CFL < CSL < Regular < Unrestricted

Q.no 57. The problems which have no algorithm, regardless of whether or not they are accepted
by a turing machine that fails to halt on some input are referred as:

A : Decidable

B : Undecidable

C : Computable

D : Recognizable

Q.no 58. Consider the following statements.

I. The complement of every Turing decidable language is Turing decidable
II. There exists some language which is in NP but is not Turing decidable
III. If L is a language in NP, L is Turing decidable
Which of the above statements is/are true?

A : Only II

B : Only III

C : Only I and II

D : Only I and III

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 16/17
12/27/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1

Q.no 59. Which of the following grammars are in Chomsky Normal Form:

A : S->AB | BC | CD,
A->0,
B->1,
C->2,
D->3

B : S->AB,
S->BCA | 0 | 1 | 2 | 3

C : S->Ab0,
A->001,
B->A2

D : SA->Aba,
A->aab,
B->Ac

Q.no 60.

A : X is undecidable but partially decidable

B : X is decidable

C : X is not a decision problem

D : X is undecidable and not even partially decidable.

https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=1550&code=1052000&showTest=320&actForm=edit&set=1 17/17
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 1. is b

Answer for Question No 2. is b

Answer for Question No 3. is a

Answer for Question No 4. is d

Answer for Question No 5. is c

Answer for Question No 6. is b

Answer for Question No 7. is a

Answer for Question No 8. is b

Answer for Question No 9. is c

Answer for Question No 10. is b

Answer for Question No 11. is b

Answer for Question No 12. is b

Answer for Question No 13. is a

Answer for Question No 14. is a

Answer for Question No 15. is b

Answer for Question No 16. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 1/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 17. is a

Answer for Question No 18. is d

Answer for Question No 19. is a

Answer for Question No 20. is a

Answer for Question No 21. is b

Answer for Question No 22. is a

Answer for Question No 23. is b

Answer for Question No 24. is a

Answer for Question No 25. is d

Answer for Question No 26. is d

Answer for Question No 27. is a

Answer for Question No 28. is c

Answer for Question No 29. is b

Answer for Question No 30. is a

Answer for Question No 31. is d

Answer for Question No 32. is b

Answer for Question No 33. is d

https://sppu.wheebox.com/WAC-3/openanswers.obj 2/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 34. is a

Answer for Question No 35. is b

Answer for Question No 36. is c

Answer for Question No 37. is b

Answer for Question No 38. is a

Answer for Question No 39. is d

Answer for Question No 40. is a

Answer for Question No 41. is c

Answer for Question No 42. is a

Answer for Question No 43. is b

Answer for Question No 44. is d

Answer for Question No 45. is c

Answer for Question No 46. is a

Answer for Question No 47. is b

Answer for Question No 48. is d

Answer for Question No 49. is b

https://sppu.wheebox.com/WAC-3/openanswers.obj 3/4
12/27/2020 https://sppu.wheebox.com/WAC-3/openanswers.obj

Answer for Question No 50. is a

Answer for Question No 51. is b

Answer for Question No 52. is c

Answer for Question No 53. is a

Answer for Question No 54. is d

Answer for Question No 55. is b

Answer for Question No 56. is b

Answer for Question No 57. is b

Answer for Question No 58. is d

Answer for Question No 59. is a

Answer for Question No 60. is a

https://sppu.wheebox.com/WAC-3/openanswers.obj 4/4