CS : Computer Science and Information Technology

GATE Paper 2022

Duration : Three Hours Total Marks : 100

Read the following specific instructions carefully for online exam.

Carefully go through various question palette symbols and understand their meanings
before starting the examination.
1. This question paper has 65 questions totalling 100 marks. It consists of 2 sections,
General Aptitude (GA) section for 15 marks and the subject specific section (CS) for
85 marks. Both the sections are compulsory.
2. The GA section consists of 10 questions carrying 15 marks, out of which 5 questions
carry 1 mark each, while the remaining 5 questions carry 2 marks each.
3. The subject specific CS section consists of 55 questions, out of which 25 questions
carry 1 mark each, while the remaining 30 questions carry 2 marks each.
4. The candidates should use the USEFUL DATA given in the question for answering
the question.
5. The question paper consists of some Multiple Choice Questions (MCQ). The
remaining questions are Multiple Select Questions (MSQ) and/or Numerical Answer
Type (NAT) questions. (a) MCQs have four choices out of which only ONE is the
correct answer. The candidate has to choose the correct answer by clicking with the
help of a mouse on the radio button (O) placed before the choice. (b) MSQs have
four choices out of which ONE or MORE than ONE choice(s) is/are correct. The
candidate is required to consider all of the choices and determine the correct
answer(s). Then select ONLY the CORRECT choices by clicking with the help of a
mouse on the respective button(s) (O) placed before the choice(s). (c) For NAT
questions, a numerical answer should be entered with the help of the mouse using
the numeric key pad that appears on the monitor/screen. (d) ALL questions appear in
a random manner. Candidate can find the type of the question and the corresponding
marks displayed above the individual question.
6. All questions that are not attempted will result in zero marks. (a) However, wrong
answers for multiple choice type questions (MCQ) will result in NEGATIVE marks.
For MCQ, a wrong answer will result in deduction of ⅓ marks for a 1-mark question
and ⅔ marks for a 2-mark question. (b) There is NO negative marking for multiple
select questions (MSQ) and numerical answer type (NAT) questions. (c) There is NO
partial marking for MSQ and NAT. (d) For MSQ, to get full credit, the candidate needs
to select ALL the correct choice(s) ONLY and NO wrong choice(s).
7. Your answers will be updated and saved on the server periodically and also at the
end of the examination. The examination will stop automatically at the end of 180
minutes. A candidate is NOT allowed to leave the examination hall till the completion
of the examination.
8. Charts, graph sheets, books, papers, loose sheets, any type of watch, box/pouch,
calculators, electronic gadgets and mathematical tables are NOT allowed in the
examination hall.
9. Candidates may use the scribble pad provided to them in the examination hall for all
rough work. Write name and registration number on the scribble pad before using it.
The candidate can possess ONLY one scribble pad at any point of time. If the
candidate requires a second scribble pad, the first scribble pad MUST be returned to
the invigilator. Any scribble pad in the possession of the candidate MUST be returned
to the invigilators after the end of the examination.

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General Aptitude (GA)

Q.1 to Q.5 Carry ONE mark each.

1. The ______ is too high for it to be considered ________.

(A) fair / fare (B) faer / fair (C) fare / fare (D) fare / fair
2. A function y(x) is defined in the interval [0, 1] on the x-axis as
 1
 2if0 x 3

 1 3
y(x)3if x
 3 4
 3
 1if 4 x1

Which one of the following is the area under the curve for the interval [0, 1] on the
x-axis?
5 6 13 6
(A) (B) (C) (D)
6 5 6 13

3. Let r be a root of the equation x2 + 2x + 6 = 0.

Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is
(A) 51 (B) 51 (C) 126 (D) 126
4. Given below are four statements.
Statement 1 : All students are inquisitive.
Statement 2 : Some students are inquisitive.
Statement 3 : No student is inquisitive.
Statement 4 : Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE
simultaneously, assuming that there is at least one student in the class.
(A) Statement 1 and Statement 3 (B) Statement 1 and Statement 2
(C) Statement 2 and Statement 4 (D) Statement 3 and Statement 4
5. A palindrome is a word that reads the same forwards and backwards. In a game of
words, a player has the following two plates painted with letters.

From the additional plates given in the options, which one of the combinations of
additional plates would allow the player to construct a five-letter palindrome. The
player should use all the five plates exactly once. The plates can be rotated in their
plane.
(A)

(B)

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(C)

(D)

Q.6 to Q.10 Carry TWO marks each.

6. Some people believe that “what gets measured, improves”. Some others believe that
“what gets measured, gets gamed”. One possible reason for the difference in the
beliefs is the work culture in organizations. In organizations with good work culture,
metrics help improve outcomes. However, the same metrics are counterproductive in
organizations with poor work culture.
Which one of the following is the CORRECT logical inference based on the
information in the above passage?
(A) Metrics are useful in organizations with poor work culture
(B) Metrics are useful in organizations with good work culture
(C) Metrics are always counterproductive in organizations with good work culture
(D) Metrics are never useful in organizations with good work culture

7. In a recently conducted national entrance test, boys constituted 65% of those who
appeared for the test. Girls constituted the remaining candidates and they accounted
for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information
provided in the above passage?
(A) Equal number of boys and girls qualified
(B) Equal number of boys and girls appeared for the test
(C) The number of boys who appeared for the test is less than the number of girls
who appeared
(D) The number of boys who qualified the test is less than the number of girls who
qualified

8. A box contains five balls of same size and shape. Three of them are green coloured
balls and two of them are orange coloured balls. Balls are drawn from the box one at
a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is
replaced with another orange ball.
First ball is drawn. What is the probability of getting an orange ball in the next draw?
1 8 19 23
(A) (B) (C) (D)
2 25 50 50

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9. The corners and mid-points of the sides of a triangle are named using the distinct
letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the
following statements:
 The line joining P and R is parallel to the line joining Q and S.
 P is placed on the side opposite to the corner T.
 S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information.
(A) P cannot be placed at a corner
(B) S cannot be placed at a corner
(C) U cannot be placed at a mid-point
(D) R cannot be placed at a corner

10. A plot of land must be divided between four families. They want their individual plots
to be similar in shape, not necessarily equal in area. The land has equally spaced
poles, marked as dots in the below figure. Two ropes, R1 and R2, are already
present and cannot be moved.
What is the least number of additional straight ropes needed to create the desired
plots? A single rope can pass through three poles that are aligned in a straight line.

(A) 2 (B) 4 (C) 5 (D) 3

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Computer Science and Information Technology(CS)

Q.11 – Q.22 Multiple Choice Questions (MCQ), carry ONE mark each.

11. Which one of the following statements is TRUE for all positive functions f (n) ?
(A) f(n2) = (f(n)2), when f(n) is a polynomial
(B) f(n2) = o(f(n)2)
(C) f(n2) = O(f(n)2), when f(n) is an exponential function
(D) f(n2) = (f(n)2)

12. Which one of the following regular expressions correctly represents the language of
the finite automaton given below?

(A) ab*bab* + ba*aba* (B) (ab*b)* ab* + (ba*a)* ba*

(C) (ab*b + ba*a)* (a* + b*) (D) (ba*a + ab*b)* (ab* + ba*)

13. Which one of the following statements is TRUE?

(A) The LALR(1) parser for a grammar G cannot have reduce-reduce conflict if the
LR(1) parser for G does not have reduce-reduce conflict.
(B) Symbol table is accessed only during the lexical analysis phase.
(C) Data flow analysis is necessary for run-time memory management.
(D) LR(1) parsing is sufficient for deterministic context-free languages.

14. In a relational data model, which one of the following statements is TRUE?
(A) A relation with only two attributes is always in BCNF.
(B) If all attributes of a relation are prime attributes, then the relation is in BCNF.
(C) Every relation has at least one non-prime attribute.
(D) BCNF decompositions preserve functional dependencies.

15. Consider the problem of reversing a singly linked list. To take an example, given the
linked list below,

the reversed linked list should look like

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Which one of the following statements is TRUE about the time complexity of
algorithms that solve the above problem in O(1) space?
(A) The best algorithm for the problem takes (n) time in the worst case.
(B) The best algorithm for the problem takes (n log n) time in the worst case.
(C) The best algorithm for the problem takes (n2) time in the worst case.
(D) It is not possible to reverse a singly linked list in O(1) space.

16. Suppose we are given n keys, m hash table slots, and two simple uniform hash
functions h1 and h2. Further suppose our hashing scheme uses h1 for the odd keys
and h2 for the even keys. What is the expected number of keys in a slot?
m n 2n n
(A) (B) (C) (D)
n m m 2m

17. Which one of the following facilitates transfer of bulk data from hard disk to main
memory with the highest throughput?
(A) DMA based I/O transfer
(B) Interrupt driven I/O transfer
(C) Polling based I/O transfer
(D) Programmed I/O transfer

18. Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form.
For the operation R1 + R2, which one of the following values of R1 and R2 gives an
arithmetic overflow?
(A) R1 = 1011 and R2 = 1110
(B) R1 = 1100 and R2 = 1010
(C) R1 = 0011 and R2 = 0100
(D) R1 = 1001 and R2 = 1111

19. Consider the following threads, T1, T2, and T3 executing on a single processor,
synchronized using three binary semaphore variables, S1, S2, and S3, operated upon
using standard wait ( ) and signal ( ). The threads can be context switched in any
order and at any time.
T1 T2 T3

while (true) { while (true) { while (true) {

wait (S3); wait (S1); wait (S2);
print (C) ; print (B) ; print (A) ;
signal (S2) ; } signal (S3) ; } signal (S1) ; }

Which initialization of the semaphores would print the sequence BCABCABCA….?

(A) S1 = 1; S2 = 1; S3 = 1
(B) S1 = 1; S2 = 1; S3 = 0
(C) S1 = 1; S2 = 0; S3 = 0
(D) S1 = 0; S2 = 1; S3 = 1

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20. Consider the following two statements with respect to the matrices Am×n, Bn×m, Cn×n
and Dn×n.
Statement 1 : tr(AB) = tr(BA)
Statement 2 : tr(CD) = tr(DC)
where tr() represents the trace of a matrix. Which one of the following holds?
(A) Statement 1 is correct and Statement 2 is wrong.
(B) Statement 1 is wrong and Statement 2 is correct.
(C) Both Statement 1 and Statement 2 are correct.
(D) Both Statement 1 and Statement 2 are wrong.

21. What is printed by the following ANSI C program?

# include<stdio.h>
int main (int argc, char *argv [ ] )
{

int x = 1, z [ 2 ] = {10, 11} ;

int *p = NULL ;
p = &x ;
*p = 10 ;
p = &z [ 1 ] ;
*(&z [ 0 ] + 1 ) += 3 ;
printf ( %d, %d, %d \ n, x, z [ 0 ], z [ 1 ] ;
return 0 ;

}
(A) 1, 10, 11 (B) 1, 10, 14 (C) 10, 14, 11 (D) 10, 10, 14

22. Consider an enterprise network with two Ethernet segments, a web server and a
firewall, connected via three routers as shown below.

What is the number of subnets inside the enterprise network?

(A) 3 (B) 12 (C) 6 (D) 8

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Q.23 – Q.27 Multiple Select Questions (MSQ), carry ONE mark each.

23. Which of the following statements is/are TRUE?

(A) Every subset of a recursively enumerable language is recursive.
(B) If a language L and its complement L are both recursively enumerable, then L
must be recursive.
(C) Complement of a context-free language must be recursive.
(D) If L1 and L2 are regular, then L1  L2 must be deterministic context-free.

24. Let WB and WT be two set associative cache organizations that use LRU algorithm
for cache block replacement. WB is a write back cache and WT is a write through
cache. Which of the following statements is/are FALSE?
(A) Each cache block in WB and WT has a dirty bit.
(B) Every write hit in WB leads to a data transfer from cache to main memory.
(C) Eviction of a block from WT will not lead to data transfer from cache to main
memory.
(D) A read miss in WB will never lead to eviction of a dirty block from WB.

25. Consider the following three relations in a relational database.

Employee(eld, Name), Brand(bld, bName), Own(eld, bld)
Which of the following relational algebra expressions return the set of eIds who own
all the brands?
(A) eld (eld,bld(Own / bld (Brand))
(B) eld(Own)  eld ((eld (Own) × bld (Brand))  eld,bld (Own))
(C) eld (eld,bld(Own / bld (Own))
(D) eld (eld,(Own) × bld (Own)) / bld (Brand))

26. Which of the following statements is/are TRUE with respect to deadlocks?
(A) Circular wait is a necessary condition for the formation of deadlock.
(B) In a system where each resource has more than one instance, a cycle in its wait-
for graph indicates the presence of a deadlock.
(C) If the current allocation of resources to processes leads the system to unsafe
state, then deadlock will necessarily occur.
(D) In the resource-allocation graph of a system, if every edge is an assignment
edge, then the system is not in deadlock state.

27. Which of the following statements is/are TRUE for a group G ?

(A) If for all x, y  G, (xy)2 = x2y2, then G is commutative.
(B) If for all x  G, x2 = 1, then G is commutative. Here, 1 is the identity element of G.
(C) If the order of G is 2, then G is commutative.
(D) If G is commutative, then a subgroup of G need not be commutative.

Q.28 to Q.35 Numerical Answer Type (NAT), carry ONE mark each.

28. Suppose a binary search tree with 1000 distinct elements is also a complete binary
tree. The tree is stored using the array representation of binary heap trees. Assuming
that the array indices start with 0, the 3rd largest element of the tree is stored at
index_____________.

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29. Consider the augmented grammar with {+, , (,), id} as the set of terminals
S  S
SS+R|R
RRP|P
P  (S) | id
If I0 is the set of two LR(0) items {[S  S.], [S  S. + R]},
then goto(closure(Icontains exactly _______ items.

30. Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then
the maximum number of edges it can have is ____________.
31. Consider a relation R(A, B, C, D, E) with the following three functional dependencies.
AB  C; BC  D; C  E;
The number of superkeys in the relation R is _____________.

32. The number of arrangements of six identical balls in three identical bins is______.
33. A cache memory that has a hit rate of 0.8 has an access latency 10 ns and miss
penalty 100 ns. An optimization is done on the cache to reduce the miss rate.
However, the optimization results in an increase of cache access latency to 15 ns,
whereas the miss penalty is not affected. The minimum hit rate (rounded off to two
decimal places) needed after the optimization such that it should not increase the
average memory access time is _____________.
34. The value of the following limit is _____________
x
lim 
x 0 
1  e2 x
35. Consider the resolution of the domain name www.gate.org.in by a DNS resolver.
Assume that no resource records are cached anywhere across the DNS servers and
that iterative query mechanism is used in the resolution. The number of DNS query-
response pairs involved in completely resolving the domain name is_____________.

Q.36 to Q.45 Multiple Choice Questions (MCQ), carry TWO marks each.
36. Which one of the following is the closed form for the generating function of the
sequence {an}n≥0 defined below?
n  1, nisodd
an  
 1, otherwise
x(1  x 2 ) 1 x(3  x 2 ) 1
(A)  (B) 
(1  x 2 )2 1  x (1  x 2 )2 1  x
2x 1 x 1
(C)  (D) 
2 2
(1  x ) 1 x 2 2
(1  x ) 1 x

37. Consider a simple undirected unweighted graph with at least three vertices. If A is the
adjacency matrix of the graph, then the number of 3-cycles in the graph is given by
the trace of
(A) A3 (B) A3 divided by 2
3
(C) A divided by 3 (D) A3 divided by 6

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38. Which one of the following statements is FALSE?

(A) The TLB performs an associative search in parallel on all its valid entries using
page number of incoming virtual address.
(B) If the virtual address of a word given by CPU has a TLB hit, but the subsequent
search for the word results in a cache miss, then the word will always be present
in the main memory.
(C) The memory access time using a given inverted page table is always same for all
incoming virtual addresses.
(D) In a system that uses hashed page tables, if two distinct virtual addresses V1 and
V2 map to the same value while hashing, then the memory access time of these
addresses will not be the same.

39. Let Ri(z) and Wi(z) denote read and write operations on a data element z by a
transaction Ti, respectively. Consider the schedule S with four transactions.
S : R4(x)R2(x)R3(x)R1(y)W1(y) W2(x) W3(y) R4(y)
Which one of the following serial schedules is conflict equivalent to S?
(A) T1  T3  T4  T2 (B) T1  T4  T3  T2
(C) T4  T1  T3  T2 (D) T3  T1  T4  T2

40. Consider a digital display stem (DS) shown in the figure that displays the contest of
register X. A 16-bit code word is used to load word in X, either from S from R. S is a
1024-word memory segment and R is a 32-word register file. Based on the value of
mode bit M, T selects an input word to load in X. P and Q interface with the
corresponding bits in the code word to choose the addressed word. Which one of the
following represent the functionality of P, Q and T?

(A) P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer

(B) P is 10:210 decoder; Q is 5:25 decoder; T is 2:1 encoder
(C) P is 10:210 decoder; Q is 5:25 decoder; T is 2:1 multiplexer
(D) P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

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41. Consider three floating point numbers A, B and C stored in registers RA, RB and RC,
respectively as per IEEE-754 single precision floating point format. The 32-bit content
stored in these registers (in hexadecimal form) are as follows.

RA = 0xC1400000 RB = 0x42100000 RC = 0x41400000

Which one of the following is FALSE?

(A) A + C = 0 (B) C = A + B (C) B = 3C (D) (B  C) > 0

42. Consider four processes P, Q, R, and S scheduled on a CPU as per round robin
algorithm with a time quantum of 4 units. The processes arrive in the order P, Q, R,
S, all at time t = 0. There is exactly one context switch from S to Q, exactly one
context switch from R to Q, and exactly two context switches from Q to R. There is no
context switch from S to P. Switching to a ready process after the termination of
another process is also considered a context switch. Which one of the following is
NOT possible as CPU burst time (in time units) of these processes?
(A) P = 4, Q = 10, R = 6, S = 2 (B) P = 2, Q = 9, R = 5, S = 1
(C) P = 4, Q = 12, R = 5, S = 4 (D) P = 3, Q = 7, R = 7, S = 3

43. What is printed by the following ANSI C program?

#include<stdio.h>
int main (int argc, char *argv [ ])
{
int a [ 3 ] [ 3 ] [ 3 ] =
{ {1, 2, 3, 4, 5, 6, 7, 8, 9} ,
{10, 11, 12, 13, 14, 15, 16, 17, 18} ,
{19, 20, 21, 22, 23, 24, 25, 26, 27} };
int i = 0, j = 0 , k = 0 ;
for ( i = 0; i < 3 ; i + + ) {
for (k = 0 ; k < 3; k + + )
printf (%d , a [ i ] [ j ] [ k ] ) ;
printf ( \ n ) ;
}
return 0 ;
}

(A) 1 2 3 (B) 1 4 7

10 11 12 10 13 16

19 20 21 19 22 25

(C) 1 2 3 (B) 1 2 3

4 5 6 13 14 15

7 8 9 25 26 27

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44. What is printed by the following ANSI C program?

#include<stdio.h>
int main ( int argc, char *argv [ ] ) {
char a =  P  ;
char b =  x  ;
char c = (a & b) +    ;
char d = (a | b)     ;
char e = (a  b) +  +  ;
printf (% c % c % c \ n  , c, d, e ) ;
return 0 ;
}
ASCII encoding for relevant characters is given below
A B C … Z a b c … z
65 66 67 … 90 97 98 99 … 122

 + 
42 43 45

(A) z K S (B) 122 75 83

(C)   + (D) P x +

45. Consider solving the following system of simultaneous equations using LU

decomposition.
x1 + x2  2x3 = 4
x1 + 3x2  x3 = 7
2x1 + x2  5x3 = 7
where L and U are denoted as
 L11 0 0   U11 U12
U13 
   
L L 21 L 22 0  ,U 0 U22 U23 
L   0 U33 
 31 L 32 L 33   0
Which one of the following is the correct combination of values for L32, U33, and x1?
1
(A) L32 = 2, U33 =  , x1 = 1 (B) L32 = 2, U33 = 2, x1 = 1
2
1 1 1
(C) L32 =  , U33 = 2, x1 = 0 (D) L32 =  , U33 =  , x1 = 0
2 2 2

Q.46 to Q.55 Multiple Select Questions (MSQ), carry TWO marks each.

46. Which of the following is/are undecidable?

(A) Given two Turing machines M1 and M2, decide if L(M1) = L(M2).
(B) Given a Turing machine M, decide if L (M) is regular.
(C) Given a Turing machine M, decide if M accepts all strings.
(D) Given a Turing machine M, decide if M takes more than 1073 steps on every
string.

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47. Consider the following languages;

n n
L1 = {a wa | w{a,b}*}
L2 = {wxwR | w, x{a,b)*, |w|, |x|> 0}
Note that wR is the reversal of the string w. Which of the following is/are TRUE?
(A) L1 and L2 are regular.
(B) L1 and L2 are context-free.
(C) L1 is regular and L2 is context-free.
(D) L1 and L2 are context-free but not regular.
48. Consider the following languages:
L1 = {ww|w{a,b}*}
L2 = {anbncm|m, n ≥ 0}
L3 = {ambncn|m, n ≥ 0}
Which of the following statements is/are FALSE?
(A) L1 is not context-free but L2 and L3 are deterministic context-free.
(B) Neither L1 nor L2 is context-free.
(C) L2, L3 and L2  L3 all are context-free.
(D) Neither L1 nor its complement is context-free.
49. Consider a simple undirected weighted graph G, all of whose edge weights are
distinct. Which of the following statements about the minimum spanning trees of G
is/are TRUE?
(A) The edge with the second smallest weight is always part of any minimum
spanning tree of G.
(B) One or both of the edges with the third smallest and the fourth smallest weights
are part of any minimum spanning tree of G.
(C) Suppose S  V be such that S   and S V. Consider the edge with the
minimum weight such that one of its vertices is in S and the other in V \ S . Such
an edge will always be part of any minimum spanning tree of G.
(D) G can have multiple minimum spanning trees.
50. The following simple undirected graph is referred to as the Peterson graph.

Which of the following statements is/are TRUE?

(A) The chromatic number of the graph is 3.
(B) The graph has a Hamiltonian path.
(C) The following graph is isomorphic to the Peterson graph.

(D) The size of the largest independent set of the given graph is 3. (A subset of
vertices of a graph form an independent set if no two vertices of the subset are
adjacent.)

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Vidyalankar : GATE/CS

51. Consider the following recurrence:

f(1) = 1;
f(2n) = 2f (n)  1 for n ≥ 1 ;
f(2n + 1) = 2 f (n) + 1 for n ≥ 1.
Then, which of the following statements is/are TRUE?
(A) f(2n  1) = 2n  1
(B) f(2n) = 1
(C) f(52n) = 2n+1 + 1
(D) f(2n + 1) = 2n + 1

52. Which of the properties hold for the adjacency matrix A of a simple undirected
unweighted graph having n vertices?
(A) The diagonal entries of A2 are the degrees of the vertices of the graph.
(B) If the graph is connected, then none of the entries of An1 + In can be zero.
(C) If the sum of all the elements of A is at most 2(2n  1), then the graph must be
acyclic.
(D) If there is at least a 1 in each of A’s rows and columns, then the graph must be
connected.

53. Which of the following is/are the eigenvector(s) for the matrix given below?
 9 6 2 4 
 
 8 6 3 1
 20 15 8 5 
 
 32 21 7 12 

 1  1  1  0
       
1 0 0 1
(A)   (B)   (C)   (D)  
0  1 2  3 
       
 1 0 2  0

54. Consider a system with 2 KB direct mapped data cache with a block size of 64 bytes.
The system has a physical address space of 64 KB and a word length of 16 bits.
During the execution of a program, four data words P, Q, R, and S are accessed in
that order 10 times (i.e., PQRSPQRS…). Hence, there are 40 accesses to data
cache altogether. Assume that the data cache is initially empty and no other data
words are accessed by the program. The addresses of the first bytes of P, Q, R, and
S are 0xA248, 0xC28A, 0xCA8A, and 0xA262, respectively. For the execution of the
above program, which of the following statements is/are TRUE with respect to the
data cache?
(A) Every access to S is a hit.
(B) Once P is brought to the cache it is never evicted.
(C) At the end of the execution only R and S reside in the cache.
(D) Every access to R evicts Q from the cache.

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55. Consider routing table of an organization’s router shown below:

Subnet Number Subnet Mask Next Hop

12.20.164.0 255.255.252.0 R1

12.20.170.0 255.255.254.0 R2

12.20.168.0 255.255.254.0 Interface 0

12.20.166.0 255.255.254.0 Interface 1

default R3

Which of the following prefixes in CIDR notation can be collectively used to correctly
aggregate all of the subnets in the routing table?
(A) 12.20.164.0/20 (B) 12.20.164.0/22
(C) 12.20.164.0/21 (D) 12.20.168.0/22

Q.56 to Q.65 Numerical Answer Type (NAT), carry TWO marks each.

56. Consider the relational database with the following four schemas and their respective
instances.
Student ( sNo, sName, dNo) Dept (dNo, dName)
Course (cNo, cName, dNo) Register (sNo, cNo)
Student Dept Course Register
sNo sName dNo dNo dName cNo cName dNo sNo cNo
S01 James D01 D01 CSE C11 DS D01 S01 C11
S02 Rocky D01 D02 EEE C12 OS D01 S01 C12
S03 Jackson D02 C21 DE D02 S02 C11
S04 Jane D01 C22 PT D02 S03 C21
S05 Milli D02 C23 CV D03 S03 C22
S03 C23
S04 C11
S04 C12
S05 C11
S05 C21

SQL Query :
SELECT * FROM Student AS S WHERE NOT EXIST
(SELECT cNO FROM Course WHERE dNo = D01
EXCEPT
SELECT cNo FROM Register WHERE sNo = S . sNo)
The number of rows returned by the above SQL query is _________.

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Vidyalankar : GATE/CS

57. Consider a network with three routers P, Q, R shown in the figure below. All the links
have cost of unity.

P Q R

The routers exchange distance vector routing information and have converged on the
routing tables, after which the link QR fails. Assume that P and Q send out routing
updates at random times, each at the same average rate. The probability of a routing
loop formation (rounded off to one decimal place) between P and Q, leading to count-
to-infinity problem, is ________.

58. Let G(V, E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E
is the set of directed edges, as defined by the following adjacency matrix A.
 1, 1j
i 5
A[i ][j]
0, otherwise
A [ i ] [ j ] = 1 indicates a directed edge from node i to node j. A directed spanning tree
of G, rooted at r  V, is defined as a subgraph T of G such that the undirected
version of T is a tree, and T contains a directed path from r to every other vertex in V.
The number of such directed spanning trees rooted at vertex 5 is ________.

59. Consider a 100 Mbps link between an earth station (sender) and a satellite (receiver)
at an altitude of 2100 km. The signal propagates at a speed of 3 ×108 m/s. The time
taken (in milliseconds, rounded off to two decimal places) for the receiver to
completely receive a packet of 1000 bytes transmitted by the sender is_________.

60. Consider the data transfer using TCP over a 1 Gbps link. Assuming that the
maximum segment lifetime (MSL) is set to 60 seconds, the minimum number of bits
required for the sequence number field of the TCP header, to prevent the sequence
number space from wrapping around during the MSL is____________.

61. A processor X1 operating at 2 GHz has a standard 5-stage RISC instruction pipeline
having a base CPI (cycles per instruction) of one without any pipeline hazards. For a
given program P that has 30% branch instructions, control hazards incur 2 cycles
stall for every branch. A new version of the processor X2 operating at same clock
frequency has an additional branch predictor unit (BPU) that completely eliminates
stalls for correctly predicted branches. There is neither any savings nor any additional
stalls for wrong predictions. There are no structural hazards and data hazards for X1
and X2. If the BPU has a prediction accuracy of 80%, the speed up (rounded off to
two decimal places) obtained by X2 over X1 in executing P is____________.

62. Consider the queues Q1 containing four elements and Q2 containing none (shown as
the Initial State in the figure). The only operations allowed on these two queues are
Enqueue (Q, element) and Dequeue (Q). The minimum number of Enqueue
operations on Q1 required to place the elements of Q1 in Q2 in reverse order (shown
as the Final State in the figure) without using any additional storage is___________.

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63. Consider two files systems A and B, that use contiguous allocation and linked
allocation, respectively. A file of size 100 blocks is already stored in A and also in B.
Now, consider inserting a new block in the middle of the file (between 50th and 51st
block), whose data is already available in the memory. Assume that there are enough
free blocks at the end of the file and that the file control blocks are already in
memory. Let the number of disk accesses required to insert a block in the middle of
the file in A and B are nA and, nB respectively, then the value of nA + nB is_________.

64. Consider a demand paging system with four page frames (initially empty) and LRU
page replacement policy. For the following page reference string
7, 2,7,3, 2,5,3, 4,6,7,7,1,5,6,1
the page fault rate, defined as the ratio of number of page faults to the number of
memory accesses (rounded off to one decimal place) is_________.

65. Consider the following grammar along with translation rules.

S  S1 # T {S.val = S1.val * T.val}
ST {S.val = T.val}
T  T1%R {T.val = T1.val  R.val}
TR {T.val = R.val}
Rid {R.val = id.val}
Here # and % are operators and id is a token that represents an integer and id.val
represents the corresponding integer value. The set of non-terminals is {S, T, R, P}
and a subscripted non-terminal indicates an instance of the non-terminal.

Using this translation scheme, the computed value of S.val for root of the parse tree
for the expression 20#10%5#8%2%2 is _________.



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