Multiple Choice Questions 2016

Topics: Linear Programming Problem

DR. Sunil Kumar Yadav

Department of Mathematics

Poornima Group of Institutions, JAIPUR INDIA

Q.1. Linear programming model which involves funds allocation of limited investment is
classified as

a) Ordination budgeting model b) capital budgeting models

c) Funds investment models d) funds origin models

Ans. b) capital budgeting models

Q.2.In transportation models designed in linear programming, points of demand is classified as

a) Ordination b) transportation c) destinations d) origins

Ans. c) destinations

Q.3.In linear programming, lack of points for a solution set is said to

a) have no feasible solution b) have a feasible solution

c) have single point method d) have infinite point method

Ans. b) have a feasible solution

Q.4. In maximization problem, optimal solution occurring at corner point yields the

a) mean values of z b) highest value of z c) lowest value of z d) mid values of z

Ans. b) highest value of z

Q.5.In linear programming, oil companies used to implement resources available is classified as

a) Implementation modeling b) transportation models c) oil model d) resources modeling

Ans. b) transportation models

Multiple Choice Questions 2016

Q.6. In minimization problem, better solution can be formed if positive quantities are assigned to

a) Positive basic variables b) negative basic variables

c) Negative non-basic variables d) positive non-basic variables

Ans. d) positive non-basic variables

Q.7. In less than or equal to constraint equations, variable which is used to balance both side of
equations is classified as

a) Solving variable b) condition variable c) slack variable d) positive variable

Ans. c) slack variable

Q.8.Column in simplex initial table used to represent new basic variable is classified as

a) column variable b) key column c)key row d) row variable

Ans. b) key column

Q.9.In simplex method, slack, surplus and artificial variables are restricted to be

a) multiplied b) negative c) non-negative d)divided

Ans. c) non-negative

Q.10.In simplex method basic solution set as (n-m), all variables other than basic are classified
as

a) constant variable b) non positive variables c) basic variables d) non-basic variable

Ans. d) non-basic variable

Q.11.In simplex method, feasible basic solution must satisfy the

a)non-negativity constraint b)negativity constraint c)basic constraint d)common constraint

Ans. a) non-negativity constraint

Q.12.Third requirement of simplex method is that all variables are restricted to include
Multiple Choice Questions 2016

a) negative even values b) odd values c)even values d)non-negative values

Ans. d)non-negative values

Q.13.According to algebra of simplex method, slack variables are assigned zero coefficients
because

a) no contribution in objective function b)high contribution in objective function

c) divisor contribution in objective function d) base contribution in objective function

Ans. a) no contribution in objective function

Q.14.Right hand side constant in ith constraint in primal must be equal to objective coefficient for

a) jth primal variable b) ith dual variable c) ith primal variable d) jth dual variable

Ans. b) ith dual variable

Q.15.In linear programming, related problems in linear programming are classified as

a) dual variables b)single problems c)double problems d)dual problems

Ans. d) dual problems

Q.16. Dual problem statement is formulated with help of information available in another
statement called

a) primal problem b) prime problem c) optimal problem d) primal constants

Ans. a) primal problem

Q.17. Variable in dual problem which can assume negative values, positive values or zero values
is classified as

a)unrestricted constant b)restricted constant c) restricted variable d)unrestricted variable

Ans.d) unrestricted variable

Q.18. In primal-dual solutions, dual problem solution can be obtained by solving other problems
classified as

a)unrestricted problem b)original problem c) double problem d)restricted

problem
Multiple Choice Questions 2016

Ans. b) original problem

Q.19.If in a LPP, the solution of a variable can be made infinity large without violating the constraints,
the solution is ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

a) Infeasible b) Unbounded c) Alternative d) None of the

above
Ans.b) Unbounded

Q.20.In maximization cases, ‐‐‐‐‐‐‐‐‐‐‐‐‐ are assigned to the artificial variables as their coefficients in the
objective function
a) +m b)–m c) 0 d) none of the above
Ans.a) +m

Q.21.In simplex method, we add ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ variables in the case of ‘=’

a) Slack Variable b) Surplus Variable c) Artificial Variable d) None of the above

Ans. c) Artificial Variable

Q.22.A BFS of a LPP is said to be ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ if at least one of the basic variable is zero

a) Degenerate b) Non‐degenerate c) Infeasible d) Unbounded

Ans.a) Degenerate

Q.23.In LPP, degeneracy occurs in ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ stages

a) One b) Two c) Three d)Four

Ans.b) Two

Q.24.Every LPP is associated with another LPP is called ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

a)Primal b)Dual c)Non‐linear programming d)None of the above

Ans. b) Dual

Q.25‐‐‐‐‐‐‐‐‐‐‐ is another method to solve a given LPP involving some artificial variable?

a) MODI method b) Method of penalties c) Two‐phase simplex method d) None of the above

Ans. c) Two‐phase simplex method

Multiple Choice Questions 2016

Topics: Algebraic Structure

DR. Sunil Kumar Yadav

Department of Mathematics

Poornima Group of Institutions, JAIPUR INDIA

Q.1. {- 3 n: n belongs to Z} is an abelian group under

a) Subtraction b) division c) multiplication d) addition

Ans. d) addition

Q.2. If G = {1, -1, I, - I} is group under multiplication, then inverse of - ι is

a)1 b)−1 c) I d) none of Above

Ans. c) I

Q.3. A monoid is always a

a) a group b)a commutative group c) a non abelian group d) semi-group

Ans. d) semi-group

Q.4. If a, b are elements of a group G, then (ba)-1 =

a) a-1 b-1 b) b-1 a-1 c) a-1 b d) b-1 a

Ans. a) a-1 b-1

Q.5.The greatest common deviser of 17 and 22

a) 1 b) 2 c)3 d)4

Ans.a) 1

Q.6. The value of gcd(18,30,60,75,132)

a) 1 b) 2 c) 3 d) 4
Multiple Choice Questions 2016

Ans. c) 3

Q.7. which is the smallest prime number

a) 1 b)2 c) 3 d) 0

Ans. b) 2

Q.8.Every integer n  2 has a

a) prime factor b) composite factor c) remainder factor d) none of these

Ans. a) prime factor

Q.9. If a  b(modn) and c is any integer then one of the following is true

a) a 2  b 2 (mod n) b) b 2  a 2 (mod n) c) a 2  b 2 (mod n) d) a 2  b 2 (mod n)

Ans. a) a 2  b 2 (mod n)

Q.10.The remainder when 1! 2! 3! .........100! is divisible by 15

a) 1 b) 2 c)3 d)4

Ans. c)3

Q.11.The value of 7 222 mod11

a) 5 b) 6 c) 7 d) 8

Ans. a) 5

Q.12. The value of  (11) ,where  (n) is Eulers phi function

a) 10 b) 11 c)12 d)13

Ans. a)10

Q.13.The value of 125 / 17 if given that 5 / 17  1

Multiple Choice Questions 2016

a) -1 b) -2 c) -3 d)-4

Ans.a) -1

Q.14. In which algebraic structure is not semi group

a) (N,+) b) (Z,-) c) (N,+),(Z,-) d) none of these

Ans. b) (Z,-)

Q.15.Every cyclic group is an

a) Abelian group b) group c) monoid d) ring

Ans. a) abelian group

Q.16. How many generator are there of the cyclic group G=[a] of order 8.

a) 4 b) 5 c) 6 d) 7

Ans. a) 4

Q.17.If every element of a group G is its own inverse the G is a

a) Abelian group b) semi group c) ring d) field

Ans. a) abelian group

Q.18.Every subgroup of a cyclic is

a) Cyclic b) group c) subgroup d)

monoid

Ans. a) cyclic

Q.19.The characteristic of a finite field is always a

a) Prime number b) composite number c) rational number d) none of

these

Ans. a) prime number

Multiple Choice Questions 2016

Q.20.In which algebraic structure is a field

a) (Q,+,.) b) (R,+,.) c) (C,+,.) d) all of these

Ans. d) all of these

Q.21.If R is a ring, then for all a, b, c is a real number which is true

a) (-a)(-b)=ab b) a0=0a=0 c) a(-b)=(-a)b=-ab d) all of these

Ans. d) all of these

Q.22. The algebraic structure (Q,,), (R,,) represent

a) Ring b) group c) field d) commutative ring with unity

Ans. d) commutative ring with unity

Q.23. If H and K be the subgroup of a group G then H  K is a subgroup of G iff.

a) H  K or K  H b) H UK or KUH c) H  K or K  H d) HK or KH  

Ans. a) H  K or K  H

Q.24.The value of the Jacobi symbols 55 / 273

a) -1 b) 1 c) -2 d) 2

Ans. a)-1

Q.25. Let a, b be any two positive integer with a  b if a  b then gcd (a,b)=a is represent

a) Euclidean algorithm b) Remainder theorem c) Chain’s theorem d) none of these

Ans. a) Euclidean algorithm

Multiple Choice Questions 2016

Topics: Differential Calculus

DR. Sunil Kumar Yadav

Department of Mathematics

Poornima Group of Institutions, JAIPUR INDIA

Q.1. If u  e xyz then find u yz

a) e xyz{x  x 2 yz} b) e xyz{x  x 2 yz} c) e xyz{x  xyz} d) e xyz{x  xyz}

Ans. a) e xyz{x  x 2 yz}

Q.2.The commutative property of partial differential equations

a) z xy  z yx b) z x  z y c) z x 2 y  z yx d) z xy  z y 2 x

Ans.a) z xy  z yx

r2
 
Q.3. If   t 100
e 4t then value of
r

2 2 2 2
r r r r r r r 99 r
a)  t 99 e 4t b)  t 100 e 4t c)  t 101e 4t d) t e 4t
2 2 2 2
2
r r
Ans. a)  t 99 e 4t
2

x y
Q.4.The degree of homogeneous functions
x3  y3

a) 3/2 b) -3/2 c) 5/2 d) -5/2

Ans. a) 3/2

Q.5. Euler’s theorem for homogeneous function is

a) xf x  yf y  nf b) xf x  yf y  nf c) xf x  yf y  (n  1) f d)
xf x  yf y  (n  1) f
Multiple Choice Questions 2016

Ans. a xf x  yf y  nf

Q.6. which is homogeneous function of degree 1 / 2

 x2  y2   x3  y3   x4  y4   x y 
a) u  sin 1   b) u  sin 1   c) u  sin 1   d) u  sin 1  
 x y  x y  x y  x y
       

 x y 
Ans. d) u  sin  
1
 x y
 

1  x  1  y 
Q.7. The degree of homogeneous functions u  sin    tan  
 y x

a) 0 b)1 c) 2 d) 3

du
Q.8. If u  x 5 y 4 , x  t 2 y  t 3 then
dt

21 21 21 21
a) 20t b) 22t c) 24t d) 26t

Ans. b) 22t 21

Q.9.The function y  sin 100 x cos 200 x attains the maximum value if

1 1 1 1 1 1
a) x  tan1 b) x  tan c) x  tan1 d) x  tan
2 3 4 5

1
Ans. a) x  tan1
2

Q.10. the maximum rectangle inscribed in a circle is a square if

a)   450 b)   900 c)   1200 d)   1800

Ans. a)   450

Q.11.A partial differential equation requires

a) Exactly one independent variable b) two or more independent variables
c) More than one dependent variable d) equal number of dependent and independent variables
Multiple Choice Questions 2016

Ans. b) two or more independent variables

Q.12. the degree of homogeneous functions M(x,y)= 3x2+xy is

a) 1 b)2 c)3 d)4

Ans. b) 2

Q.13. If f(x,y,z) is a homogeneous function of x,y,z of degree 500,the value of xf x  yf y  zf z 

a) 250f b) 500f c) 750f d) 1000f

Ans. a) 500f

 x 1000  y 1000 
Q.14. If u  log  then value of xu x  yu y 

 x y 

a) 999 b) 888 c)777 d)666

Ans.a) 999

dy
Q.15,.If u  f ( x, y)  cons tan t , y  f ( x) then value of
dx

 fx fx fy fy
a) fy b) fy c) f d) f
x x

 fx
Ans. a) f
y

2
Q.16.The power dissipated in a registrant is P  E R ,find the percentage error in P if E is increased by
3% and R is decreases by 2%.

a) 8 b) 9 c) 10 d)11

Ans. a) 8

z
Q.17. If x x y y z z  100, and z=f(x,y),then value of
x

(1  log x) (1  log x) (1  log x) (1  log x)

a) b) c) d)
(1  log z ) (1  log z ) (1  log z ) (1  log z )

(1  log x)
Ans. a)
(1  log z )
Multiple Choice Questions 2016

 2u
Q.18. If u  x y then value of
xy

a) x y 1 ( y log x  1) b) x y 1 ( y log x  1) c) x y ( y log x  1) d)

x y ( y log x  1)

Ans. a) x y 1 ( y log x  1)

l
Q.19. The time period of the simple pendulum is given by T  2 ,the maximum relative error in T
g
if error 1 is in l and 2.5 in g.

a) 1.75 b) 2.75 c) 3.75 d) 4.75

Ans.a) 1.75


Q.20.Using theory of approximation if u  (3.82) 2  2(2.1) 3  1
5
and x=4 ,y=2 then value of
u
x

a) 110 b) 1 20 c) 1 30 d) 1 40

Ans. a) 110

25 9
Q.21.The maximum radius vector of a point on the curve 2
  1 is
x y2

a) 8 b) 9 c)10
d)11

Ans. a) 8

Q.22. The condition (rt  s 2 )  0 implies that

a) maxima b) minima c) saddle point d) none of

these

Ans. c) saddle point

Q.23. At a point p  (a, a) if r  6a , rt  s 2  27a 2 then this point will be maxima if

a) a<0 b) a>0 c) a=0 d) none of

these
Multiple Choice Questions 2016

Ans. a) a<0

5
Q.24. what does  2 k  1
k 1

a) 2(1+2+3+4+5)+1 b) 3+11 c) 3+5+7+9+11 d) none of

these

Ans. c) 3+5+7+9+11

Q.25.If f(x) has a local extremum at x=a and f is differentiable at x=a then f ( x)  0 is knows as

a) Euler’s theorem b) Lagrange’s theorem c) Fermat’s theorem d0 none of these

Ans. c) Fermat’s theorem

Multiple Choice Questions 2016

Topics: Integral Calculus

DR. Sunil Kumar Yadav

Department of Mathematics

Poornima Group of Institutions, JAIPUR INDIA

Q.1.The volume of the solid of the revolution about the parallel to x-axis

b b b b
a)   ( y  k ) 2 dx b)   ( y  k ) 2 dx c)  ( y  k ) 2 dx d)  ( y  k ) 2 dx
a a a a

b
Ans. a)   ( y  k ) 2 dx
a

x
Q.2.Evaluate   sin ydydx
00

a)  b) 2 c) 3 d) 4

Ans. a) 

 a
Q.3. .Evaluate   r 3 ddr
0 0

a 4 5 a 4 5 a 4 5 a 4 5
a) b) c) d)
20 10 40 50

a 4 5
Ans. a)
20


Q.4.Value of   e ( x  y2 )
2
dxdy
00

   
a) b) c) d)
4 2 3 5
Multiple Choice Questions 2016


Ans.a)
4

Q.5. If r  ae cot then the length of the arc between r1 and r2 are

a) sec  (r2  r1 ) b) sec  (r2  r1 ) c) sec r2 d) sec r1

Ans. a) sec  (r2  r1 )

Q.6.the parametric form of the asteroid

a) x  a cos3 t. y  a sin 3 t b) x  a cos t. y  a sin t c) x  a cos 2 t. y  a sin 2 t d) x  a cos 2 t. y  a sin 3 t

Ans. a) x  a cos3 t. y  a sin 3 t

1
 x (1  x) dx
29 99
Q.7. The value of the integral
0

a) B(100,50) b) B(200,100) c) B(300,200) d) none of these

Ans. a) B(100,50)

Q.8. 50 is defined as,   gamma function

   
a)  e  x x 49 dx b)  e  x x 50 dx c)  e  x x100 dx d)  e 50 x 49 dx
0 0 0 0


Ans.a)  e  x x 49 dx
0

1
Q.9. value of     gamma function
2,

a)  b) 1 c) 0 d) 

Ans. a) 

Q.10.the symmetrical property of the functions B(m,n)

a)B(m,n)=B(n,m) b) B(m+1,n)=B(m,n+1) c) a&b d)

none of these

Ans. a) B(m,n)=B(n,m)
Multiple Choice Questions 2016

Q.11.the relations between beta and gamma functions(  )

m n m n m n
a) B(m, n)  b) B(m, n)  m  n c) B(m, n)  m  n d) B(m, n)  m  n
m  n

m n
Ans. a) B(m, n)  m  n

Q.12. which is true of the following relations

a) B(2,3)=B(3,2) b) B(5)=B(4) c) B(5)=B(6) d) none of these

Ans. a) B(2,3)=B(3,2)

Q.13. Value of B(4,5) ?

a) B(5,5)+B(4,6) b)B(6,6)+B(5,7) c) B(7,7)+B(6,8) d) none of these

 1
Q.14.Value of    ,   gamma function
 2

a)  2  b) 2  c)  d)  

Ans. a)  2 

2 2
Q.15. the whole length of the astroid x 3  y2 a 3
3

a) 6a b) 7a c) 8a d) 9a

Ans.a) 6a

Q.16.The length of the arc of the cycloid x  a(  sin  ) , y  a(1  cos )

a) 8a b) 9a c) 10a d) 11a

Ans.a) 8a
Multiple Choice Questions 2016


2
Q.17.Value of  sin 6 xdx
0

5 6 7 8
a) b) c) d)
32 32 32 32

5
Ans. a)
32


2
Q.18. Value of  sin 49 x cos 9 x dx,   gamma function
0

5 5 5 5

   5    5    5    5
a)   b)   c)   d)  
2 2 2 2
230 330 430 530

5
   5
Ans.a)  
2
230

Q.19.Evaluate  xydxdy over x  y  1

A

1 1 1 1
a) b) c) d)
24 25 26 27

1
Ans.a )
24

1x y
Q.20.Evaluate   e x dxdy
00

1 1 1 1
a) (e  1) b) (e  1) c) (e  1) d) (e  1)
2 4 6 8

1
Ans. a) (e  1)
2
Multiple Choice Questions 2016


Q.21. If y  log sec x then length between x  0 to
2

a) log( 2  3 ) b) log( 2  3 ) c) log(3  5 ) d) log(3  5 )

Ans. a) log( 2  3 )


2
Q.22.Value of 120  sin 4  d
0

45 45 45 45

a) b) c) d)
2 3 4 6

45
Ans. a)
2


Q.23.Evaluate  e  x x 99 dx,   gamma function
0

a) 100 b) 200 c) 300 d) 500

Ans. a) 100

Yey
Q.24. Evaluate   dydx
00 y

a) 1 b) 2 c)3 d)4

Q.25 Find the length of the curve r = 4Sin θ from θ = 0º to θ = 90º and also the total length of
curve.

a) π; 2π b). 2π; 4π c) 3π; 6π d) 4π; 8π

Ans. b). 2π; 4π