Q.20.In maximization cases, ------------- are assigned to the artificial variables as their coefficients in the objective function a) +m b)âm c) 0 d) none of the above.
2016
Multiple Choice Questions
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 Ans. b) transportation models
c) oil model
d) resources modeling
2016
Multiple Choice Questions
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
2016
Multiple Choice Questions 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 problem
b)original problem
c) double problem
d)restricted
2016
Multiple Choice Questions 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 above Ans.b) Unbounded
b) Unbounded
c) Alternative
d) None of the
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 Ans. c) Artificial Variable
c) Artificial Variable
d) None of the above
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 Ans. c) Two‐phase simplex method
c) Two‐phase simplex method
d) None of the above
2016
Multiple Choice Questions
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
2016
Multiple Choice Questions 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
Ans. a)10 Q.13.The value of 125 / 17 if given that 5 / 17 1
c)12
d)13
2016
Multiple Choice Questions 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 these Ans. a) prime number
b) composite number
c) rational number
d) none of
2016
Multiple Choice Questions
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
c) H K or K H
b) H UK or KUH
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 Ans. a) Euclidean algorithm
b) Remainder theorem
c) Chain’s theorem
d) none of these
2016
Multiple Choice Questions
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
c) z x 2 y z yx
b) z x z y
d) z xy z y 2 x
Ans.a) z xy z yx
Q.3. If t
100
r r a) t 99 e 2
e
r2 4t
2
r
r r b) t 100 e 2
4t
r r Ans. a) t 99 e 2
then value of
2
2 r r c) t 101e 4t 2
4t
r 99 r t e 2
d)
2
4t
Q.4.The degree of homogeneous functions a) 3/2
x y x3 y3
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 xf x yf y (n 1) f
b) xf x yf y nf
c) xf x yf y (n 1) f
d)
2
4t
2016
Multiple Choice Questions Ans. a xf x yf y nf
Q.6. which is homogeneous function of degree 1 / 2 x2 y2 a) u sin 1 x y
x3 y3 b) u sin 1 x y
x4 y4 c) u sin 1 x y
x y d) u sin 1 x y
x y 1 Ans. d) u sin x y 1 x 1 y Q.7. The degree of homogeneous functions u sin tan x y
a) 0
b)1
Q.8. If u x 5 y 4 , x t 2 y t 3 then 21 a) 20t
c) 2
d) 3
du dt
21 b) 22t
21 c) 24t
21 d) 26t
Ans. b) 22t 21 Q.9.The function y sin 100 x cos 200 x attains the maximum value if a) x tan1
1 2
Ans. a) x tan1
b) x tan
1
1 3
c) x tan1
1 4
1 d) x tan
1 5
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
2016
Multiple Choice Questions 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 x y
Q.14. If u log a) 999
then value of xu x yu y
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 fy
a)
fy c) f x
fx fy
b)
fy d) f 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 Q.17. If x x y y z z 100, and z=f(x,y),then value of
a)
(1 log x) (1 log z )
Ans. a)
(1 log x) (1 log z )
b)
(1 log x) (1 log z )
z x
c)
(1 log x) (1 log z )
d)
(1 log x) (1 log z )
2016
Multiple Choice Questions
Q.18. If u x y then value of
2u xy
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) Q.19. The time period of the simple pendulum is given by T 2
l g
,the maximum relative error in T
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 a) 110
1 5
and x=4 ,y=2 then value of
c) 1 30
b) 1 20
u x
d) 1 40
Ans. a) 110 Q.21.The maximum radius vector of a point on the curve a) 8 d)11
b) 9
25 x
2
9 y2
1 is
c)10
Ans. a) 8 Q.22. The condition (rt s 2 ) 0 implies that a) maxima these
b) minima
c) saddle point
d) none of
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) a0
c) a=0
d) none of
2016
Multiple Choice Questions Ans. a)
a
