MA Mathematics - 2016 GATE Paper (Practice Test)


65 Questions MCQ Test GATE Past Year Papers for Practice (All Branches) | MA Mathematics - 2016 GATE Paper (Practice Test)


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This mock test of MA Mathematics - 2016 GATE Paper (Practice Test) for GATE helps you for every GATE entrance exam. This contains 65 Multiple Choice Questions for GATE MA Mathematics - 2016 GATE Paper (Practice Test) (mcq) to study with solutions a complete question bank. The solved questions answers in this MA Mathematics - 2016 GATE Paper (Practice Test) quiz give you a good mix of easy questions and tough questions. GATE students definitely take this MA Mathematics - 2016 GATE Paper (Practice Test) exercise for a better result in the exam. You can find other MA Mathematics - 2016 GATE Paper (Practice Test) extra questions, long questions & short questions for GATE on EduRev as well by searching above.
QUESTION: 1

Q. 1 – Q. 5 carry one mark each.

Q. An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.

Solution:
QUESTION: 2

The Buddha said, “Holding on to anger is like "grasping" a hot coal with the intent of throwing it at someone else; you are the one who gets burnt.”
Select the word below which is closest in meaning to the word underlined above.

Solution:
QUESTION: 3

M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-inlaw
of M. How is P related to M?

Solution:
*Multiple options can be correct
QUESTION: 4

The number that least fits this set: (324, 441, 97 and 64) is ________.

Note: Question may have more than one correct answer)

Solution:

QUESTION: 5

It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.

Solution:
QUESTION: 6

Q. 6 – Q. 10 carry two marks each.

Q.

The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m)?

Solution:
QUESTION: 7

The overwhelming number of people infected with rabies in In dia has been flagged by the World  Health Organization as a source of concern. It is estimated that inoculating 70% of pets and stray  dogs against rabies can lead to a significant reduction in the number of people infected w ith rabies.

Which of the fo llowing can be logically inferred from the above sentences?

Solution:
QUESTION: 8

A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat?

Solution:
QUESTION: 9

Find the area bounded by the lines 3x+2 y=14, 2x-3y =5 in the first quadrant

Solution:
QUESTION: 10

A straight line is fit to a data set (ln x, y) . This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?

Solution:
QUESTION: 11

Q. 11 – Q. 35 carry one mark each.

Q.

Let {X,Y,Z} be a basis of . Consider the following statements P and Q:
(P) : {X+Y, Y+Z,X-Z} is a basis of
.
(Q) : {X+Y+Z, X+2Y-Z, X-3Z} is a basis of
.
Which of the above statements hold TRUE?

 

Solution:
QUESTION: 12

Consider the following statements P and Q:
(P) : If  M= then M is singular

(Q) : Let S be a diagonalizable matrix. If T is a matrix such that S + 5 T = Id, then T is
diagonalizable

Which of the above statements hold TRUE?

Solution:
QUESTION: 13

Consider the following statements P and Q:

(P) : If M is an n x n complex matrix, then  

(Q) : There exists a unitary matrix with an eigenvalue λ such that |λ| <1.

Which of the above statements hold TRUE?

Solution:
QUESTION: 14

Consider a real vector space V of dimension n and a non-zero linear transformation
T : V → V. If dimension(T(V)) < n and T2 = λ T, for some then which of the following statements is TRUE?

Solution:
QUESTION: 15

Let  and  and   be a strictly increasing function such that f(S) is connected. Which of the following statements is TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 16

Let a1=1 and   then

 is equal to _____________________


Solution:
*Answer can only contain numeric values
QUESTION: 17

Maximum   is equal to _________________


Solution:
QUESTION: 18

Let a,b,c such that c2+d2 0. Then, the Cauchy problem

has a unique solution if

Solution:
*Answer can only contain numeric values
QUESTION: 19

Let u(x,t)  be the d'Alembert's solution of the initial value problem for the wave
equation

where c is a positive real number and f, g are smooth odd functions. Then, u(0,1) is
equal to ___________


Solution:
*Answer can only contain numeric values
QUESTION: 20

Let the probability density function of a random variable X be

Then, the value of c is equal to ________________________


Solution:
*Answer can only contain numeric values
QUESTION: 21

Let V be the set of all solutions of the equation y" +a y'+by=0 satisfying  y(0) =y(1), where a, b are positive real numbers. Then, dimension(V ) is equal to
_____________________


Solution:
*Answer can only contain numeric values
QUESTION: 22

Let  where p(x) and q(x)are continuous functions. If   cos(x) are two linearly independent solutions of the above equation, then |4p(0)+2q(1)| is equal to ____________________

 


Solution:
QUESTION: 23

Let Pn(x) be the Legendre polynomial of degree n and   where k
is a non-negative integer. Consider the following statements P and Q:

(P) : I = 0 if k < n.
(Q) : I = 0 if n - k is an odd integer.
Which of the above statements hold TRUE?

Solution:
QUESTION: 24

Consider the following statements P and Q:

(P) :   has two linearly independent Frobenius series
solutions near x=0.

(Q) : has two linearly independent Frobenius series
solutions near x=0.

Which of the above statements hold TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 25

Let the polynomial x4 be approximated by a polynomial of degree 2, which
interpolates x4 at x=-1, 0 and 1. Then, the maximum absolute interpolation error
over the interval [-1, 1] is equal to ______________________


Solution:
QUESTION: 26

Let  (zn)be a sequence of distinct points in  with    

Consider the following statements P and Q:

(P) : There exists a unique analytic function f on D(0,1) such that f(zn) = sin(zn) for
all n.
(Q) : There exists an analytic function f on D(0,1) such that f(zn) = 0 if n is even
and f(zn) = 1 if n is odd.

Which of the above statements hold TRUE?

Solution:
QUESTION: 27

Let be a topological space with the cofinite topology. Every infinite subset of
is

Solution:
*Answer can only contain numeric values
QUESTION: 28

Let 

Then, dimension(C0/M) is equal to _______________________


Solution:
*Answer can only contain numeric values
QUESTION: 29


Solution:
*Multiple options can be correct
QUESTION: 30

Which of the following statements is TRUE for the function f(x)  =x-x2/2 ?

 

Note: Question may have more than one correct answer)

Solution:
QUESTION: 31

Let be the set of all n x  n real matrices with the usual norm topology. Consider the
following statements P and Q:
(P) : The set of all symmetric positive definite matrices in is connected.
(Q) : The set of all invertible matrices in is compact.

Which of the above statements hold TRUE?

Solution:
QUESTION: 32

Let X1, X2, X3, … , Xn be a random sample from the following probability density
function for 0 < μ < ∞, 0 < α < 1,

Here α and μ are unknown parameters. Which of the following statements is TRUE?

Solution:
QUESTION: 33

Suppose X and Y are two random variables such that aX+bY  is a normal random a,b 
variable for all. Consider the following statements P, Q, R and S:

(P) : X is a standard normal random variable.
(Q) : The conditional distribution of X given Y is normal.
(R) : The conditional distribution of X given X+Y is normal.
(S) : X-Y has mean 0.
Which of the above statements ALWAYS hold TRUE?

Solution:
QUESTION: 34

Consider the following statements P and Q:
(P) : If H is a normal subgroup of order 4 of the symmetric group S4, then S4/H is
abelian.

Which of the above statements hold TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 35

Let F be a field of order 32. Then the number of non-zero solutions (a,b) ∈ FxF of
the equation x2+xy+y2 =0 is equal to __________________


Solution:
*Answer can only contain numeric values
QUESTION: 36

Q. 36 – Q. 65 carry two marks each.

Q.

Let   be oriented in the counter-clockwise direction. Let

Then, the value of I is equal to __________________________


Solution:
*Answer can only contain numeric values
QUESTION: 37

Let  be a harmonic function and v(x,y) its harmonic conjugate. If  is equal to _______________


Solution:
*Answer can only contain numeric values
QUESTION: 38

Let λ be the triangular path connecting the points (0,0), (2,2) and (0,2) in the counterclockwise
direction in R2. Then

is equal to _____________________


Solution:
QUESTION: 39

Let y be the solution of 

Then y(1) is equal to

Solution:
*Answer can only contain numeric values
QUESTION: 40

Let X be a random variable with the following cumulative distribution function:

Then P(1/4 <X<1) is equal to ___________________


Solution:
QUESTION: 41

Let γ be the curve which passes through (0,1) and intersects each curve of the family y=cx2 orthogonally. Then γ also passes through the point

Solution:
*Answer can only contain numeric values
QUESTION: 42

Let  be the Fourier series of the
2 π periodic function defined by   then 

 is equal to ________________


Solution:
*Answer can only contain numeric values
QUESTION: 43

Let y(t) be a continuous function on [0, ∞). If 

 then   is equal to _______________.


Solution:
QUESTION: 44

Let  then, S10 + I10  is equal to 

Solution:
*Answer can only contain numeric values
QUESTION: 45

For any 

Then, is equal to ____________________


Solution:
*Answer can only contain numeric values
QUESTION: 46

Let 

 equal to ______________


Solution:
*Answer can only contain numeric values
QUESTION: 47

Let M= be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors
corresponding to 1 and 0 are (1,1,1)T and (1, -1,0)T respectively, then the value of
3f is equal to _________________


Solution:
*Answer can only contain numeric values
QUESTION: 48

Let M=  and   then

 is equal to ________________________


Solution:
QUESTION: 49

Let the integral 

Consider the following statements P and Q:
(P) : If I2 is the value of the integral obtained by the composite trapezoidal rule with
two equal sub-intervals, then I2 is exact.
(Q) : If I3 is the value of the integral obtained by the composite trapezoidal rule with
three equal sub-intervals, then I3 is exact.

Which of the above statements hold TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 50

The difference between the least two eigenvalues of the boundary value problem

is equal to ______________________________


Solution:
*Answer can only contain numeric values
QUESTION: 51

The number of roots of the equation x2- cos(x)= 0 in the interval  

 is equal to ____________


Solution:
QUESTION: 52

For the fixed point iteration   consider the following statements P and Q:

(P) : if g(x) =1+2/x then the fixed point iteration converges to 2 for all  

(Q) : if g(x) =  then the fixed point iteration converges to 2 for all 

Which of the above statements hold TRUE?

Solution:
QUESTION: 53

Let T: l1-lbe defined by

 Then

Solution:
*Answer can only contain numeric values
QUESTION: 54

Minimize w =x+2y subject to

2x+y 3

x+y2

x0, y0

Then, the minimum value of w is equal to _________________________


Solution:
*Answer can only contain numeric values
QUESTION: 55

Maximize w=11 x-z subject to

10x+y-z1

2x-2y+z2

x,y,z0

Then, the maximum value of w is equal to _________________________


Solution:
*Answer can only contain numeric values
QUESTION: 56

Let X1, X2, X3, … be a sequence of i.i.d. random variables with mean 1. If N is a geometric random variable with the probability mass function P(N=K) =1/2K.  K=1,2,3, .... and it is independent of the XI's then E(X1+X2+X3) is equal to ____________


Solution:
*Answer can only contain numeric values
QUESTION: 57

Let x1 be an exponential random variable with mean 1 and x2 a gamma random
variable with mean 2 and variance 2. If x1 and x2 are independently distributed, then
P(x1 < x2) is equal to _________________________


Solution:
*Answer can only contain numeric values
QUESTION: 58

Let x1, x2, x3, … be a sequence of i.i.d. uniform (0,1) random variables. Then, the value
of 

is equal to ____________________


Solution:
QUESTION: 59

Let X be a standard normal random variable. Then  is equal to

Solution:
QUESTION: 60

Let X1,X2,X3... Xn be a random sample from the probability density function

where α>0, 0 θ 1 are parameters. Consider the following testing problem:

Ho: θ = 1, α = 1 versus H1: θ = 0, α = 2.

Which of the following statements is TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 61

Let X1,X2,X3... be a sequence of i.i.d. N(μ,1) random variables. Then,

is equal to _____________________________


Solution:
QUESTION: 62

Let X1,X2,X3... Xn be a random sample from uniform [1,θ] for some  θ >1. if Xn  = Maximum (X1,X2,X3... Xn) then the UMVUE of θ is

Solution:
*Answer can only contain numeric values
QUESTION: 63

Let x1=x2=x3=1, x4=x5=x6 =2 be a random sample from a Poisson random
variable with mean θ, where  Then, the maximum likelihood estimator of θ
is equal to ____________________


Solution:
*Answer can only contain numeric values
QUESTION: 64

The remainder when 98! is divided by 101 is equal to ____________________________


Solution:
QUESTION: 65

Let G be a group whose presentation is  

Then G is isomorphic to

Solution: