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MA Mathematics - 2016 GATE Paper (Practice Test) - 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.

MA Mathematics - 2016 GATE Paper (Practice Test) - 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.

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

*Multiple options can be correct

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 4

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

**Note: Question may have more than one correct answer)**

Detailed Solution for MA Mathematics - 2016 GATE Paper (Practice Test) - Question 4

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 ____________.

MA Mathematics - 2016 GATE Paper (Practice Test) - 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)?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 9

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

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 T^{2} = λ T, for some then which of the following statements is TRUE?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 15

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

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 16

Let a_{1}=1 and then

is equal to _____________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 17

Maximum is equal to _________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 18

Let a,b,c such that c^{2}+d^{2} 0. Then, the Cauchy problem

has a unique solution if

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 ___________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 20

Let the probability density function of a random variable X be

Then, the value of c is equal to ________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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

_____________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 ____________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 23

Let P_{n}(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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 25

Let the polynomial x^{4} be approximated by a polynomial of degree 2, which

interpolates x^{4} at x=-1, 0 and 1. Then, the maximum absolute interpolation error

over the interval [-1, 1] is equal to ______________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 26

Let (z_{n})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(z_{n}) = sin(z_{n}) 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(z_{n}) = 1 if n is odd.

Which of the above statements hold TRUE?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 27

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

is

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 28

Let

Then, dimension(C_{0}/M) is equal to _______________________

*Answer can only contain numeric values

*Multiple options can be correct

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 30

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

**Note: Question may have more than one correct answer)**

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 32

Let X_{1}, X_{2}, X_{3}, … , X_{n} 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 34

Consider the following statements P and Q:

(P) : If H is a normal subgroup of order 4 of the symmetric group S_{4}, then S_{4}/H is

abelian.

Which of the above statements hold TRUE?

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 35

Let F be a field of order 32. Then the number of non-zero solutions (a,b) ∈ FxF of

the equation x^{2}+xy+y^{2 }=0 is equal to __________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 __________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 37

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

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 38

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

direction in R^{2}. Then

is equal to _____________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 39

Let y be the solution of

Then y(1) is equal to

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 40

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

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

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 41

Let γ be the curve which passes through (0,1) and intersects each curve of the family y=cx^{2} orthogonally. Then γ also passes through the point

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 42

Let be the Fourier series of the

2 π periodic function defined by then

is equal to ________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 43

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

then is equal to _______________.

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 44

Let then, S_{10 }+ I_{10 } is equal to

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 45

For any

Then, is equal to ____________________

*Answer can only contain numeric values

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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

3*f* is equal to _________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 48

Let M= and then

is equal to ________________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 49

Let the integral

Consider the following statements P and Q:

(P) : If I_{2} is the value of the integral obtained by the composite trapezoidal rule with

two equal sub-intervals, then I_{2} is exact.

(Q) : If I_{3} is the value of the integral obtained by the composite trapezoidal rule with

three equal sub-intervals, then I_{3} is exact.

Which of the above statements hold TRUE?

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 50

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

is equal to ______________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 51

The number of roots of the equation x^{2}- cos(x)= 0 in the interval

is equal to ____________

MA Mathematics - 2016 GATE Paper (Practice Test) - 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?

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 53

Let T: l_{1}-l_{2 }be defined by

Then

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 54

Minimize w =x+2y subject to

2x+y 3

x+y2

x0, y0

Then, the minimum value of w is equal to _________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - 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 _________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 56

Let X_{1}, X_{2}, X_{3}, … 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) =1/2^{K}. K=1,2,3, .... and it is independent of the X_{I}'s then E(X_{1}+X_{2}+X_{3}) is equal to ____________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 57

Let x_{1} be an exponential random variable with mean 1 and x_{2} a gamma random

variable with mean 2 and variance 2. If x_{1} and x_{2} are independently distributed, then

P(x_{1} < x_{2)} is equal to _________________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 58

Let x_{1}, x_{2}, x_{3}, … be a sequence of i.i.d. uniform (0,1) random variables. Then, the value

of

is equal to ____________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 59

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

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 60

Let X_{1},X_{2},X_{3}... Xn be a random sample from the probability density function

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

H_{o}: θ = 1, α = 1 versus H_{1}: θ = 0, α = 2.

Which of the following statements is TRUE?

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 61

Let X_{1},X_{2},X_{3}... be a sequence of i.i.d. N(μ,1) random variables. Then,

is equal to _____________________________

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 62

Let X_{1},X_{2},X_{3}... Xn be a random sample from uniform [1,θ] for some θ >1. if X_{n }= Maximum (X_{1},X_{2},X_{3}... Xn) then the UMVUE of θ is

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 63

Let x_{1}=x_{2}=x_{3}=1, x_{4}=x_{5}=x_{6 =2 }be a random sample from a Poisson random

variable with mean θ, where Then, the maximum likelihood estimator of θ

is equal to ____________________

*Answer can only contain numeric values

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 64

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

MA Mathematics - 2016 GATE Paper (Practice Test) - Question 65

Let G be a group whose presentation is

Then G is isomorphic to

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