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# 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

Solution:
QUESTION: 2

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+y 2

x 0, y 0

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-z 1

2x-2y+z 2

x,y,z 0

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: