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# MA Mathematics - 2015 GATE Paper (Practice Test)

## 65 Questions MCQ Test GATE Past Year Papers for Practice (All Branches) | MA Mathematics - 2015 GATE Paper (Practice Test)

Description
This mock test of MA Mathematics - 2015 GATE Paper (Practice Test) for GATE helps you for every GATE entrance exam. This contains 65 Multiple Choice Questions for GATE MA Mathematics - 2015 GATE Paper (Practice Test) (mcq) to study with solutions a complete question bank. The solved questions answers in this MA Mathematics - 2015 GATE Paper (Practice Test) quiz give you a good mix of easy questions and tough questions. GATE students definitely take this MA Mathematics - 2015 GATE Paper (Practice Test) exercise for a better result in the exam. You can find other MA Mathematics - 2015 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

### Choose the statement where underlined word is used correctly.

Solution:
QUESTION: 4

Tanya is older than Eric.

Cliff is polder than Tanya

Eric is older than cliff.

If the first two statements are true, then the third statement is :

Solution:
QUESTION: 5

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to completer the league round of matches?

Solution:
QUESTION: 6

Q No 6 - 10 carry Two marks each

Q.

Select the appropriate option in place of underlined part of the sentnce.

" Increased productivity necessary " reflects greater efforts made by the employee.

Solution:
QUESTION: 7

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.

Statements:

I. No manager is leader.

II All leaders are executives.

Conclusions:

I No manager is an executive

II No executive is a manager.

Solution:
*Answer can only contain numeric values
QUESTION: 8

In the given figure angle  is a right angle, PS:QS= 3:1, RT: QT=5:2 and PU: UR = 1:1. if area of triangle QTS is 20 cm2.  then the area of triangle PQR in cm2 is ________________.

(Important : you should answer only the numeric value)

Solution:
QUESTION: 9

Right triangle PQR is to be constructed in the xy- plane so that the right angle is at P and line PR is parallel to the x-axis. The x and y coordinates of P,Q, and R are to be integers that satisfy the inequalities -4x5 and 6 16. How many diffrent triangles could be constructed with these properties ?

Solution:
QUESTION: 10

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the  above information, which one of the following statements is TRUE?

Solution:
*Answer can only contain numeric values
QUESTION: 11

Q. 11 – Q. 35 carry one mark each.

Q.

Let T : R4 → R4 be a linear map defined by

Then the rank of T is equal to _________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 12

Let M be a 3 x 3 matrix and suppose that 1, 2 and 3 are the eigenvalues of M. If

for some scalar α 0, then α is equal to ___________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 13

Let M be a 3 x 3 singular matrix and suppose that 2 and 3 are eigenvalues of M. Then the number
of linearly independent eigenvectors of M3 + 2 M +I3  is equal to _________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 14

Let M be a 3 x 3 matrix such that   and suppose that  for
some . Then | α| is equal to _______

(Important : you should answer only the numeric value)

Solution:
QUESTION: 15

Let be defined by

Then the function f is

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

Consider the power series

The radius of convergence of the series is equal to __________

(Important : you should answer only the numeric value)

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

Let C={zC : |z-i|=2} . then  is equal to ____________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 18

Let   is equal to ___________

(Important : you should answer only the numeric value)

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

Let the random variable X have the distribution function

Then P(2X<4) is equal to ___________

(Important : you should answer only the numeric value)

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

Let X be a random variable having the distribution function

Then E(X) is equal to _________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 21

In an experiment, a fair die is rolled until two sixes are obtained in succession. The probability that
the experiment will end in the fifth trial is equal to

Solution:
QUESTION: 22

Let x1 = 2.2, x2 = 4.3, x3 = 3.1, x4 = 4.5, x5 = 1.1 and x6 = 5.7 be the observed values of a
random sample of size 6 from a U(θ - 1, θ + 4) distribution, where θ ∈ (0, ∞) is unknown. Then
a maximum likelihood estimate of θ is equal to

Solution:
QUESTION: 23

Let  be the open unit disc in  with boundary is the solution of the Dirichlet problem

then u(1/2,0) is equal to

Solution:
*Answer can only contain numeric values
QUESTION: 24

Let c ∈ Z3 be such that  is a field. Then c is equal to __________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 25

Let  Then V is

Solution:
*Answer can only contain numeric values
QUESTION: 26

Let  be defined by  is equal to __________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 27

Let 1be the usual topology on R. Let 2 be the topology on R generated by

Solution:
QUESTION: 28

Let X be a connected topological space such that there exists a non-constant continuous function
f : X → R, where R is equipped with the usual topology. Let f(X) = { f(x): x ∈ X}. Then

Solution:
QUESTION: 29

Let d1 and d2 denote the usual metric and the discrete metric on R, respectively. Let  be defined by f(x) = x, x ∈ R. Then

Solution:
*Answer can only contain numeric values
QUESTION: 30

If the trapezoidal rule with single interval [0, 1] is exact for approximating the integral

then the value of c is equal to ________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 31

Suppose that the Newton-Raphson method is applied to the equation with an
initial approximation xo sufficiently close to zero. Then, for the root x = 0, the order of convergence of the method is equal to _________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 32

The minimum possible order of a homogeneous linear ordinary differential equation with real constant coefficients having  xsin (x) as a solution is equal to  _______

(Important : you should answer only the numeric value)

Solution:
QUESTION: 33

The Lagrangian of a system in terms of polar coordinates (r,θ) is given by

where m is the mass, g is the acceleration due to gravity and denotes the derivative of s with
respect to time. Then the equations of motion are

Solution:
*Answer can only contain numeric values
QUESTION: 34

If y(x) satisfies the initial value problem

then y(2) is equal to __________

(Important : you should answer only the numeric value)

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

It is known that Bessel functions Jn(x). for n 0, satisfy the identity

for all t > 0 and  xR. The value of   is equal to _________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 36

Q. 36 – Q. 65 carry two marks each.

Q.

Let X and Y be two random variables having the joint probability density function

Then the conditional probability  is equal to

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

Let Ω = (0,1] be the sample space and let  be a probability function defined by

Then P({1/2})  is equal to __________

(Important : you should answer only the numeric value)

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

Let X1, X2 and X3 be independent and identically distributed random variables with E(X1) =0 and  is defined through the conditional expectation

then   is equal to __________

(Important : you should answer only the numeric value)

Solution:
*Answer can only contain numeric values
QUESTION: 39

Let X ∼ Poisson(λ), where λ> 0 is unknown. If δ(X) is the unbiased estimator of  is equal to ___________

(Important : you should answer only the numeric value)

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

Let X1,, … , Xn be a random sample from N(μ,1) distribution, where  For testing the null
hypothesis Ho :μ=0 against the alternative hypothesis consider the critical region

where c is some real constant. If the critical region R has size 0.025 and power 0.7054, then the
value of the sample size n is equal to ___________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 41

Let X and Y be independently distributed central chi-squared random variables with degrees of
freedom m(3) and n(3) respectively. If E(X/Y) =3 and m+n =14 then E(Y/X ) is equal to

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

Let X1, X2, … be a sequence of independent and identically distributed random variables with  for n= 1, 2,…,, then   is equal to __________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 43

Let  be a solution of the initial value problem

Then f(1) is equal to

Solution:
*Answer can only contain numeric values
QUESTION: 44

Let   be the solution of the initial value problem

Then u(2,2) is equal to ________

(Important : you should answer only the numeric value)

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

Let  be a subspace of the Euclidean space R4. Then the
square of the distance from the point (1,1,1,1) to the subspace W is equal to _______

(Important : you should answer only the numeric value)

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

Let T : R4 → Rbe a linear map such that the null space of T is

and the rank of (T-4I4) is 3. If the minimal polynomial of T is x(x-4)α. then α is equal to _______

(Important : you should answer only the numeric value)

Solution:
QUESTION: 47

Let M be an invertible Hermitian matrix and let x,y  R be such that x2 <4y. then

Solution:
QUESTION: 48

Let   Then the number
of elements in the center of the group G is equal to

Solution:
*Answer can only contain numeric values
QUESTION: 49

The number of ring homomorphisms from   is equal to __________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 50

Let  and   be two polynomials in
Q [x]. Then, over Q,

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

Consider the linear programming problem

Then the maximum value of the objective function is equal to ______

(Important : you should answer only the numeric value)

Solution:
QUESTION: 52

Let . Under the usual metric on R2,

Solution:
QUESTION: 53

Let . Then H

Solution:
QUESTION: 54

Let V be a closed subspace of   be given by f(x) =x and g(x) = x2. if     and pg is the orthogonal projection of g on V, then

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

Let p(x) be the polynomial of degree at most 3 that passes through the points (-2,12), (-1,1), (0.2) and (2,-8).  Then the coefficient of x in p(x) is equal to _____________

(Important : you should answer only the numeric value)

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

If, for some α,β  R the integration formula

holds for all polynomials p(x) of degree at most 3, then the value of

3(α-β)is equal to _____.

(Important : you should answer only the numeric value)

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

Let y(t) be a continuous function on (0, ∞) whose Laplace transform exists. If y(t) satisfies

then y(1) is equal to _______

(Important : you should answer only the numeric value)

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

Consider the initial value problem

if y(x) → 0 as x→ 0+, then α is equal to ______________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 59

Define  by

Then

Solution:
*Answer can only contain numeric values
QUESTION: 60

Consider the unit sphere   and the unit normal vector

at each point (x,y,z) on S. The value of the surface integral

is equal to _______

(Important : you should answer only the numeric value)

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

Let

Define Then the minimum value of f on D is equal to ________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 62

Let    Then there exists a non-constant analytic function f on D such that for all n = 2, 3, 4, …

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

Let   be the Laurent series expansion of  in the annulus 3/2 <|z| <5 . Then a1/a2  is equal to _________

(Important : you should answer only the numeric value)

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

The value of  is equal to __________

(Important : you should answer only the numeric value)

Solution:
QUESTION: 65

Suppose that among all continuously differentiable functions y(x), x R with y(0) =0 and y(1) = 1/2, the function y0(x)  minimizes the functional

then yo (1/2) is equal to

Solution: