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MA Mathematics - 2015 GATE Paper (Practice Test)


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

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MA Mathematics - 2015 GATE Paper (Practice Test) - Question 1

Q 1- 5 Carry one mark each.

Q.

Choose the appropriate word/ pharase , out of the four options given below, to complete the following sentence:

apparent lifelessness ___________________ dormant life.

MA Mathematics - 2015 GATE Paper (Practice Test) - Question 2

Fill in te blank with the correct idiom/ pharase.

That boy from the worn was a ___________________ in the sleepy village.

MA Mathematics - 2015 GATE Paper (Practice Test) - Question 3

Choose the statement where underlined word is used correctly.

MA Mathematics - 2015 GATE Paper (Practice Test) - 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 :

MA Mathematics - 2015 GATE Paper (Practice Test) - 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?

MA Mathematics - 2015 GATE Paper (Practice Test) - 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.

MA Mathematics - 2015 GATE Paper (Practice Test) - 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.

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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 ?

MA Mathematics - 2015 GATE Paper (Practice Test) - 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?

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 15

Let be defined by 

         Then the function f is

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 16

Consider the power series 

The radius of convergence of the series is equal to __________

 

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 17

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

 

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 18

Let   is equal to ___________

 

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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

MA Mathematics - 2015 GATE Paper (Practice Test) - 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

MA Mathematics - 2015 GATE Paper (Practice Test) - 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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 24

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

(Important : you should answer only the numeric value)
 


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 25

Let  Then V is

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 26

Let  be defined by  is equal to __________

 

(Important : you should answer only the numeric value)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 27

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

MA Mathematics - 2015 GATE Paper (Practice Test) - 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

MA Mathematics - 2015 GATE Paper (Practice Test) - 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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 34

If y(x) satisfies the initial value problem 

then y(2) is equal to __________

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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 

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 43

Let  be a solution of the initial value problem

Then f(1) is equal to

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 47

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

MA Mathematics - 2015 GATE Paper (Practice Test) - Question 48

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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 49

The number of ring homomorphisms from   is equal to __________

 

(Important : you should answer only the numeric value)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 50

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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 52

Let . Under the usual metric on R2,

MA Mathematics - 2015 GATE Paper (Practice Test) - Question 53

Let . Then H

MA Mathematics - 2015 GATE Paper (Practice Test) - 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  

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 59

Define  by

Then

 

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 61

Let   

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

(Important : you should answer only the numeric value)


MA Mathematics - 2015 GATE Paper (Practice Test) - Question 62

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

*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - 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)


*Answer can only contain numeric values
MA Mathematics - 2015 GATE Paper (Practice Test) - Question 64

The value of  is equal to __________

 

(Important : you should answer only the numeric value)


MA Mathematics - 2015 GATE Paper (Practice Test) - 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 

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