GATE MA year:2021 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 2 of 7

Let

be a

matrix and

be a

matrix with real entries such that

is non-singular. Consider the following statements:

P: Nullity of

is 0.

is a non-singular matrix.

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

for

, where

and

are real numbers, be a non-constant analytic function on the complex plane

. Let

and

denote the first order partial derivatives of

and

with respect to real variables

and

, respectively. Consider the following two functions defined on

Then

Your answerChoose one option.

both

and

are analytic in

is analytic in

and

is NOT analytic in

and

is analytic in

neither

nor

is analytic in

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Let

, be the Möbius transformation which maps the points

in the

-plane onto the points

in the

-plane, respectively. Then the image of the set

under the map

Your answerChoose one option.

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Let

be the row reduced echelon form of a

real matrix

and let the third column of

. Consider the following statements:

P: If

is a solution of

, then

Q: For all

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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The eigenvalues of the boundary value problem

are given by

Your answerChoose one option.

, where

are the roots of

, where

are the roots of

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The family of surfaces given by

, where

is a differentiable function, satisfies

Your answerChoose one option.

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The function

satisfies the initial value problem

Then

Your answerChoose one option.

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Consider the fixed-point iteration

with

and the initial approximation

Then, the order of convergence of the fixed-point iteration method is

Your answerChoose one option.

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Let

be an orthonormal basis of a complex Hilbert space

. Consider the following statements:

P: There exists a bounded linear functional

such that

for

Q: There exists a bounded linear functional

such that

for

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be given by

. Consider the following statements:

for all

has a fixed point.

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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GATE MA year:2021 PYQs

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10