GATE MA year:2022 PYQs & Answers — Page 4

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

The maximum value of

on the line

is _____.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

If the function

attains its local minimum value at the point

, then the value of

is _____ (round off to TWO decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

If the ordinary differential equation

has a solution of the form

, where

’s are constants and

, then the value of

is _____.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The Bessel function

satisfy

. Then, the value of

is _____.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The partial differential equation

is transformed to

using

and

. Then, the value of

is _____.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

denote the ring of polynomials in

with real coefficients. Then, the quotient ring

Your answerChoose one option.

a field

an integral domain, but not a field

not an integral domain, but has 0 as the only nilpotent element

a ring which contains non-zero nilpotent elements

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the following conditions on two proper non-zero ideals

and

of a non-zero commutative ring

.\n\nP: For any

, there exists a unique

such that

and

.\n\nQ:

\n\nThen, which of the following statements is TRUE?

Your answerChoose one option.

P implies Q but Q does not imply P

Q implies P but P does not imply Q

P implies Q and Q implies P

P does not imply Q and Q does not imply P

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be a continuous function such that

for some

satisfying

. Define

, for

. Then, which of the following statements is TRUE?

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

P: Suppose that

converges at

and diverges at

. Then

converges.\n\nQ: The interval of convergence of the series

.\n\nWhich of the following statements is TRUE?

Your answerChoose one option.

P is true and Q is true

P is false and Q is false

P is true and Q is false

P is false and Q is true

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

. Then, which of the following statements is TRUE?

Your answerChoose one option.

is not equicontinuous on

is uniformly convergent on

is equicontinuous on

is uniformly bounded and has a subsequence converging uniformly on

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MA year:2022 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40