GATE MA area:engineering-mathematics PYQs & Answers — Page 24

Home
GATE
Mathematics
Topics
area:engineering-mathematics

Questions 231–240 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 24 of 41

Let

be a complex Hilbert space. Let

be such that

. Then

__________.

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 integers. Consider the subring

of the field

of complex numbers. Consider the following statements: P:

is an irreducible element. Q:

is a prime element. 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

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

Consider the second-order partial differential equation (PDE)

Consider the following statements: P: The PDE is parabolic on the ellipse

. Q: The PDE is hyperbolic inside the ellipse

. 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

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

is the solution for the Cauchy problem

then

is equal to

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

Let

be the Hilbert space of real valued square integrable functions on

equipped with the norm

. Consider the subspace

. For

, define

. Then

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

Let

be the Banach space of real valued continuous functions on

equipped with the supremum norm. Define

Let

denote the range space of

. Consider the following statements: P:

is a bounded linear operator. Q:

exists and is bounded. 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

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

Let

be the sequence space equipped with the norm

. Consider the subspace

and the linear transformation

given by

for

. Then

Your answerChoose one option.

is closed but NOT bounded

is bounded

is neither closed nor bounded

exists and is an open map

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

Let

be given by

for

. Consider the following statements: P:

is equicontinuous on

. Q:

does NOT converge uniformly on

. 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

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

Let

be given by

Consider the following statements: P:

is continuous at

but

is NOT differentiable at

. Q: The directional derivative

exists in the direction of every unit vector

. 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

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

Let

be the solid region in

bounded by the paraboloid

and the plane

. Then the value of

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

GATE MA area:engineering-mathematics PYQs

Question 25

Question 26

Question 27

Question 28

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38