GATE MA exam:gate PYQs & Answers — Page 62

Questions 611–620 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 62 of 65

and

are the null spaces of

and

, respectively, then the dimension of the subspace

equals ________.

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

Given two

matrices

and

with entries in

, consider the following statements: (P): If

and

have the same minimal polynomial, then

is similar to

. (Q): If

has

distinct eigenvalues, then there exists

such that

are linearly independent. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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

Let

be a

matrix such that

for

and

, where

. Let

and

be the largest and the smallest eigenvalues of

, respectively. If

, then

equals ________.

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

Let

be the simple, positively oriented circle of radius 2 centered at the origin in the complex plane. Then

equals ________.

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

Let

and

, respectively, denote the real part and the imaginary part of a complex number

. Let

be the bilinear transformation such that

and

. Then, the image of

under the mapping

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

and

be two sequences in a complete metric space

such that

and

for all

. Then

Your answerChoose one option.

both

and

converge

converges but

need NOT converge

converges but

need NOT converge

neither

nor

converges

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

is rational, and if

is irrational then

, where

is the number of zeroes immediately after the decimal point in the decimal representation of

. Then the Lebesgue integral

equals ________.

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

Let

be defined by

Then, at

Your answerChoose one option.

is continuous and the directional derivative of

does NOT exist in some direction

is NOT continuous and the directional derivatives of

exist in all directions

is NOT differentiable and the directional derivatives of

exist in all directions

is differentiable

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

Let

be the region in

bounded by the parabola

and the line

. Then

equals ________.

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

Let

and

for

. Consider the following statements: (P):

and

are linearly independent solutions of

. (Q): The Wronskian

for all

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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

GATE MA exam:gate PYQs

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35