GATE MA area:engineering-mathematics PYQs & Answers — Page 13

Home
GATE
Mathematics
Topics
area:engineering-mathematics

Questions 121–130 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 13 of 41

Let

be a function such that

Which of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

is continuous at

, but not differentiable at

is differentiable at

All the directional derivatives of

exist and they are equal to zero

Both the partial derivatives of

exist and they are equal to zero

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

For an integer

, let

, where

. Let

. Consider the metric space

, where

Which of the following statement(s) is/are true?

Your answerSelect all correct options. You can choose more than one.

is an equi-continuous family of continuous functions

is closed in

is bounded in

is compact in

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

Let

be an

-linear transformation such that 1 and 2 are the only eigenvalues of

. Suppose the dimensions of

and

are 1 and 2, respectively. Which of the following is/are possible (upper triangular) Jordan canonical form(s) of

Your answerSelect all correct options. You can choose more than one.

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

Let

denote the space of all real-valued Lebesgue square-integrable functions on

, with the usual norm

. Let

be the subspace of

consisting of all the polynomials of degree at most 1. Let

be such that

, and

. Then

(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

Let

be the field extension of

obtained by adding all the roots of the polynomial equation

. The number of distinct fields

such that

is equal to

(answer in integer)

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

Let

be the subset of

consisting of all

such that

for all

. The number of elements in

is equal to

(answer in integer)

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

Let

be a continuously differentiable path from

and let

be defined by

. The line integral of

along

is equal to

(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

Let

be the solution of the initial value problem

, then

is equal to

(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

The global maximum of

is equal to

(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

Let

and

. Let

be the solution of the following boundary value problem

, then the value of

is equal to

(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

GATE MA area:engineering-mathematics PYQs

Question 54

Question 55

Question 56

Question 57

Question 59

Question 60

Question 61

Question 62

Question 64

Question 65