GATE MA discipline:mathematics-and-statistics PYQs & Answers — Page 44

Home
GATE
Mathematics
Topics
discipline:mathematics-and-statistics

Questions 431–440 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 44 of 65

Let

be defined by

, where

is the characteristic function of the interval

. For

, let

. Then

Your answerChoose one option.

is open

is not measurable

is closed

is measurable

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

For

, let

be functions defined by

and

. Then

Your answerChoose one option.

converges uniformly but

does not converge uniformly

converges uniformly but

does not converge uniformly

both

and

converge uniformly

neither

nor

converge uniformly

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

Let

be a solution of the differential equation

and let

be a solution of the differential equation

satisfying

and

. 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

For

, let

be a solution of the differential equation

satisfying

. For which of the following functions

, the integral

is equal to zero?

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

Suppose that

and

are metric spaces with metrics induced by the Euclidean metric of

. Let

and

be the open unit balls around

and

, respectively. Consider the following statements: I: The closure of

is compact. II: The closure of

is compact. Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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

is a function such that

and its restriction to the unit circle is continuous, then

Your answerChoose one option.

is continuous but not necessarily analytic

is analytic but not necessarily a constant function

is a constant function

exists

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

For a subset

of a topological space, let

and

denote the interior and closure of

, respectively. Then which of the following statements is TRUE?

Your answerChoose one option.

is open, then

If the boundary of

is empty, then

is open

If the boundary of

is empty, then

is not closed

is a proper subset of the boundary of

, then

is open

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

Suppose

and

are the smallest topologies on

containing

and

, respectively, where

. 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

. Consider the following statements: I: There exists a lower triangular matrix

such that

, where

denotes transpose of

. II: Gauss-Seidel method for

(

) converges for any initial choice

. Then

Your answerChoose one option.

I is not true when

II is not true when

I is true when

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

Let

and

be the ideals generated by

and

in the ring

, respectively. Then

Your answerChoose one option.

both

and

are maximal ideals

is a maximal ideal but

is not a prime ideal

is not a maximal ideal but

is a prime ideal

neither

nor

is a maximal ideal

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

GATE MA discipline:mathematics-and-statistics PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40