GATE MA topic:mathematics PYQs & Answers — Page 15

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Questions 141–150 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 15 of 65

Consider the following condition on a function

for all

such that

. (P)

Which one of the following is correct?

Your answerChoose one option.

There is a non-constant analytic polynomial

satisfying (P)

Every entire function

satisfying (P) is a constant function

Every entire function

satisfying (P) has no zeroes in

There is an entire function

satisfying (P) with infinitely many zeroes in

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Let

be the ellipse

traversed counter-clockwise. The value of the contour integral

is equal to

Your answerChoose one option.

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Let

be a topological space and

. Given a subset

, let

, and

denote the interior, boundary, and closure, respectively, of the set

. Which one of the following is NOT necessarily true?

Your answerChoose one option.

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Consider the following limit

Which one of the following is correct?

Your answerChoose one option.

The limit does not exist

The limit exists and is equal to 0

The limit exists and is equal to 3

The limit exists and is equal to

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Let

be the subring of

generated by

and

. Consider the following statements.

I. The ring

is a unique factorization domain.

II. The ring

is a principal ideal domain.

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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Given a prime number

, let

denote the number of

–Sylow subgroups of a finite group

. Which one of the following is TRUE for every group

of order 2024?

Your answerChoose one option.

and

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Consider the following statements.

I. Every compact Hausdorff space is normal.

II. Every metric space is normal.

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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Consider the topology on

with basis

, where

Consider the following statements.

is both open and closed for each

with

II. The only connected set containing

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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Let

and

be the linear transformation given by

. The characteristic polynomial of

Your answerChoose one option.

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Let

be a normal matrix. Consider the following statements.

I. If all the eigenvalues of

are real, then

is Hermitian.

II. If all the eigenvalues of

have absolute value 1, then

is unitary.

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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GATE MA topic:mathematics PYQs

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