GATE MA format:mcq PYQs & Answers — Page 9

Questions 81–90 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 9 of 37

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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Let

and

be a

real column vector. Consider the statements.

I. The Jacobi iteration method for the system

converges for any initial approximation and

II. The Gauss–Seidel iteration method for the system

converges for any initial approximation and

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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For the initial value problem

generate approximations

, for a fixed

and

, using the recursion formula

Which one of the following choices of

for the above recursion formula gives the Runge–Kutta method of order 2?

Your answerChoose one option.

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Let

be the solution of

Define

, for

. Which one of the following is correct?

Your answerChoose one option.

is decreasing on

and

is decreasing on

and

is increasing on

and

does not exist

is increasing on

and

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and

are two different solutions of the ordinary differential equation

then which one of the following is its general solution on

Your answerChoose one option.

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GATE MA format:mcq PYQs

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