GATE MA format:msq PYQs & Answers — Page 6

Questions 51–60 of 62. Imported answers require independent review unless marked reviewed.

Topic practice 62 questionsPage 6 of 7

Let

be defined by

Then

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

the directional derivative of

in the direction of

the directional derivative of

in the direction of

the directional derivative of

in the direction of

is NOT differentiable at

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

Let

and

For each

, define

for all

Let

Which of the following statements is/are correct?

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

is totally bounded in

is bounded in

is closed in

is open 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 abelian group and

be a surjective group homomorphism. Let

for some

. Consider the following statements:

: For every

, there exists an

such that

: Let

be the identity of

and

be the subgroup generated by

. Then

and

Which of the following statements is/are correct?

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

is TRUE

is FALSE

is TRUE

is FALSE

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

Consider the linear system of equations

with

Which of the following statements are TRUE?

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

The Jacobi iterative matrix is

The Jacobi iterative method converges for any initial vector

The Gauss-Seidel iterative method converges for any initial vector

The spectral radius of the Jacobi iterative matrix is less than 1

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

Let

denote the subset of

consisting of elements algebraic over

. Then, which of the following statements are TRUE?

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

No element of

is algebraic over

is an algebraically closed field

For any bijective ring homomorphism

, we have

There is no bijection between

and

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

Let

be a Möbius transformation such that

and

, where

. Let

denote the straight line passing through the origin with slope

, and let

denote the circle of unit radius centred at the origin. Then, which of the following statements are TRUE?

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

maps

to a straight line

maps

to a circle

maps

to a straight line

maps

to a circle

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

Let

. Define

, almost everywhere, for

. Then, which of the following statements are TRUE?

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

is a linear isometry

is a bijection

is bounded from below

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

Let

be an orthonormal set in

such that

, where

is a constant and

is the Legendre polynomial of degree

, for each

. Then, which of the following statements are TRUE?

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

, where

is the smallest topology on

in which all the singleton sets are closed. Then, which of the following statements are TRUE?

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

is compact in

is not first countable

is second countable

is first countable

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

Consider

, where

is the topology generated by sets of the form

, for

and

. Then, which of the following statements are TRUE?

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

is connected

Each

is a closed subset of

is Hausdorff

is metrizable

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

GATE MA format:msq PYQs

Question 52

Question 53

Question 54

Question 25

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54