GATE MA format:mcq PYQs & Answers — Page 13

Questions 121–130 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 13 of 37

Consider

with the usual Euclidean metric. Let

and

Consider the following statements:

is a connected subset of

. Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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:

is diagonalizable.

is diagonalizable. Which of the following statements is correct?

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

Both

and

are FALSE

Both

and

are TRUE

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

Let

. Consider the metric space

, where

Let

for all

and

Let

be defined by

and

for all

. Consider the following statements:

is in the interior of

. Which of the following statements is correct?

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

Both

and

are FALSE

Both

and

are TRUE

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

Consider the metrics

and

, defined by

Let

and

. Define

Consider the following statements:

: The function

is uniformly continuous.

: The function

is uniformly continuous.

Then

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

both

and

are FALSE

both

and

are TRUE

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

Let

be a linear transformation and the null space of

be the subspace of

given by

, where

is the identity map on

, then the minimal polynomial of

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

denote the set of all real valued continuous functions defined on

and

for all

. Let

Define

for all

. Denote

. Then the set

has

Your answerChoose one option.

NO element

exactly one element

exactly two elements

an infinite number of elements

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

Let

and

be two topological spaces. A continuous map

is said to be proper if

is compact in

for every compact subset

, where

is defined by

. Consider

with the usual topology. If

has the subspace topology induced from

and

has the product topology, then which of the following maps is proper?

Your answerChoose one option.

defined by

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

Let

denote the group of

invertible complex matrices with usual matrix multiplication. For

denotes the subgroup generated by

and

. Let

and

be three subgroups of

given by

Let

denote the center of

for

. Which of the following statements is correct?

Your answerChoose one option.

is isomorphic to

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

Let

. For a sequence

, define

. Let

and

be defined by

Then

Your answerChoose one option.

is a compact linear map and

is NOT a compact linear map

is NOT a compact linear map and

is a compact linear map

both

and

are compact linear maps

NEITHER

NOR

is a compact linear map

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

Let

. For

, let

. Define

for all

. Then

Your answerChoose one option.

is continuous but

is NOT continuous

is NOT continuous but

is continuous

both

and

are continuous

NEITHER

NOR

is continuous

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

GATE MA format:mcq PYQs

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 36

Question 37

Question 38