GATE MA year:2023 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 2 of 7

Let

be defined by

and

for all

. Consider the following statements: P:

has a saddle point at

. Q:

has a saddle point at

. Then

Your answerChoose one option.

both P and Q are TRUE

P is FALSE but Q is TRUE

P is TRUE but Q is FALSE

both P and Q are FALSE

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Let

be a topological space with the usual topology and

denote the set of rational numbers. Define the subspaces

and

as follows:

;

. Which of the following statements is correct?

Your answerChoose one option.

is homeomorphic to

is NOT homeomorphic to

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Let

. Then

is equal to

Your answerChoose one option.

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Let

be a linear transformation satisfying

and

. Then

Your answerChoose one option.

is one-one but

is NOT onto

is one-one and onto

is NEITHER one-one NOR onto

is NOT one-one but

is onto

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Let

and

be defined by

Consider the following statements:

has three zeros (counting multiplicity) in

has one zero in

. Then

Your answerChoose one option.

is TRUE but

is FALSE

is FALSE but

is TRUE

both

and

are TRUE

both

and

are FALSE

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Let

be a non-measurable set with respect to the Lebesgue measure on

. Consider the following statements:

: If

, then

is Lebesgue measurable.

: The boundary of

has positive Lebesgue outer measure. Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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For

, let

be a measurable subset of

with Lebesgue measure

. Define

Consider the following statements:

: Lebesgue measure of

is equal to zero.

: Lebesgue measure of

is equal to zero. Then

Your answerChoose one option.

both

and

are TRUE

both

and

are FALSE

is TRUE but

is FALSE

is TRUE but

is FALSE

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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

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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

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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

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GATE MA year:2023 PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20