GATE MA topic:mathematical-sciences PYQs & Answers — Page 22

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Questions 211–220 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 22 of 65

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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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

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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.

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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

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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

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Consider the following Linear Programming Problem P:

The optimal value of the problem P is ____________.

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GATE MA topic:mathematical-sciences PYQs

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25