GATE MA topic:real-analysis PYQs & Answers

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topic:real-analysis

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Questions 1–10 of 43. Imported answers require independent review unless marked reviewed.

Topic practice 43 questionsPage 1 of 5

Let

denote the Cantor set and

be defined as follows:

The value of the Lebesgue integral of

over the interval

is equal to

Your answerChoose one option.

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Let

be a set with at least two elements. Let

and

be metrics on

. Which one of the following is NOT a metric on

Your answerChoose one option.

for all

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Let

. The value of

is equal to ________. (answer in integer)

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Consider the function

given by

Then, for the function

, the inverse function theorem is

Your answerChoose one option.

applicable at all points of

not applicable at exactly one point of

not applicable at exactly two points of

not applicable at exactly three points of

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Let the functions

and

be given by

Consider the following statements:

S1: For every compact subset

is compact.

S2: For every compact subset

is compact.

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Consider the function

given by

Then, which of the following is/are TRUE?

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

is open in

, then

is open in

is closed in

, then

is closed in

is dense in

, then

is dense in

is surjective

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Consider the sequence

of continuous functions on

defined by

Then, which of the following is/are TRUE?

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

The sequence

converges pointwise but not uniformly on

The sequence

converges uniformly on

for all

and

for all

and

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For

, let

. Then, which of the following is/are TRUE?

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

converges uniformly on

converges pointwise but not uniformly on

converges uniformly on every compact subset of

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Consider the following limit

Which one of the following is correct?

Your answerChoose one option.

The limit does not exist

The limit exists and is equal to 0

The limit exists and is equal to 3

The limit exists and is equal to

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Let

be a function. Which one of the following is a sufficient condition for

to be Lebesgue measurable?

Your answerChoose one option.

is a Lebesgue measurable function

There exist continuous functions

such that

is continuous almost everywhere on

For each

, the set

is Lebesgue measurable

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GATE MA topic:real-analysis PYQs

How to practice topic:real-analysis

Question 13

Question 20

Question 31

Question 21

Question 22

Question 53

Question 55

Question 56

Question 14

Question 38