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Mathematics

GATE MA topic:real-analysis PYQs

Build your understanding with focused practice from past exam papers.

Questions 41–43 of 43. Imported answers require independent review unless marked reviewed.

Topic practice 43 questionsPage 5 of 5

Question 7

Open question
MAMCQ1 markNeeds review
Consider the following statements: (P): There exists an unbounded subset of

whose Lebesgue measure is equal to 5. (Q): If

is continuous and

is such that

almost everywhere on

, then

must be continuous almost everywhere on

.
Which of the above statements hold TRUE?
Your answerChoose one option.

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Question 31

Open question
MAMCQ2 marksNeeds review
Let

and

be two sequences in a complete metric space

such that

and

for all

. Then
Your answerChoose one option.

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Question 32

Open question
MANAT2 marksNeeds review
Let

be given by

if

is rational, and if

is irrational then

, where

is the number of zeroes immediately after the decimal point in the decimal representation of

. Then the Lebesgue integral

equals ________.

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