Mathematics
GATE MA concept:lebesgue-integral PYQs
Build your understanding with focused practice from past exam papers.
How to practice concept:lebesgue-integral
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–3 of 3. Imported answers require independent review unless marked reviewed.
Question 13
Open questionMAMCQ1 markNeeds review
Let
denote the Cantor set and
be defined as follows:
The value of the Lebesgue integral of
over the interval
is equal toYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 54
Open questionMANAT2 marksNeeds review
For each
, consider the decimal representation
. Define
by
if
is rational and
if
is irrational, where
is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of
. Then the Lebesgue integral
__________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 32
Open questionMANAT2 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 ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer