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Previous year question hub

Definite Integration - Calculus - Mathematics Previous Year Questions

Practice Definite Integration - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

53Papers
41Years
88Questions
1Topics

Definite Integration question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Definite Integration. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 49 55.7%
Easy 20 22.7%
Hard 16 18.2%
Not classified 3 3.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 57 64.8%
Numerical Answer Type (NAT) 18 20.5%
Subjective 13 14.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
88 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
88 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Definite Integration
88 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
6 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
4 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
4 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
3 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
3 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
2 Qs
IIT JEE 2008 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
2 Qs
IIT JEE 2004
1 Qs
IIT JEE 2003 SCREENING
2 Qs
IIT JEE 2003
1 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2001 SCREENING
1 Qs
IIT JEE 2000 SCREENING
3 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
3 Qs
IIT JEE 1997
3 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995 SCREENING
2 Qs
IIT JEE 1995
1 Qs
IIT JEE 1993
1 Qs
IIT JEE 1992
1 Qs
IIT JEE 1990
3 Qs
IIT JEE 1989
2 Qs
IIT JEE 1988
1 Qs
IIT JEE 1985
1 Qs
IIT JEE 1984
1 Qs
IIT JEE 1983
1 Qs
IIT JEE 1982
1 Qs
IIT JEE 1981
3 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20216View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20201View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20202View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20171View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20162View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20154View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20143View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20144View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2012 PAPER 2 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2010 PAPER 1 OFFLINE20103View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 2 OFFLINE20092View paper
IIT JEE 2008 PAPER 1 OFFLINE20081View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420041View paper
IIT JEE 2004 SCREENING20042View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20032View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 2001 SCREENING20011View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20003View paper
IIT JEE 199919992View paper
IIT JEE 199819983View paper
IIT JEE 199719973View paper
IIT JEE 199619961View paper
IIT JEE 199519951View paper
IIT JEE 1995 SCREENING19952View paper
IIT JEE 199319931View paper
IIT JEE 199219921View paper
IIT JEE 199019903View paper
IIT JEE 198919892View paper
IIT JEE 198819881View paper
IIT JEE 198519851View paper
IIT JEE 198419841View paper
IIT JEE 198319831View paper
IIT JEE 198219821View paper
IIT JEE 198119813View paper

All Definite Integration previous year questions

Practice every matching question in batches of 20, with every available option.

1
1981 · Mathematics · Calculus · Definite Integration
IIT JEE 1981
Show that : \(\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n}}} \right) = \log 6\)
Write your response
Open complete paper
2
1981 · Mathematics · Calculus · Definite Integration
IIT JEE 1981
Let \(a, b, c\) be non-zero real numbers such that
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx = \int\limits_0^2 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx.} }$$
Then the quadratic equation \(a{x^2} + bx + c = 0\) has
A
no root in \((0, 2)\)
B
at least one root in \((0, 2)\)
C
a double root in \((0, 2)\)
D
two imaginary roots
Open complete paper
3
1981 · Mathematics · Calculus · Definite Integration
IIT JEE 1981
The value of the definite integral \(\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx\)
A
\(-1\)
B
\(2\)
C
\(1 + {e^{ - 1}}\)
D
none of these
Open complete paper
4
1982 · Mathematics · Calculus · Definite Integration
IIT JEE 1982
Show that \(\int\limits_0^\pi {xf\left( {\sin x} \right)dx} = {\pi \over 2}\int\limits_0^\pi {f\left( {\sin x} \right)dx.}\)
Write your response
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5
1983 · Mathematics · Calculus · Definite Integration
IIT JEE 1983
The value of the integral \(\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx}\) is
A
\(\pi /4\)
B
\(\pi /2\)
C
\(\pi\)
D
none of these
Open complete paper
6
1984 · Mathematics · Calculus · Definite Integration
IIT JEE 1984
Given a function \(f(x)\) such that
(i) it is integrable over every interval on the real line and
(ii) \(f(t+x)=f(x),\) for every \(x\) and a real \(t\), then show that
the integral \(\int\limits_a^{a + 1} {f\,\,\left( x \right)} \,dx\) is independent of a.
Write your response
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7
1985 · Mathematics · Calculus · Definite Integration
IIT JEE 1985
For any integer \(n\) the integral ...........
\(\int\limits_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^3}\left( {2n + 1} \right)xdx}\) has the value
A
\(\pi\)
B
\(1\)
C
\(0\)
D
none of these
Open complete paper
8
1988 · Mathematics · Calculus · Definite Integration
IIT JEE 1988
The value of the integral \(\int\limits_0^{2a} {[{{f\left( x \right)} \over {\left\{ {f\left( x \right) + f\left( {2a - x} \right)} \right\}}}]\,dx}\) is equal to \(a\).
A
TRUE
B
FALSE
Open complete paper
9
1989 · Mathematics · Calculus · Definite Integration
IIT JEE 1989
If \(f\) and \(g\) are continuous function on \(\left[ {0,a} \right]\) satisfying
\(f\left( x \right) = f\left( {a - x} \right)\) and \(g\left( x \right) + g\left( {a - x} \right) = 2,\)
then show that \(\int\limits_0^a {f\left( x \right)g\left( x \right)dx = \int\limits_0^a {f\left( x \right)dx} }\)
Write your response
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10
1989 · Mathematics · Calculus · Definite Integration
IIT JEE 1989
The value of \(\int\limits_{ - 2}^2 {\left| {1 - {x^2}} \right|dx}\) is ...............
Write your response
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11
1990 · Mathematics · Calculus · Definite Integration
IIT JEE 1990
Show that \(\int\limits_0^{\pi /2} {f\left( {\sin 2x} \right)\sin x\,dx = \sqrt 2 } \int\limits_0^{\pi /4} {f\left( {\cos 2x} \right)\cos x\,dx}\)
Write your response
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12
1990 · Mathematics · Calculus · Definite Integration
IIT JEE 1990
Prove that for any positive integer \(k\),
$${{\sin 2kx} \over {\sin x}} = 2\left[ {\cos x + \cos 3x + ......... + \cos \left( {2k - 1} \right)x} \right]$$
Hence prove that \(\int\limits_0^{\pi /2} {\sin 2kx\,\cot \,x\,dx = {\pi \over 2}}\)
Write your response
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13
1990 · Mathematics · Calculus · Definite Integration
IIT JEE 1990
Let \(f:R \to R\) and \(\,\,g:R \to R\) be continuous functions. Then the value of the integral
\(\int\limits_{ - \pi /2}^{\pi /2} {\left[ {f\left( x \right) + f\left( { - x} \right)} \right]\left[ {g\left( x \right) - g\left( { - x} \right)} \right]dx}\) is
A
\(\pi\)
B
\(1\)
C
\(-1\)
D
\(0\)
Open complete paper
14
1992 · Mathematics · Calculus · Definite Integration
IIT JEE 1992
Determine a positive integer \(n \le 5,\) such that \(\int\limits_0^1 {{e^x}{{\left( {x - 1} \right)}^n}dx = 16 - 6e}\)
Write your response
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15
1993 · Mathematics · Calculus · Definite Integration
IIT JEE 1993
The value of \(\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}}\) is
A
\(0\)
B
\(1\)
C
\(\pi /2\)
D
\(\pi /4\)
Open complete paper
16
1995 · Mathematics · Calculus · Definite Integration
IIT JEE 1995
Let \({I_m} = \int\limits_0^\pi {{{1 - \cos mx} \over {1 - \cos x}}} dx.\) Use mathematical induction to prove that \({I_m} = m\,\pi ,m = 0,1,2,........\)
Write your response
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17
1995 · Mathematics · Calculus · Definite Integration
IIT JEE 1995 SCREENING
If \(f\left( x \right)\,\,\, = \,\,\,A\sin \left( {{{\pi x} \over 2}} \right)\,\,\, + \,\,\,B,\,\,\,f'\left( {{1 \over 2}} \right) = \sqrt 2\) and
\(\int\limits_0^1 {f\left( x \right)dx = {{2A} \over \pi },}\) then constants \(A\) and \(B\) are
A
\({\pi \over 2}\) and \({\pi \over 2}\)
B
\({2 \over \pi }\) and \({3 \over \pi }\)
C
\(0\) and \({-4 \over \pi }\)
D
\({4 \over \pi }\) and \(0\)
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18
1995 · Mathematics · Calculus · Definite Integration
IIT JEE 1995 SCREENING
The value of \(\int\limits_\pi ^{2\pi } {\left[ {2\,\sin x} \right]\,dx}\) where [ . ] represents the greatest integer function is
A
\({{ - 5\pi } \over 3}\)
B
\(\pi\)
C
\({{ 5\pi } \over 3}\)
D
\(- 2\pi\)
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19
1996 · Mathematics · Calculus · Definite Integration
IIT JEE 1996
For \(n>0,\) \(\int_0^{2\pi } {{{x{{\sin }^{2n}}x} \over {{{\sin }^{2n}}x + {{\cos }^{2n}}x}}} dx =\)
Write your response
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20
1997 · Mathematics · Calculus · Definite Integration
IIT JEE 1997
Determine the value of \(\int_\pi ^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} \,dx.\)
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Showing 20 of 88 questions