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Previous year question hub

Calculus - Mathematics Previous Year Questions

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

72Papers
46Years
387Questions
1Topics

Calculus question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 216 55.8%
Hard 85 22%
Easy 57 14.7%
Not classified 29 7.5%

Question type distribution

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

Multiple Choices 274 70.8%
Numerical Answer Type (NAT) 61 15.8%
Subjective 52 13.4%

Subject weightage

Top subjects by unique question coverage.

Mathematics
387 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
387 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Derivatives
99 Qs
Definite Integration
88 Qs
Limits Continuity And Differentiability
54 Qs
Application Of Integration
43 Qs
Differential Equations
35 Qs
Functions
31 Qs
Differentiation
30 Qs
Indefinite Integrals
7 Qs

Paper coverage

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

JEE ADVANCED 2025 PAPER 1 ONLINE
6 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
6 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
8 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
5 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
5 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
5 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
3 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
9 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
7 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
7 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
5 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
4 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
6 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
5 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
9 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
6 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
6 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
8 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
7 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
8 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
7 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
4 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
4 Qs
IIT JEE 2012 PAPER 1 OFFLINE
8 Qs
IIT JEE 2012 PAPER 2 OFFLINE
6 Qs
IIT JEE 2011 PAPER 2 OFFLINE
7 Qs
IIT JEE 2011 PAPER 1 OFFLINE
5 Qs
IIT JEE 2010 PAPER 1 OFFLINE
6 Qs
IIT JEE 2010 PAPER 2 OFFLINE
6 Qs
IIT JEE 2009 PAPER 2 OFFLINE
6 Qs
IIT JEE 2009 PAPER 1 OFFLINE
3 Qs
IIT JEE 2008 PAPER 2 OFFLINE
8 Qs
IIT JEE 2008 PAPER 1 OFFLINE
7 Qs
IIT JEE 2007 PAPER 2 OFFLINE
7 Qs
IIT JEE 2007 PAPER 1 OFFLINE
2 Qs
IIT JEE 2006
14 Qs
IIT JEE 2005 SCREENING
9 Qs
IIT JEE 2005 MAINS
6 Qs
IIT JEE 2005
2 Qs
IIT JEE 2004 SCREENING
7 Qs
IIT JEE 2004
3 Qs
IIT JEE 2003 SCREENING
6 Qs
IIT JEE 2003
5 Qs
IIT JEE 2002 SCREENING
6 Qs
IIT JEE 2001 SCREENING
5 Qs
IIT JEE 2001
1 Qs
IIT JEE 2000 SCREENING
9 Qs
IIT JEE 2000
3 Qs
IIT JEE 1999
7 Qs
IIT JEE 1998
9 Qs
IIT JEE 1997
7 Qs
IIT JEE 1996
3 Qs
IIT JEE 1995 SCREENING
6 Qs
IIT JEE 1995
2 Qs
IIT JEE 1994
6 Qs
IIT JEE 1993
3 Qs
IIT JEE 1992
2 Qs
IIT JEE 1991
2 Qs
IIT JEE 1990
6 Qs
IIT JEE 1989
3 Qs
IIT JEE 1988
2 Qs
IIT JEE 1987
4 Qs
IIT JEE 1986
3 Qs
IIT JEE 1985
3 Qs
IIT JEE 1984
3 Qs
IIT JEE 1983
10 Qs
IIT JEE 1982
6 Qs
IIT JEE 1981
6 Qs
IIT JEE 1979
1 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Application Of Derivatives

Explore previous-paper coverage, trends and focused practice for Application Of Derivatives.

123 questions59 papers44 years

Definite Integration

Explore previous-paper coverage, trends and focused practice for Definite Integration.

112 questions61 papers46 years

Limits Continuity And Differentiability

Explore previous-paper coverage, trends and focused practice for Limits Continuity And Differentiability.

63 questions37 papers21 years

Differential Equations

Explore previous-paper coverage, trends and focused practice for Differential Equations.

45 questions35 papers29 years

Functions

Explore previous-paper coverage, trends and focused practice for Functions.

33 questions21 papers16 years

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 1 ONLINE20256View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20256View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20242View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20248View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20235View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20235View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20223View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20225View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20212View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20219View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20207View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20207View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20194View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20195View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20186View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20185View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20172View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20179View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20166View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20166View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20157View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20158View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20148View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20147View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20134View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20134View paper
IIT JEE 2012 PAPER 1 OFFLINE20128View paper
IIT JEE 2012 PAPER 2 OFFLINE20126View paper
IIT JEE 2011 PAPER 1 OFFLINE20115View paper
IIT JEE 2011 PAPER 2 OFFLINE20117View paper
IIT JEE 2010 PAPER 1 OFFLINE20106View paper
IIT JEE 2010 PAPER 2 OFFLINE20106View paper
IIT JEE 2009 PAPER 1 OFFLINE20093View paper
IIT JEE 2009 PAPER 2 OFFLINE20096View paper
IIT JEE 2008 PAPER 1 OFFLINE20087View paper
IIT JEE 2008 PAPER 2 OFFLINE20088View paper
IIT JEE 2007 PAPER 1 OFFLINE20072View paper
IIT JEE 2007 PAPER 2 OFFLINE20077View paper
IIT JEE 2006200614View paper
IIT JEE 200520052View paper
IIT JEE 2005 MAINS20056View paper
IIT JEE 2005 SCREENING20059View paper
IIT JEE 200420043View paper
IIT JEE 2004 SCREENING20047View paper
IIT JEE 200320035View paper
IIT JEE 2003 SCREENING20036View paper
IIT JEE 2002 SCREENING20026View paper
IIT JEE 200120011View paper
IIT JEE 2001 SCREENING20015View paper
IIT JEE 200020003View paper
IIT JEE 2000 SCREENING20009View paper
IIT JEE 199919997View paper
IIT JEE 199819989View paper
IIT JEE 199719977View paper
IIT JEE 199619963View paper
IIT JEE 199519952View paper
IIT JEE 1995 SCREENING19956View paper
IIT JEE 199419946View paper
IIT JEE 199319933View paper
IIT JEE 199219922View paper
IIT JEE 199119912View paper
IIT JEE 199019906View paper
IIT JEE 198919893View paper
IIT JEE 198819882View paper
IIT JEE 198719874View paper
IIT JEE 198619863View paper
IIT JEE 198519853View paper
IIT JEE 198419843View paper
IIT JEE 1983198310View paper
IIT JEE 198219826View paper
IIT JEE 198119816View paper
IIT JEE 197919791View paper

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
1979 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1979
Prove that the minimum value of \({{\left( {a + x} \right)\left( {b + x} \right)} \over {\left( {c + x} \right)}},\)
\(a,b > c,x > - c\) is \({\left( {\sqrt {a - c} + \sqrt {b - c} } \right)^2}\).
Write your response
Open complete paper
2
1981 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1981
For all \(x\) in \(\left[ {0,1} \right]\), let the second derivative \(f''(x)\) of a function \(f(x)\) exist and satisfy \(\left| {f''\left( x \right)} \right| < 1.\) If \(f(0)=f(1)\), then show that \(\left| {f\left( x \right)} \right| < 1\) for all \(x\) in \(\left[ {0,1} \right]\).
Write your response
Open complete paper
3
1982 · Mathematics · Calculus · Differentiation
IIT JEE 1982
Let \(f\) be a twice differentiable function such that

\(f''\left( x \right) = - f\left( x \right),\) and \(f'\left( x \right) = g\left( x \right),h\left( x \right) = {\left[ {f\left( x \right)} \right]^2} + {\left[ {g\left( x \right)} \right]^2}\)

Find \(h\left( {10} \right)\) if \(h(5)=11\)

Write your response
Open complete paper
4
1983 · Mathematics · Calculus · Differentiation
IIT JEE 1983
The derivative of an even function is always an odd function.
A
TRUE
B
FALSE
Open complete paper
5
1984 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1984
For \(0 < a < x,\) the minimum value of the function \(lo{g_a}x + {\log _x}a\) is \(2\).
A
TRUE
B
FALSE
Open complete paper
6
1985 · Mathematics · Calculus · Differentiation
IIT JEE 1985
If \(f\left( x \right) = {\log _x}\left( {In\,x} \right),\) then \(f'\left( x \right)\) at \(x=e\) is ................
Write your response
Open complete paper