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Previous year question hub

Differentiation - Calculus - Mathematics Previous Year Questions

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

31Papers
28Years
36Questions
1Topics

Differentiation question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 20 55.6%
Easy 7 19.4%
Hard 7 19.4%
Not classified 2 5.6%

Question type distribution

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

MCQ 19 52.8%
Subjective 11 30.6%
MSQ 4 11.1%
Fill in the blanks 1 2.8%
Numerical Answer Type (NAT) 1 2.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
36 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
36 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differentiation
36 Qs

Paper coverage

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

JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 1 OFFLINE
2 Qs
IIT JEE 2008 PAPER 2 OFFLINE
2 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 MAINS
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2001 SCREENING
1 Qs
IIT JEE 2000
1 Qs
IIT JEE 1998
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1994
1 Qs
IIT JEE 1991
1 Qs
IIT JEE 1990
2 Qs
IIT JEE 1989
1 Qs
IIT JEE 1988
1 Qs
IIT JEE 1986
1 Qs
IIT JEE 1985
2 Qs
IIT JEE 1984
1 Qs
IIT JEE 1983
1 Qs
IIT JEE 1982
2 Qs
IIT JEE 1981
1 Qs
IIT JEE 1980
1 Qs
IIT JEE 1979
1 Qs
IIT JEE 1978
1 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2008 PAPER 1 OFFLINE20082View paper
IIT JEE 2008 PAPER 2 OFFLINE20082View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2001 SCREENING20011View paper
IIT JEE 200020001View paper
IIT JEE 199819981View paper
IIT JEE 199619961View paper
IIT JEE 199419941View paper
IIT JEE 199119911View paper
IIT JEE 199019902View paper
IIT JEE 198919891View paper
IIT JEE 198819881View paper
IIT JEE 198619861View paper
IIT JEE 198519852View paper
IIT JEE 198419841View paper
IIT JEE 198319831View paper
IIT JEE 198219822View paper
IIT JEE 198119811View paper
IIT JEE 198019801View paper
IIT JEE 197919791View paper
IIT JEE 197819781View paper

All Differentiation previous year questions

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

1
1978 · Mathematics · Calculus · Differentiation
IIT JEE 1978
Find the derivative of \(\sin \left( {{x^2} + 1} \right)\) with respect to \(x\) first principle.
Open complete paper
2
1979 · Mathematics · Calculus · Differentiation
IIT JEE 1979
Find the derivative of \(f\left( x \right) = \left\{ {\matrix{ \[{{{x - 1} \over {2{x^2} - 7x + 5}}} & {when\,\,x \ne 1} \cr\] \[{ - {1 \over 3}} & {when\,\,x = 1} \cr\] } } \right.\)
at \(x=1\)
Open complete paper
3
1980 · Mathematics · Calculus · Differentiation
IIT JEE 1980
Given \(y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)\); Find \({{dy} \over {dx}}\).
Open complete paper
4
1981 · Mathematics · Calculus · Differentiation
IIT JEE 1981
Let \(y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}\). Find \({{dy} \over {dx}}\)
Open complete paper
5
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 \(h(5)=11\)

Open complete paper
6
1982 · Mathematics · Calculus · Differentiation
IIT JEE 1982
If \(y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)\) and \(f'\left( x \right) = \sin {x^2}\), then \({{dy} \over {dx}} = ..........\)
Open complete paper
7
1983 · Mathematics · Calculus · Differentiation
IIT JEE 1983
The derivative of an even function is always an odd function.
Open complete paper
8
1984 · Mathematics · Calculus · Differentiation
IIT JEE 1984
If \(\alpha\) be a repeated root of a quadratic equation \(f(x)=0\) and \(A(x), B(x)\) and \(C(x)\) be polynomials of degree \(3\), \(4\) and \(5\) respectively,
then show that \(\left| {\matrix{ \[{A\left( x \right)} & {B\left( x \right)} & {C\left( x \right)} \cr\] \[{A\left( \alpha \right)} & {B\left( \alpha \right)} & {C\left( \alpha \right)} \cr\] \[{A'\left( \alpha \right)} & {B'\left( \alpha \right)} & {C'\left( \alpha \right)} \cr\] } } \right|\) is
divisible by \(f(x)\), where prime denotes the derivatives.
Open complete paper
9
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 ................
Open complete paper
10
1985 · Mathematics · Calculus · Differentiation
IIT JEE 1985
If \({f_r}\left( x \right),{g_r}\left( x \right),{h_r}\left( x \right),r = 1,2,3\) are polynomials in \(x\) such that \({f_r}\left( a \right) = {g_r}\left( a \right) = {h_r}\left( a \right),r = 1,2,3\)
and \(F\left( x \right) = \left| {\matrix{ \[{{f_1}\left( x \right)} & {{f_2}\left( x \right)} & {{f_3}\left( x \right)} \cr\] \[{{g_1}\left( x \right)} & {{g_2}\left( x \right)} & {{g_3}\left( x \right)} \cr\] \[{{h_1}\left( x \right)} & {{h_2}\left( x \right)} & {{h_3}\left( x \right)} \cr\] } } \right|\) then \(F'\left( x \right)\) at \(x = a\) is ...........
Open complete paper
11
1986 · Mathematics · Calculus · Differentiation
IIT JEE 1986
The derivative of \({\sec ^{ - 1}}\left( {{1 \over {2{x^2} - 1}}} \right)\) with respect to \(\sqrt {1 - {x^2}}\) at \(x = {1 \over 2}\) is ...............
Open complete paper
12
1988 · Mathematics · Calculus · Differentiation
IIT JEE 1988
If \({y^2} = P\left( x \right)\), a polynomial of degree \(3\), then \(2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^2}}}} \right)\) equals
Open complete paper
13
1989 · Mathematics · Calculus · Differentiation
IIT JEE 1989
If \(x = \sec \theta - \cos \theta\) and \(y = {\sec ^n}\theta - {\cos ^n}\theta\), then show
that \(\left( {{x^2} + 4} \right){\left( {{{dy} \over {dx}}} \right)^2} = {n^2}\left( {{y^2} + 4} \right)\)
Open complete paper
14
1990 · Mathematics · Calculus · Differentiation
IIT JEE 1990
If \(f\left( x \right) = \left| {x - 2} \right|\) and \(g\left( x \right) = f\left[ {f\left( x \right)} \right]\), then \(g'\left( x \right) = ...............\) for \(x > 20\)
Open complete paper
15
1990 · Mathematics · Calculus · Differentiation
IIT JEE 1990
Let \(f(x)\) be a quadratic expression which is positive for all the real values of \(x\). If \(g(x)=f(x)+f''(x)\), then for any real \(x\),
Open complete paper
16
1991 · Mathematics · Calculus · Differentiation
IIT JEE 1991
Find \({{{dy} \over {dx}}}\) at \(x=-1\), when
$${\left( {\sin y} \right)^{\sin \left( {{\pi \over 2}x} \right)}} + {{\sqrt 3 } \over 2}{\sec ^{ - 1}}\left( {2x} \right) + {2^x}\tan \left( {In\left( {x + 2} \right)} \right) = 0$$
Open complete paper
17
1994 · Mathematics · Calculus · Differentiation
IIT JEE 1994
If \(y = {\left( {\sin x} \right)^{\tan x}},\) then \({{dy} \over {dx}}\) is equal to
Open complete paper
18
1996 · Mathematics · Calculus · Differentiation
IIT JEE 1996
If \(x{e^{xy}} = y + {\sin ^2}x,\) then at \(x = 0,{{dy} \over {dx}} = ..............\)
Open complete paper
19
1998 · Mathematics · Calculus · Differentiation
IIT JEE 1998
If\(\,\,\,\) \(y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)\left( {x - c} \right)}} + {{bx} \over {\left( {x - b} \right)\left( {x - c} \right)}} + {c \over {x - c}} + 1\),
prove that \({{y'} \over y} = {1 \over x}\left( {{a \over {a - x}} + {b \over {b - x}} + {c \over {c - x}}} \right)\).
Open complete paper
20
2000 · Mathematics · Calculus · Differentiation
IIT JEE 2000
If \({x^2} + {y^2} = 1\) then
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Showing 20 of 36 questions