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Previous year question hub

Application Of Derivatives - Calculus - Mathematics Previous Year Questions

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

49Papers
37Years
99Questions
1Topics

Application Of Derivatives question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Application Of Derivatives. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 64 64.6%
Easy 18 18.2%
Hard 9 9.1%
Not classified 8 8.1%

Question type distribution

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

Multiple Choices 65 65.7%
Subjective 24 24.2%
Numerical Answer Type (NAT) 10 10.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
99 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
99 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Derivatives
99 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 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
3 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
3 Qs
IIT JEE 2012 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
3 Qs
IIT JEE 2008 PAPER 1 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2006
5 Qs
IIT JEE 2005 MAINS
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004
2 Qs
IIT JEE 2004 SCREENING
2 Qs
IIT JEE 2003
4 Qs
IIT JEE 2003 SCREENING
2 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2001 SCREENING
3 Qs
IIT JEE 2001
1 Qs
IIT JEE 2000 SCREENING
5 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
4 Qs
IIT JEE 1997
2 Qs
IIT JEE 1995 SCREENING
3 Qs
IIT JEE 1995
1 Qs
IIT JEE 1994
3 Qs
IIT JEE 1993
2 Qs
IIT JEE 1990
1 Qs
IIT JEE 1987
4 Qs
IIT JEE 1986
2 Qs
IIT JEE 1984
1 Qs
IIT JEE 1983
7 Qs
IIT JEE 1982
2 Qs
IIT JEE 1981
3 Qs
IIT JEE 1979
1 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 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20201View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20192View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20133View paper
IIT JEE 2012 PAPER 1 OFFLINE20122View paper
IIT JEE 2012 PAPER 2 OFFLINE20123View paper
IIT JEE 2010 PAPER 1 OFFLINE20101View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 2 OFFLINE20093View paper
IIT JEE 2008 PAPER 1 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 200620065View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20052View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420042View paper
IIT JEE 2004 SCREENING20042View paper
IIT JEE 200320034View paper
IIT JEE 2003 SCREENING20032View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 200120011View paper
IIT JEE 2001 SCREENING20013View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20005View paper
IIT JEE 199919992View paper
IIT JEE 199819984View paper
IIT JEE 199719972View paper
IIT JEE 199519951View paper
IIT JEE 1995 SCREENING19953View paper
IIT JEE 199419943View paper
IIT JEE 199319932View paper
IIT JEE 199019901View paper
IIT JEE 198719874View paper
IIT JEE 198619862View paper
IIT JEE 198419841View paper
IIT JEE 198319837View paper
IIT JEE 198219822View paper
IIT JEE 198119813View paper
IIT JEE 197919791View paper

All Application Of Derivatives previous year questions

Practice every matching question in batches of 20, 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
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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
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3
1981 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1981
Let \(x\) and \(y\) be two real variables such that \(x>0\) and \(xy=1\). Find the minimum value of \(x+y\).
Write your response
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4
1981 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1981
Use the function \(f\left( x \right) = {x^{1/x}},x > 0\). to determine the bigger of the two numbers \({e^\pi }\) and \({\pi ^e}\)
Write your response
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5
1982 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1982
If \(f(x)\) and \(g(x)\) are differentiable function for \(0 \le x \le 1\) such that \(f(0)=2\), \(g(0)=0\), \(f(1)=6\); \(g(1)=2\), then show that there exist \(c\) satisfying \(0 < c < 1\) and \(f'(c)=2g'(c)\).
Write your response
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6
1982 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1982
If \(a{x^2} + {b \over x} \ge c\) for all positive \(x\) where \(a>0\) and \(b>0\) show that \(27a{b^2} \ge 4{c^3}\).
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7
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
If \(x-r\) is a factor of the polynomial \(f\left( x \right) = {a_n}{x^4} + ..... + {a_0},\) repeated \(m\) times \(\left( {1 < m \le n} \right)\), then \(r\) is a root of \(\left( x \right) = 0\) repeated \(m\) times.
A
TRUE
B
FALSE
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8
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
Find the coordinates of the point on the curve \(y = {x \over {1 + {x^2}}}\)
where the tangent to the curve has the greatest slope.
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9
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
Show that \(1+x\) \(In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}}\) for all \(x \ge 0\)
Write your response
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10
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
The normal to the curve \(\,x = a\left( {\cos \theta + \theta \sin \theta } \right)\), \(y = a\left( {\sin \theta - \theta \cos \theta } \right)\) at any point \('\theta '\) is such that
A
it makes a constant angle with the \(x\)-axis
B
it passes through the origin
C
it is at a constant distance from the origin
D
none of these
Open complete paper
11
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
If \(a+b+c=0\), then the quadratic equation \(3a{x^2} + 2bx + c = 0\) has
A
at least one root in \(\left[ {0,1} \right]\)
B
one root in \(\left[ {2,3} \right]\) and the other in \(\left[ {-2,-1} \right]\)
C
imaginary roots
D
none of these
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12
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then
A
the area of \(\Delta ABC\) is maximum when it is isosceles
B
the area of \(\Delta ABC\) is minimum when it is isosceles
C
the perimeter of \(\Delta ABC\) is minimum when it is isosceles
D
none of these
Open complete paper
13
1983 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1983
If \(y = a\,\,In\,x + b{x^2} + x\) has its extreamum values at \(x=-1\) and \(x=2\), then
A
\(a = 2,b = - 1\)
B
\(a = 2,b = - {1 \over 2}\)
C
\(a = - 2,b = {1 \over 2}\)
D
none of these
Open complete paper
14
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
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15
1986 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1986
Let \(P\left( x \right) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + ...... + {a_n}{x^{2n}}\) be a polynomial in a real variable \(x\) with
\(0 < {a_0} < {a_1} < {a_2} < ..... < {a_n}.\) The function \(P(x)\) has
A
neither a maximum nor a minimum
B
only one maximum
C
only one minimum
D
only one maximum and only one minimum
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16
1986 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1986
If the line \(ax+by+c=0\) is a normal to the curve \(xy=1\), then
A
\(a > 0,b > 0\)
B
\(a > 0,b < 0\)
C
\(a < 0,b > 0\)
D
\(a < 0,b < 0\)
Open complete paper
17
1987 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1987
Find the point on the curve \(\,\,\,4{x^2} + {a^2}{y^2} = 4{a^2},\,\,\,4 < {a^2} < 8\)
that is farthest from the point \((0, -2)\).
Write your response
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18
1987 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1987
The set of all \(x\) for which \(in\left( {1 + x} \right) \le x\) is equal to ..........
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19
1987 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1987
Let \(f\) and \(g\) be increasing and decreasing functions, respectively from \(\left[ {0,\infty } \right)\) to \(\left[ {0,\infty } \right)\). Let \(h\left( x \right) = f\left( {g\left( x \right)} \right).\) If \(h\left( 0 \right) = 0,\) then \(h\left( x \right) - h\left( 1 \right)\) is
A
always zero
B
always negative
C
always positive
D
strictly increasing
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20
1987 · Mathematics · Calculus · Application Of Derivatives
IIT JEE 1987
The smallest positive root of the equation, \(\tan x - x = 0\) lies in
A
\(\left( {0,{\pi \over 2}} \right)\)
B
\(\left( {{\pi \over 2},\pi } \right)\)
C
\(\left( {\pi ,{{3\pi } \over 2}} \right)\)
D
\(\left( {{{3\pi } \over 2},2\pi } \right)\)
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Showing 20 of 99 questions