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Previous year question hub

Differential Equations - Calculus - Mathematics Previous Year Questions

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

26Papers
24Years
35Questions
1Topics

Differential Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 21 60%
Hard 8 22.9%
Easy 5 14.3%
Not classified 1 2.9%

Question type distribution

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

Multiple Choices 25 71.4%
Numerical Answer Type (NAT) 7 20%
Subjective 3 8.6%

Subject weightage

Top subjects by unique question coverage.

Mathematics
35 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
35 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
35 Qs

Paper coverage

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

JEE ADVANCED 2025 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
2 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
2 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2005 SCREENING
4 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2000 SCREENING
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
1 Qs
IIT JEE 1997
1 Qs
IIT JEE 1994
1 Qs
IIT JEE 1983
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 1 ONLINE20251View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20232View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20222View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20162View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20152View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2011 PAPER 2 OFFLINE20111View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 2005 SCREENING20054View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 2000 SCREENING20001View paper
IIT JEE 199919992View paper
IIT JEE 199819981View paper
IIT JEE 199719971View paper
IIT JEE 199419941View paper
IIT JEE 198319831View paper

All Differential Equations previous year questions

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

1
1983 · Mathematics · Calculus · Differential Equations
IIT JEE 1983
If \(\left( {a + bx} \right){e^{y/x}} = x,\) then prove that \({x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {dx}} - y} \right)^2}\)
Write your response
Open complete paper
2
1994 · Mathematics · Calculus · Differential Equations
IIT JEE 1994
A normal is drawn at a point \(P(x,y)\) of a curve. It meets the \(x\)-axis at \(Q.\) If \(PQ\) is of constant length \(k,\) then show that the differential equation describing such curves is \(y = {{dy} \over {dx}} = \pm \sqrt {{k^2} - {y^2}}\)

Find the equation of such a curve passing through \((0,k).\)

Write your response
Open complete paper
3
1997 · Mathematics · Calculus · Differential Equations
IIT JEE 1997
Let \(u(x)\) and \(v(x)\) satisfy the differential equation \({{du} \over {dx}} + p\left( x \right)u = f\left( x \right)\) and \({{dv} \over {dx}} + p\left( x \right)v = g\left( x \right),\) where \(p(x) f(x)\) and \(g(x)\) are continuous functions. If \(u\left( {{x_1}} \right) > v\left( {{x_1}} \right)\) for some \({{x_1}}\) and \(f(x)>g(x)\) for all \(x > {x_1},\) prove that any point \((x,y)\) where \(x > {x_1},\) does not satisfy the equations \(y=u(x)\) and \(y=v(x)\)
Write your response
Open complete paper
4
1998 · Mathematics · Calculus · Differential Equations
IIT JEE 1998
The order of the differential equation whose general solution is given by
\(y = \left( {{C_1} + {C_2}} \right)\cos \left( {x + {C_3}} \right) - {C_4}{e^{x + {C_5}}},\) where
\({C_1},{C_2},{C_3},{C_4},{C_5},\) are arbitrary constants, is
A
\(5\)
B
\(4\)
C
\(3\)
D
\(2\)
Open complete paper
5
1999 · Mathematics · Calculus · Differential Equations
IIT JEE 1999
A solution of the differential equation
\({\left( {{{dy} \over {dx}}} \right)^2} - x{{dy} \over {dx}} + y = 0\) is
A
\(y=2\)
B
\(y=2x\)
C
\(y=2x-4\)
D
\(y = 2{x^2} - 4\)
Open complete paper
6
1999 · Mathematics · Calculus · Differential Equations
IIT JEE 1999
The differential equation representing the family of curves
\({y^2} = 2c\left( {x + \sqrt c } \right),\) where \(c\) is a positive parameter, is of
A
order \(1\)
B
order \(2\)
C
degree \(3\)
D
degree \(4\)
Open complete paper
7
2000 · Mathematics · Calculus · Differential Equations
IIT JEE 2000 SCREENING
If \({x^2} + {y^2} = 1,\) then
A
\(yy'' - 2{\left( {y'} \right)^2} + 1 = 0\)
B
\(yy'' + {\left( {y'} \right)^2} + 1 = 0\)
C
\(yy'' + {\left( {y'} \right)^2} - 1 = 0\)
D
\(yy'' + 2{\left( {y'} \right)^2} + 1 = 0\)
Open complete paper
8
2003 · Mathematics · Calculus · Differential Equations
IIT JEE 2003 SCREENING
If \(y(t)\) is a solution of \(\left( {1 + t} \right){{dy} \over {dt}} - ty = 1\) and \(y\left( 0 \right) = - 1,\) then \(y(1)\) is equal to
A
\(- 1/2\)
B
\(e+1/2\)
C
\(e-1/2\)
D
\(1/2\)
Open complete paper
9
2004 · Mathematics · Calculus · Differential Equations
IIT JEE 2004 SCREENING
If \(y=y(x)\) and \({{2 + \sin x} \over {y + 1}}\left( {{{dy} \over {dx}}} \right) = - \cos x,y\left( 0 \right) = 1,\)
then \(y\left( {{\pi \over 2}} \right)\) equals
A
\(1/3\)
B
\(2/3\)
C
\(-1/3\)
D
\(1\)
Open complete paper
10
2005 · Mathematics · Calculus · Differential Equations
IIT JEE 2005 SCREENING
If \(y=y(x)\) and it follows the relation \(x\cos \,y + y\,cos\,x = \pi\) then \(y''(0)=\)
A
\(1\)
B
\(-1\)
C
\({\pi}\)
D
\(- \pi\)
Open complete paper
11
2005 · Mathematics · Calculus · Differential Equations
IIT JEE 2005 SCREENING
For the primitive integral equation \(ydx + {y^2}dy = x\,dy;\)
\(x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1 \right) = 1,\) then \(y(-3)\) is
A
\(3\)
B
\(2\)
C
\(1\)
D
\(5\)
Open complete paper
12
2005 · Mathematics · Calculus · Differential Equations
IIT JEE 2005 SCREENING
The differential equation \({{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}\) determines a family of circles with
A
variable radii and a fixed centre at \((0,1)\)
B
variable radii and a fixed centre at \((0,-1)\)
C
fixed radius \(1\) and variable centres along the \(x\)-axis.
D
fixed radius \(1\) and variable centrs along the \(y\)-axis.
Open complete paper
13
2005 · Mathematics · Calculus · Differential Equations
IIT JEE 2005 SCREENING
The solution of primitive integral equation \(\left( {{x^2} + {y^2}} \right)dy = xy\)
\(dx\) is \(y=y(x),\) If \(y(1)=1\) and \(\left( {{x_0}} \right) = e\), then \({{x_0}}\) is equal to
A
\(\sqrt {2\left( {{e^2} - 1} \right)}\)
B
\(\sqrt {2\left( {{e^2} + 1} \right)}\)
C
\(\sqrt 3 \,e\)
D
\(\sqrt {{{2\left( {{e^2} + 1} \right)} \over 2}}\)
Open complete paper
14
2007 · Mathematics · Calculus · Differential Equations
IIT JEE 2007 PAPER 2 OFFLINE

The differential equation \(\frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{y}\) determines a family of circles with :

A
variable radii and a fixed centre at \((0,1)\)
B
variable radii and a fixed centre at \((0,-1)\)
C
fixed radius 1 and variable centres along the \(x\)-axis
D
fixed radius 1 and variable centres along the \(y\)-axis
Open complete paper
15
2008 · Mathematics · Calculus · Differential Equations
IIT JEE 2008 PAPER 2 OFFLINE
Let a solution \(y=y(x)\) of the differential equation,

\(x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0\) satify \(y\left( 2 \right) = {2 \over {\sqrt 3 }}.\)

STATEMENT-1 : \(y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)\) and

STATEMENT-2 : \(y\left( x \right)\) given by \({1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}}\)

A
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
D
STATEMENT-1 is False , STATEMENT-2 is True
Open complete paper
16
2011 · Mathematics · Calculus · Differential Equations
IIT JEE 2011 PAPER 1 OFFLINE

Let \(f:[1,\infty ) \to [2,\infty )\) be a differentiable function such that \(f(1) = 2\). If \(6\int\limits_1^x {f(t)dt = 3xf(x) - {x^3} - 5}\) for all \(x \ge 1\), then the value of f(2) is ___________.

Enter a numerical response
Open complete paper
17
2011 · Mathematics · Calculus · Differential Equations
IIT JEE 2011 PAPER 2 OFFLINE
Let \(y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) = 0,x \in R,\) where \(f'(x)\) denotes \({{df\left( x \right)} \over {dx}}\) and \(g(x)\) is a given non-constant differentiable function on \(R\) with \(g(0)=g(2)=0.\) Then the value of \(y(2)\) is
Enter a numerical response
Open complete paper
18
2012 · Mathematics · Calculus · Differential Equations
IIT JEE 2012 PAPER 1 OFFLINE
If \(y(x)\) satisfies the differential equation \(y' - y\,tan\,x = 2x\,secx\) and \(y(0)=0,\) then
A
\(y\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {8\sqrt 2 }}\)
B
\(y'\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {18}}\)
C
\(y\left( {{\pi \over 3}} \right) = {{{\pi ^2}} \over 9}\)
D
\(y'\left( {{\pi \over 3}} \right) = {{4\pi } \over 3} + {{2{\pi ^2}} \over {3\sqrt 3 }}\)
Open complete paper
19
2013 · Mathematics · Calculus · Differential Equations
JEE ADVANCED 2013 PAPER 1 OFFLINE
A curve passes through the point \(\left( {1,{\pi \over 6}} \right)\). Let the slope of
the curve at each point \((x,y)\) be \({y \over x} + \sec \left( {{y \over x}} \right),x > 0.\)
Then the equation of the curve is
A
\(sin\left( {{y \over x}} \right) = \log x + {1 \over 2}\)
B
\(cos\,ec\left( {{y \over x}} \right) = \log x + 2\)
C
\(s\,ec\left( {{{2y} \over x}} \right) = \log x + 2\,\)
D
\(cos\left( {{{2y} \over x}} \right) = \log x + {1 \over 2}\)
Open complete paper
20
2014 · Mathematics · Calculus · Differential Equations
JEE ADVANCED 2014 PAPER 2 OFFLINE
The function \(y=f(x)\) is the solution of the differential equation
\({{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,\) in \((-1,1)\) satisfying \(f(0)=0\).
Then \(\int\limits_{ - {{\sqrt 3 } \over 2}}^{{{\sqrt 3 } \over 2}} {f\left( x \right)} \,d\left( x \right)\) is
A
\({\pi \over 3} - {{\sqrt 3 } \over 2}\)
B
\({\pi \over 3} - {{\sqrt 3 } \over 4}\)
C
\({\pi \over 6} - {{\sqrt 3 } \over 4}\)
D
\({\pi \over 6} - {{\sqrt 3 } \over 2}\)
Open complete paper

Showing 20 of 35 questions