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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.

16Papers
15Years
61Questions
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.

Not classified 61 100%

Question type distribution

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

Multiple Choices 56 91.8%
Subjective 5 8.2%

Subject weightage

Top subjects by unique question coverage.

Mathematics
61 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
61 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
61 Qs

Paper coverage

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

WB JEE 2025
2 Qs
VITEEE 2025
1 Qs
WB JEE 2024
2 Qs
WB JEE 2023
3 Qs
WB JEE 2022
3 Qs
WB JEE 2021
3 Qs
WB JEE 2020
6 Qs
WB JEE 2019
2 Qs
WB JEE 2018
2 Qs
WB JEE 2017
3 Qs
WB JEE 2016
2 Qs
WB JEE 2012
1 Qs
WB JEE 2011
7 Qs
WB JEE 2010
9 Qs
WB JEE 2009
7 Qs
WB JEE 2008
8 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520251View paper
WB JEE 202520252View paper
WB JEE 202420242View paper
WB JEE 202320233View paper
WB JEE 202220223View paper
WB JEE 202120213View paper
WB JEE 202020206View paper
WB JEE 201920192View paper
WB JEE 201820182View paper
WB JEE 201720173View paper
WB JEE 201620162View paper
WB JEE 201220121View paper
WB JEE 201120117View paper
WB JEE 201020109View paper
WB JEE 200920097View paper
WB JEE 200820088View paper

All Differential Equations previous year questions

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

1
2016 · Mathematics · Calculus · Differential Equations
WB JEE 2016
If the solution of the differential equation \(x{{dy} \over {dx}} + y = x{e^x}\,be\,xy = {e^x}\phi (x) + C\), then \(\phi\)(x) is equal to
A
x + 1
B
x \(-\) 1
C
1 \(-\) x
D
x
Open complete paper
2
2016 · Mathematics · Calculus · Differential Equations
WB JEE 2016
General solution of \(y{{dy} \over {dx}} + b{y^2} = a\cos x,0 < x < 1\) is
A
y2 = 2a(2b sin x + cos x) + ce\(-\)2bx
B
\((4{b^2} + 1){y^2} = 2a(\sin x + 2b\cos x) + C{e^{ - 2bx}}\)
C
\((4{b^2} + 1){y^2} = 2a(\sin x + 2b\cos x) + C{e^{ 2bx}}\)
D
\({y^2} = 2a(2b\sin x + \cos x) + C{e^{ - 2bx}}\)
Open complete paper
3
2017 · Mathematics · Calculus · Differential Equations
WB JEE 2017
If \(y = {e^{m{{\sin }^{ - 1}}x}}\) then \((1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} -\)ky = 0, where k is equal to
A
m2
B
2
C
\(-\) 1
D
\(-\) m2
Open complete paper
4
2017 · Mathematics · Calculus · Differential Equations
WB JEE 2017
The integrating factor of the first order differential equation \({x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x^2} - 1\) is
A
ex
B
\(x - {1 \over x}\)
C
\(x + {1 \over x}\)
D
\({1 \over {{x^2}}}\)
Open complete paper
5
2017 · Mathematics · Calculus · Differential Equations
WB JEE 2017
Solution of \({(x + y)^2}{{dy} \over {dx}} = {a^2}\) ('a' belong a constant) is
A
\({{(x + y)} \over a} = \tan {{y + C} \over a},C\) is an arbitrary constant
B
\(xy = a\tan Cx,C\) is an arbitrary constant
C
\({x \over a} = \tan {y \over C},C\) is an arbitrary constant
D
\(xy = \tan (x + C),C\) is an arbitrary constant
Open complete paper
6
2018 · Mathematics · Calculus · Differential Equations
WB JEE 2018
Let y(x) be a solution of

\((1 + {x^2}){{dy} \over {dx}} + 2xy - 4{x^2} = 0\). Then y(1) is equal to
A
\({1 \over 2}\)
B
\({1 \over 3}\)
C
\({1 \over 6}\)
D
\(-\)1
Open complete paper
7
2018 · Mathematics · Calculus · Differential Equations
WB JEE 2018
The differential equation representing the family of curves \({y^2} = 2d(x + \sqrt d )\), where d is a parameter, is of
A
order 2
B
degree 2
C
degree 3
D
degree 4
Open complete paper
8
2019 · Mathematics · Calculus · Differential Equations
WB JEE 2019
General solution of \({(x + y)^2}{{dy} \over {dx}} = {a^2},a \ne 0\) is (C is an arbitrary constant)
A
\({x \over a} = \tan {y \over a} + C\)
B
\(\tan xy = C\)
C
\(\tan (x + y) = C\)
D
\(\tan {{y + C} \over a} = {{x + y} \over a}\)
Open complete paper
9
2019 · Mathematics · Calculus · Differential Equations
WB JEE 2019
The general solution of the differential equation \(\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}} \right){e^{x/y}}dy = 0\) is (C is an arbitrary constant)
A
\(x - y{e^{{x \over y}}} = C\)
B
\(y - x{e^{{x \over y}}} = C\)
C
\(x + y{e^{{x \over y}}} = C\)
D
\(y + x{e^{{x \over y}}} = C\)
Open complete paper
10
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is
A
\({{{d^2}y} \over {d{x^2}}} - 9x = 13\)
B
\({{{d^2}y} \over {d{x^2}}} - 2{{dy} \over {dx}} + 2y = 0\)
C
\({{{d^2}y} \over {d{x^2}}} + 3y = 4\)
D
\({\left( {{{dy} \over {dx}}} \right)^2} + {{dy} \over {dx}} - xy = 0\)
Open complete paper
11
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
If \(x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0\) and \(y(1) = {\pi \over 2}\), then the value of \(\cos \left( {{y \over x}} \right)\) is
A
1
B
log x
C
e
D
0
Open complete paper
12
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
Let f be a differentiable function with \(\mathop {\lim }\limits_{x \to \infty } f(x) = 0.\) If \(y' + yf'(x) - f(x)f'(x) = 0\), \(\mathop {\lim }\limits_{x \to \infty } y(x) = 0\), then (where \(y \equiv {{dy} \over {dx}})\)
A
\(y + 1 = {e^{f(x)}} + f(x)\)
B
\(y - 1 = {e^{f(x)}} + f(x)\)
C
\(y + 1 = {e^{ - f(x)}} + f(x)\)
D
\(y - 1 = {e^{ - f(x)}} + f(x)\)
Open complete paper
13
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
Let \(y = {1 \over {1 + x + lnx}}\), then
A
\(x{{dy} \over {dx}} + y = x\)
B
\(x{{dy} \over {dx}} = y(y\ln x - 1)\)
C
\({x^2}{{dy} \over {dx}} = {y^2} + 1 - {x^2}\)
D
\(x{\left( {{{dy} \over {dx}}} \right)^2} = y - x\)
Open complete paper
14
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
Let \(y = f(x) = 2{x^2} - 3x + 2\). The differential of y when x changes from 2 to 1.99 is
A
0.01
B
0.18
C
\(-\)0.05
D
0.07
Open complete paper
15
2020 · Mathematics · Calculus · Differential Equations
WB JEE 2020
Let cos\(^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}\). Then
A
\({x^2}{y^2} + x{y_1} + {n^2}y = 0\)
B
\(x{y_{^2}} - x{y_1} + 2{n^2}y = 0\)
C
\({x^2}{y_{^2}} + 3x{y_1} - {n^2}y = 0\)
D
\(x{y_{^2}} + 5x{y_1} - 3y = 0\)

\(\left( {Here,\,{y_2} = {{{d^2}y} \over {d{x^2}}},\,{y_1} = {{dy} \over {dx}}} \right)\)
Open complete paper
16
2021 · Mathematics · Calculus · Differential Equations
WB JEE 2021
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where \(y^{\prime}\equiv{{{dx}\over {dy}}},y^{\prime\prime}\equiv{{{d^2}y\over {dx^2}}}\)
A
y2 + xy'2 \(-\) yy' = 0
B
xyy'' + xy'2 \(-\) yy' = 0
C
yy' + xy'2 \(-\) xy' = 0
D
x2y' + xy'' \(-\) 3y = 0
Open complete paper
17
2021 · Mathematics · Calculus · Differential Equations
WB JEE 2021
If \(x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}\), then | f(xy) | is equal to (where k is an arbitrary positive constant).
A
\(k{e^{{x^2}/2}}\)
B
\(k{e^{{y^2}/2}}\)
C
\(k{e^{{x^2}}}\)
D
\(k{e^{{y^2}}}\)
Open complete paper
18
2021 · Mathematics · Calculus · Differential Equations
WB JEE 2021
The differential of \(f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})\) at x = 0 and for dx = 0.2 is
A
0.5
B
0.3
C
\(-\) 0.2
D
\(-\) 0.5
Open complete paper
19
2022 · Mathematics · Calculus · Differential Equations
WB JEE 2022

The solution of

\(\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}\) is \(f(x) + {e^{ - \sin y}} = C\) (C is arbitrary real constant) where f(x) is equal to

A
\({e^x} + {1 \over 2}{x^3}\)
B
\({e^{ - x}} + {1 \over 3}{x^3}\)
C
\({e^{ - x}} + {1 \over 2}{x^3}\)
D
\({e^x} + {1 \over 3}{x^3}\)
Open complete paper
20
2022 · Mathematics · Calculus · Differential Equations
WB JEE 2022

If \(x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}\), then \(|f(xy)|\) is equal to

A
\(C{e^{{{{x^2}} \over 2}}}\) (where C is the constant of integration)
B
\(C{e^{{x^2}}}\) (where C is the constant of integration)
C
\(C{e^{2{x^2}}}\) (where C is the constant of integration)
D
\(C{e^{{{{x^2}} \over 3}}}\) (where C is the constant of integration)
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Showing 20 of 61 questions