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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.

60Papers
7Years
210Questions
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 210 100%

Question type distribution

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

Multiple Choices 210 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
210 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
210 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
210 Qs

Paper coverage

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

MHT CET 2025 25TH APRIL EVENING SHIFT
5 Qs
MHT CET 2025 19TH APRIL EVENING SHIFT
4 Qs
MHT CET 2025 19TH APRIL MORNING SHIFT
4 Qs
MHT CET 2025 20TH APRIL EVENING SHIFT
4 Qs
MHT CET 2025 20TH APRIL MORNING SHIFT
4 Qs
MHT CET 2025 21ST APRIL EVENING SHIFT
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MHT CET 2025 21ST APRIL MORNING SHIFT
4 Qs
MHT CET 2025 22ND APRIL MORNING SHIFT
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MHT CET 2025 23RD APRIL EVENING SHIFT
4 Qs
MHT CET 2025 23RD APRIL MORNING SHIFT
4 Qs
MHT CET 2025 25TH APRIL MORNING SHIFT
4 Qs
MHT CET 2025 26TH APRIL EVENING SHIFT
4 Qs
MHT CET 2025 5TH MAY EVENING SHIFT
4 Qs
MHT CET 2025 22ND APRIL EVENING SHIFT
3 Qs
MHT CET 2025 26TH APRIL MORNING SHIFT
3 Qs
MHT CET 2024 16TH MAY EVENING SHIFT
4 Qs
MHT CET 2024 4TH MAY EVENING SHIFT
4 Qs
MHT CET 2024 10TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 10TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 11TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 11TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 15TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 16TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 2ND MAY EVENING SHIFT
3 Qs
MHT CET 2024 2ND MAY MORNING SHIFT
3 Qs
MHT CET 2024 3RD MAY EVENING SHIFT
3 Qs
MHT CET 2024 4TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 9TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 9TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 15TH MAY EVENING SHIFT
2 Qs
MHT CET 2024 3RD MAY MORNING SHIFT
2 Qs
MHT CET 2023 13TH MAY MORNING SHIFT
4 Qs
MHT CET 2023 10TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 12TH MAY EVENING SHIFT
3 Qs
MHT CET 2023 12TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 13TH MAY EVENING SHIFT
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MHT CET 2023 14TH MAY EVENING SHIFT
3 Qs
MHT CET 2023 14TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 10TH MAY EVENING SHIFT
2 Qs
MHT CET 2023 11TH MAY EVENING SHIFT
2 Qs
MHT CET 2023 11TH MAY MORNING SHIFT
2 Qs
MHT CET 2023 9TH MAY EVENING SHIFT
2 Qs
MHT CET 2023 9TH MAY MORNING SHIFT
2 Qs
MHT CET 2022 11TH AUGUST EVENING SHIFT
2 Qs
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT
5 Qs
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT
5 Qs
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT
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MHT CET 2021 22TH SEPTEMBER EVENING SHIFT
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MHT CET 2021 23RD SEPTEMBER EVENING SHIFT
5 Qs
MHT CET 2021 23th September Morning Shift
5 Qs
MHT CET 2021 24TH SEPTEMBER EVENING SHIFT
5 Qs
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT
4 Qs
MHT CET 2021 22TH SEPTEMBER MORNING SHIFT
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MHT CET 2021 24TH SEPTEMBER MORNING SHIFT
4 Qs
MHT CET 2020 16TH OCTOBER EVENING SHIFT
5 Qs
MHT CET 2020 16TH OCTOBER MORNING SHIFT
5 Qs
MHT CET 2020 19TH OCTOBER EVENING SHIFT
5 Qs
MHT CET 2019 2ND MAY EVENING SHIFT
3 Qs
MHT CET 2019 2ND MAY MORNING SHIFT
2 Qs
MHT CET 2019 3RD MAY MORNING SHIFT
2 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
MHT CET 2025 19TH APRIL EVENING SHIFT20254View paper
MHT CET 2025 19TH APRIL MORNING SHIFT20254View paper
MHT CET 2025 20TH APRIL EVENING SHIFT20254View paper
MHT CET 2025 20TH APRIL MORNING SHIFT20254View paper
MHT CET 2025 21ST APRIL EVENING SHIFT20254View paper
MHT CET 2025 21ST APRIL MORNING SHIFT20254View paper
MHT CET 2025 22ND APRIL EVENING SHIFT20253View paper
MHT CET 2025 22ND APRIL MORNING SHIFT20254View paper
MHT CET 2025 23RD APRIL EVENING SHIFT20254View paper
MHT CET 2025 23RD APRIL MORNING SHIFT20254View paper
MHT CET 2025 25TH APRIL EVENING SHIFT20255View paper
MHT CET 2025 25TH APRIL MORNING SHIFT20254View paper
MHT CET 2025 26TH APRIL EVENING SHIFT20254View paper
MHT CET 2025 26TH APRIL MORNING SHIFT20253View paper
MHT CET 2025 5TH MAY EVENING SHIFT20254View paper
MHT CET 2024 10TH MAY EVENING SHIFT20243View paper
MHT CET 2024 10TH MAY MORNING SHIFT20243View paper
MHT CET 2024 11TH MAY EVENING SHIFT20243View paper
MHT CET 2024 11TH MAY MORNING SHIFT20243View paper
MHT CET 2024 15TH MAY EVENING SHIFT20242View paper
MHT CET 2024 15TH MAY MORNING SHIFT20243View paper
MHT CET 2024 16TH MAY EVENING SHIFT20244View paper
MHT CET 2024 16TH MAY MORNING SHIFT20243View paper
MHT CET 2024 2ND MAY EVENING SHIFT20243View paper
MHT CET 2024 2ND MAY MORNING SHIFT20243View paper
MHT CET 2024 3RD MAY EVENING SHIFT20243View paper
MHT CET 2024 3RD MAY MORNING SHIFT20242View paper
MHT CET 2024 4TH MAY EVENING SHIFT20244View paper
MHT CET 2024 4TH MAY MORNING SHIFT20243View paper
MHT CET 2024 9TH MAY EVENING SHIFT20243View paper
MHT CET 2024 9TH MAY MORNING SHIFT20243View paper
MHT CET 2023 10TH MAY EVENING SHIFT20232View paper
MHT CET 2023 10TH MAY MORNING SHIFT20233View paper
MHT CET 2023 11TH MAY EVENING SHIFT20232View paper
MHT CET 2023 11TH MAY MORNING SHIFT20232View paper
MHT CET 2023 12TH MAY EVENING SHIFT20233View paper
MHT CET 2023 12TH MAY MORNING SHIFT20233View paper
MHT CET 2023 13TH MAY EVENING SHIFT20233View paper
MHT CET 2023 13TH MAY MORNING SHIFT20234View paper
MHT CET 2023 14TH MAY EVENING SHIFT20233View paper
MHT CET 2023 14TH MAY MORNING SHIFT20233View paper
MHT CET 2023 9TH MAY EVENING SHIFT20232View paper
MHT CET 2023 9TH MAY MORNING SHIFT20232View paper
MHT CET 2022 11TH AUGUST EVENING SHIFT20222View paper
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT20215View paper
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT20215View paper
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT20215View paper
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT20214View paper
MHT CET 2021 22TH SEPTEMBER EVENING SHIFT20215View paper
MHT CET 2021 22TH SEPTEMBER MORNING SHIFT20214View paper
MHT CET 2021 23RD SEPTEMBER EVENING SHIFT20215View paper
MHT CET 2021 23th September Morning Shift20215View paper
MHT CET 2021 24TH SEPTEMBER EVENING SHIFT20215View paper
MHT CET 2021 24TH SEPTEMBER MORNING SHIFT20214View paper
MHT CET 2020 16TH OCTOBER EVENING SHIFT20205View paper
MHT CET 2020 16TH OCTOBER MORNING SHIFT20205View paper
MHT CET 2020 19TH OCTOBER EVENING SHIFT20205View paper
MHT CET 2019 2ND MAY EVENING SHIFT20193View paper
MHT CET 2019 2ND MAY MORNING SHIFT20192View paper
MHT CET 2019 3RD MAY MORNING SHIFT20192View paper

All Differential Equations previous year questions

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

1
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 2ND MAY EVENING SHIFT

The solution of the differential equation $\frac{d \theta}{d t}=-k\left(\theta-\theta_0\right)$ where $k$ is constant, is .............

A
$\theta=\theta_0+a e^{-k t}$
B
$\theta=\theta_0+a e^{k t}$
C
$\theta=2 \theta_0-a e^{k t}$
D
$\theta=2 \theta_0-a e^{-k t}$
Open complete paper
2
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 2ND MAY EVENING SHIFT

The solution of the differential equation $y d x-x d y=x y d x$ is ......

A
$x^2=e^x y^2$
B
$x=y e^x$
C
$x y=e^x$
D
$x^2 y^2=\log x$
Open complete paper
3
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 2ND MAY EVENING SHIFT

The particular solution of the differential equation $\log \left(\frac{d y}{d x}\right)=x$, when $x=0, y=1$ is ..............

A
$y=e^x+2$
B
$y=-e^x$
C
$y=-e^x+2$
D
$y=e^x$
Open complete paper
4
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 2ND MAY MORNING SHIFT

The general solution of $x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)$ is .............

A
$x^2 \sin \left(\frac{x}{y}\right)=c$
B
$x \sin \left(\frac{x}{y}\right)=c$
C
$x \sin \left(\frac{y}{x}\right)=c$
D
$x^2 \sin \left(\frac{y}{x}\right)=c$
Open complete paper
5
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 2ND MAY MORNING SHIFT

The order of the differential equation of all circles whose radius is 4 , is ...........

A
1
B
2
C
3
D
4
Open complete paper
6
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 3RD MAY MORNING SHIFT

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is......

A
two
B
three
C
one
D
four
Open complete paper
7
2019 · Mathematics · Calculus · Differential Equations
MHT CET 2019 3RD MAY MORNING SHIFT

The solution of differential equation $\left(x^2+1\right) \frac{d y}{d x}+\left(y^2+1\right)=0$ is $\ldots$

A
$x+y=c$
B
$\left(x^2+1\right)\left(y^2+1\right)=c$
C
$x^2=y^2+c$
D
$\tan ^{-1} x+\tan ^{-1} y=c$
Open complete paper
8
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The order and degree of the differential equation \(\left[1+\left[\frac{d y}{d x}\right]^3\right]^{\frac{7}{3}}=7 \frac{d^2 y}{d x^2}\) are respectively.

A
2, 1
B
1, 2
C
3, 2
D
2, 3
Open complete paper
9
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The integrating factor of the differential equation \(\sin y\left(\frac{d y}{d x}\right)=\cos y(1-x \cos y)\) is

A
\(e^{\sin y}\)
B
\(e^{-x}\)
C
\(e^{-\cos y}\)
D
\(e^{-y}\)
Open complete paper
10
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The micro-organisms double themselves in 3 h. Assuming that the quantity increases at a rate proportional to it self, then the number of times it multiplies themselves in 18 yr is

A
32
B
64
C
40
D
128
Open complete paper
11
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 10 min , then the time required to drop the temperature upto 295 K is

A
30 min
B
35 min
C
20 min
D
40 min
Open complete paper
12
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The particular solution of the differential equation \(y\left(\frac{d x}{d y}\right)=x \log x\) at \(x=e\) and \(y=1\) is

A
\(x y=2\)
B
\(x=e^y\)
C
\(e^{x y}=2\)
D
\(\log x=2 y\)
Open complete paper
13
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The differential equation obtained from the function \(y=a(x-a)^2\) is

A
\(8 y^2=\left(\frac{d y}{d x}\right)^2\left[x+\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2\)
B
\(4 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2\)
C
\(2 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2\)
D
\(8 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2\)
Open complete paper
14
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The bacteria increases at the rate proportional to the number of bacteria present. If the original number '\(N\)' doubles in \(4 \mathrm{~h}\), then the number of bacteria in \(12 \mathrm{~h}\) will be

A
4N
B
8N
C
6N
D
3N
Open complete paper
15
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The integrating factor of the differential equation \(\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x\) is

A
\(e^{\tan ^{-1} x}\)
B
\(-e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}\)
C
\(-e^{\tan ^{-1} x}\)
D
\(e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}\)
Open complete paper
16
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The differential equation of all lines perpendicular to the line \(5 x+2 y+7=0\) is

A
\(2 d y-5 d x=0\)
B
\(5 d y-2 d x=0\)
C
\(2 d y-3 d x=0\)
D
\(3 d y-2 d x=0\)
Open complete paper
17
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are \(27 \mathrm{~gm}\) of certain substance and \(3 \mathrm{~h}\) later it is found that \(8 \mathrm{~gm}\) are left, then the amount left after one more hour is

A
\(\frac{20}{3} \mathrm{~gm}\)
B
\(\frac{16}{3} \mathrm{~gm}\)
C
\(\frac{19}{3} \mathrm{~gm}\)
D
\(\frac{17}{3} \mathrm{~gm}\)
Open complete paper
18
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 19TH OCTOBER EVENING SHIFT

The order and degree of the differential equation $\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^2}\right]^{\frac{5}{3}}=5 \frac{d^2 y}{d x^2}$ are respectively

A
3, 2
B
5, 2
C
2, 5
D
2, 3
Open complete paper
19
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 19TH OCTOBER EVENING SHIFT

The general solution of the differential equation $\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0$ is

A
$x \cdot e^{\tan ^{-1} y}=\frac{\left(e^{\tan ^{-1} y}\right)^2}{2}+C$
B
$e^{\tan ^{-1} y}=\left(e^{\tan ^{-1} x}\right)^2+C$
C
$x \cdot e^{\tan ^{-1} y}=\frac{\left(e^{\tan ^{-1} x} x\right)^2}{2}+C$
D
$e^{\tan ^{-1} y}=\left(e^{\tan ^{-1} y}\right)^2+C$
Open complete paper
20
2020 · Mathematics · Calculus · Differential Equations
MHT CET 2020 19TH OCTOBER EVENING SHIFT

The rate of disintegration of a radio active element at time $t$ is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm . Will disintegrate into its mass of 0.5 gm . is proportional to

A
$\log 5$
B
$\log 3$
C
$\log 2$
D
$\log 4$
Open complete paper

Showing 20 of 210 questions