MHT CET PYQs for Differential Equations with Solutions: Practice MHT CET Previous Year Questions

Differential Equations is a Class 12 chapter in the Mathematics section of the MHT CET for candidates who are preparing for the PCM (Physics, Chemistry, and Mathematics).

The key topics covered in Differential Equations PYQs are:

Solution of differential equations: variable separable, homogeneous and linear
Formation of a differential equation
Order and degree
Newton's law of cooling
Radioactive decay and population growth

Practising Differential Equations MHT CET PYQ helps candidates to understand question pattern, improve calculation speed, and identify concepts which were asked in previous exams.

Based on chapter-wise analysis of the MHT CET Mathematics paper, you can get about 7 marks per paper by covering Differential Equations. The chapter recorded 245 questions across the 80 shifts in the data, and 110 of them came in the 2025 and 2026 papers, which is about 3 of the 50 Mathematics questions in a typical shift.

MHT CET Differential Equations Chapter: Question Count, Marks and Weightage:

What it shows	Number
Questions in the PDF (2016-2026)	245
Questions in the 2025 and 2026 papers (33 shifts)	110
Questions in the 2018 to 2026 papers (80 shifts)	238
Typical number of Mathematics questions from this topic in one shift	About 3 out of 50
Marks for each question	2

The PDF holds 245 questions from MHT CET 2026 to 2016, newest first, each with its exam date and shift. Options are as printed and answer keys are not included.

Differential Equations PYQ Statistics (2022-2026)

The table below shows the number of questions asked in MHT CET Differential Equations PYQs. Every shift has 50 Mathematics questions, and the last column is the number of questions asked divided by the shifts held, rounded to a whole number.

Year	Questions Asked	Shifts Held	Typical Questions in One Shift
2026	51	16	About 3 out of 50
2025	59	17	About 3 out of 50
2024	40	18	About 2 out of 50
2023	31	12	About 3 out of 50
2022	1	1	About 1 out of 50

The 2018 to 2021 papers in the PDF add 56 more questions: 2021 had 33, 2020 had 14, 2019 had 7, 2018 had 2; the papers before 2018 add 3 from 2017, 4 from 2016.

MHT CET Differential Equations Important Questions: Topic-Wise Breakdown

The major types of questions asked from Differential Equations in MHT CET cover the following topics:

Topic	Questions in the PDF	Share of the PDF
Solution Of Differential Equations By Method Of Separation Variables And Homogeneous	95	39%
Formation Of Differential Equations	29	12%
Order And Degree	28	11%
Linear Differential Equations	17	7%
Linear DE	13	5%
Variable separable	9	4%
Newton's law of cooling	6	2%
Homogeneous DE	6	2%
Other topics tagged in the PDF	42	17%

Pair PYQs with Other Study Material for MHT CET 2027

Click on the link to practise problems and time management skills:

Resource	Link
MHT CET Sample Paper	Check Here
MHT CET Mock Test	Check Here

Question Style in MHT CET Differential Equations PYQs

Every question in this PDF is a single-correct MCQ. Most ask for the solution of a given equation, and the rest are word problems on cooling, decay or a family of curves.

Question Style	What it Tests
General and particular solution	The general solution of a differential equation, and the particular solution when x = e and y = e²
Formation of an equation	The differential equation of the family of parabolas with the focus at the origin and the x-axis as the axis
Curve with a given slope	The equation of the curve passing through a point and having a given slope at that point
Newton's law of cooling	The room temperature when a body cools in 10 minutes to one temperature and in the next 10 minutes to another
Radioactive decay	The amount of radium that is present after 3200 years when its half life is 1600 years

How to Use the Differential Equations PYQ PDF for MHT CET

Start with the 2025 and 2026 papers first, because they hold 110 of the 245 questions.
Identify the type first: variable separable, homogeneous or linear, and use the method for that type.
For cooling and decay problems, write dN/dt = −kN or the cooling equation and use the two given conditions to find the constants.
Solve year-wise PYQs by timing yourself, as time management is crucial.
Re-attempt only the questions you got wrong, and note which formula or step you missed.

Video: Differential Equations PYQs and MCQs

Source: Logic Institute | IIT-JEE, MHT-CET, NEET

Differential Equations PYQ for MHT CET Mathematics FAQs

Ques. How many questions come from Differential Equations every year?

Ans. In this PDF, the questions are 51 from 2026, 59 from 2025, 40 from 2024, 31 from 2023 and 1 from 2022 and the rest from earlier papers. In 2025 and 2026 together the chapter had 110 questions across 33 shifts, which is about 3 in a typical shift.

Ques. Which topics are asked most frequently in MHT CET Differential Equations?

Ans. Solution Of Differential Equations By Method Of Separation Variables And Homogeneous is the largest topic tag in the PDF with 95 of the 245 questions, about 39%.

Ques. What kind of questions are asked from Differential Equations?

Ans. Single-correct MCQs. Common ones ask for the general or particular solution of an equation, the equation of a family of curves, or a cooling or decay problem.

Ques. What is the best way to practise Differential Equations PYQs?

Ans. First solve the 2025 and 2026 questions completely, then the older ones, and finally re-attempt the questions you got wrong.

Ques. Can I score full marks from Differential Equations?

Ans. In 2025 and 2026 together the chapter had 110 questions across 33 shifts. Learning the methods for each type of equation and the cooling and decay models is enough to secure it. Each Mathematics question in MHT CET is worth 2 marks.

Ques. Does the Differential Equations PYQ PDF include solutions?

Ans. No. The PDF contains the questions with their exam date and shift, without answer keys or solutions.

MHT CET PYQs for Differential Equations with Solutions: Practice MHT CET Previous Year Questions

Differential Equations PYQ Statistics (2022-2026)

MHT CET Differential Equations Important Questions: Topic-Wise Breakdown

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Differential Equations PYQs

How to Use the Differential Equations PYQ PDF for MHT CET

Video: Differential Equations PYQs and MCQs

Differential Equations PYQ for MHT CET Mathematics FAQs

1.
If \(tanx\) is an integrating factor of the differential equation \(\frac{dy}{dx}+Py = Q\), then \(P\) can be

2.
The solution of the differential equation \(\frac{dy}{dx} = cos(x+y)\) is...

3.
A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

4.
The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

5.
The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

6.
If the solution of the differential equation \((1+x^3)\frac{dy}{dx}+6x^2y = 1+x^2\) is \(y = \frac{1}{(1+x^3)^s}[x+\frac{x^p}{p}+\frac{x^q}{q}+\frac{x^r}{r}+c]\), then the LCM of \(p,q,r\) and \(s\) is...

7.
The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

8.
A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

9.
The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

10.
The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

11.
The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is \(α\) is... (where p and \(α\) are arbitrary constants)

12.
If \(y = f(x)\) is a monotonically increasing function such that \((\frac{dy}{dx})^2 = 6-\frac{dy}{dx}\) and \(y(0) = 5\), then \(y(3) = \cdots\)

13.
The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

14.
The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

15.
The general solution of the differential equation \(\frac{dy}{dx}+\frac{y}{x} = x^2+5\) is ....

Comments

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Differential Equations PYQ Statistics (2022-2026)

MHT CET Differential Equations Important Questions: Topic-Wise Breakdown

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Differential Equations PYQs

How to Use the Differential Equations PYQ PDF for MHT CET

Video: Differential Equations PYQs and MCQs

Differential Equations PYQ for MHT CET Mathematics FAQs

1.If \(tanx\) is an integrating factor of the differential equation \(\frac{dy}{dx}+Py = Q\), then \(P\) can be

2.The solution of the differential equation \(\frac{dy}{dx} = cos(x+y)\) is...

3.A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

4.The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

5.The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

6.If the solution of the differential equation \((1+x^3)\frac{dy}{dx}+6x^2y = 1+x^2\) is \(y = \frac{1}{(1+x^3)^s}[x+\frac{x^p}{p}+\frac{x^q}{q}+\frac{x^r}{r}+c]\), then the LCM of \(p,q,r\) and \(s\) is...

7.The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

8.A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

9.The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

10.The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

11.The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is \(α\) is... (where p and \(α\) are arbitrary constants)

12.If \(y = f(x)\) is a monotonically increasing function such that \((\frac{dy}{dx})^2 = 6-\frac{dy}{dx}\) and \(y(0) = 5\), then \(y(3) = \cdots\)

13.The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

14.The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

15.The general solution of the differential equation \(\frac{dy}{dx}+\frac{y}{x} = x^2+5\) is ....

Comments

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1.
If \(tanx\) is an integrating factor of the differential equation \(\frac{dy}{dx}+Py = Q\), then \(P\) can be

2.
The solution of the differential equation \(\frac{dy}{dx} = cos(x+y)\) is...

3.
A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

4.
The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

5.
The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

6.
If the solution of the differential equation \((1+x^3)\frac{dy}{dx}+6x^2y = 1+x^2\) is \(y = \frac{1}{(1+x^3)^s}[x+\frac{x^p}{p}+\frac{x^q}{q}+\frac{x^r}{r}+c]\), then the LCM of \(p,q,r\) and \(s\) is...

7.
The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

8.
A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

9.
The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

10.
The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

11.
The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is \(α\) is... (where p and \(α\) are arbitrary constants)

12.
If \(y = f(x)\) is a monotonically increasing function such that \((\frac{dy}{dx})^2 = 6-\frac{dy}{dx}\) and \(y(0) = 5\), then \(y(3) = \cdots\)

13.
The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

14.
The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

15.
The general solution of the differential equation \(\frac{dy}{dx}+\frac{y}{x} = x^2+5\) is ....