Mathematics · JEE

Differential Equations Previous Year Questions for JEE

14+ syllabus-aligned questions available

Quick answer

Goodmarks offers 14+ JEE-style PYQs for Differential Equations with detailed solutions. While official past papers rotate yearly, our bank covers the same concepts, difficulty, and question formats tested in JEE Mathematics.

Previous year questions are the fastest way to understand how Differential Equations is tested in JEE. Practise 14+ exam-pattern MCQs modelled on JEE Main and Advanced, with full solutions for every question.

JEE Formula Sheet

36+ important formulas for Differential Equations

View formula sheet

Subtopics in Differential Equations

View Differential Equations formula sheet — 36+ JEE formulas

Free sample questions

Attempt 8 free MCQs for Differential Equations. Unlock 6+ more with Pro.

Unlock full bank

Q1MathsUnit 9: Differential Equations

The order, degree of the differential equation satisfying the relation

\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}})

\left.y \sqrt{1}+x^{2}\right)

Q2MathsUnit 9: Differential Equations

The family of curves represented by

\frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1}

and the family represented by

\frac{\boldsymbol{d} \boldsymbol{y}_{2}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}=\mathbf{0}

Q3MathsUnit 9: Differential Equations

The order and degree of the differential equation,

\left(\frac{d^{2} y}{d x^{2}}\right)^{3}=\sin y+3 x \quad

are

Q4MathsUnit 9: Differential Equations

Solution of the differential equation

\tan y \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0

Q5MathsUnit 9: Differential Equations

\left(1-x y+x^{2} y^{2}\right) d x=x^{2} d y

Q6MathsUnit 9: Differential Equations

The order and degree of the differential equation.

\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x

are respectively.

Q7MathsUnit 9: Differential Equations

The normal at any point

\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y})

\mathbf{a}

curve meets the

x

-axis at

Q

and

N

is the foot of the ordinate at

P

N Q=\frac{x\left(1+y^{2}\right)}{1+x^{2}},

then equation of such curve, given that it passes through the point (3,1) is:

Q8MathsUnit 9: Differential Equations

Assertion A normal is drawn at a point

\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y})

\mathbf{a}

curve. It meets the

x

-axis and the

y

-axis in point

A

and

B

, respectively, such that

\frac{1}{O A}+\frac{1}{O B}=1,

where

O

is the origin. The equation of such a curve passing through

(\mathbf{5}, \mathbf{4})

(x-1)^{2}+

(y-1)^{2}=25

Reason

\boldsymbol{O A}=\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}

and

\boldsymbol{O} \boldsymbol{B}=\frac{\boldsymbol{x}+\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}}{\frac{d \boldsymbol{y}}{d \boldsymbol{x}}}

Want unlimited Differential Equations practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started free View Pro plans

Frequently asked questions

Why practise PYQs for Differential Equations?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

Does Goodmarks have actual JEE past papers?

Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Differential Equations, covering the same topics as previous year papers.

How should I use PYQs for Differential Equations?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

Are PYQ solutions step-by-step?

Yes. Every question includes the correct answer and a detailed explanation showing the reasoning.