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Differential Equations MCQs for JEE

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Differential Equations JEE MCQs on Goodmarks include 14+ multiple-choice questions with correct answers and step-by-step solutions. Attempt free samples below or unlock the full bank with Pro.

Master Differential Equations through exam-style multiple-choice questions. This page features 14+ JEE MCQs covering Ordinary differential equations, their order and degree, The solution of differential equation by the method of separation of variables, Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x), each with verified answers and clear explanations.

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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}}}

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Frequently asked questions

What type of Differential Equations MCQs appear in JEE?

JEE Main tests Differential Equations through conceptual and numerical MCQs. Goodmarks mirrors this format with four-option questions and detailed solutions.

How many MCQs should I solve for Differential Equations?

Aim for at least 50–100 MCQs per subtopic. Goodmarks has 14+ questions for Differential Equations to build speed and accuracy.

Are solutions provided for every MCQ?

Yes. Each MCQ shows the correct option, final answer, and a step-by-step explanation after you submit.

Can I filter MCQs by Differential Equations only?

Pro subscribers can filter by subject, unit, and subtopic. Free users get a random mix across all subjects.