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Online Practice: Differential Equations for JEE

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Sharpen your mathematics preparation with interactive online practice for Differential Equations. Goodmarks offers 14+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

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Subtopics in Differential Equations

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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

How do I practice Differential Equations online for JEE?

Open this page, attempt the free sample MCQs, then sign up on Goodmarks to access the full Differential Equations question bank with topic filters and detailed explanations.

How many Differential Equations questions are available?

Goodmarks currently has 14+ JEE-aligned MCQs for Differential Equations, with more added regularly.

Is this aligned with the JEE Main syllabus?

Yes. All Mathematics questions on Goodmarks are organised by official JEE Main units and subtopics, including 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).

Do I get solutions after each question?

Every question includes the correct answer and a step-by-step explanation. Free users can practise a random mix; Pro unlocks full subject and topic filters.