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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 7+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

Subtopics in Differential Equations

  • 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)

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Q1MathsUnit 9: Differential Equations
The order and degree of the differential equation, (d2ydx2)3=sin⁡y+3x\left(\frac{d^{2} y}{d x^{2}}\right)^{3}=\sin y+3 x \quad are
Q2MathsUnit 9: Differential Equations
Assertion A normal is drawn at a point P(x,y)\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) of a\mathbf{a} curve. It meets the xx -axis and the yy -axis in point AA and BB, respectively, such that 1OA+1OB=1,\frac{1}{O A}+\frac{1}{O B}=1, where OO is the origin. The equation of such a curve passing through (5,4)(\mathbf{5}, \mathbf{4}) is (x−1)2+(x-1)^{2}+ (y−1)2=25(y-1)^{2}=25 Reason OA=x+ydydx\boldsymbol{O A}=\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} and OB=x+ydydxdydx\boldsymbol{O} \boldsymbol{B}=\frac{\boldsymbol{x}+\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}}{\frac{d \boldsymbol{y}}{d \boldsymbol{x}}}
Q3MathsUnit 9: Differential Equations
Assertion The order of the differential equation, of which xy=cex+be−x+x2\boldsymbol{x} \boldsymbol{y}=\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{b} \boldsymbol{e}^{-\boldsymbol{x}}+\boldsymbol{x}^{\boldsymbol{2}} is a solution, is 2 Reason The differential equation is xd2ydx2+x \frac{d^{2} y}{d x^{2}}+ 2dydx−xy+x2−2=02 \frac{d y}{d x}-x y+x^{2}-2=0
Q4MathsUnit 9: Differential Equations
The differential equation corresponding to xy=c2,x y=c^{2}, where cc is an arbitrary constant, is:
Q5MathsUnit 9: Differential Equations
Order and degree of (x2+2x)y22+(x2−2)y13−2(x+\left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+ 3)y=0\mathbf{3}) \boldsymbol{y}=\mathbf{0} are:
Q6MathsUnit 9: Differential Equations
Consider the following statements: 1. The general solution of dydx=f(x)+\frac{d y}{d x}=f(x)+ xx is of the form y=g(x)+c,y=g(x)+c, where cc is an arbitrary constant. 2. The degree of (dydx)2=f(x)\left(\frac{d y}{d x}\right)^{2}=f(x) is 2 Which of the above statements is/are correct?
Q7MathsUnit 9: Differential Equations
A certain radioactive material is known to decay at a rate proportional to the amount present. If after one hour it is observed that 10 percent of the material has decayed, find the half-life (period of time it takes for the amount of material to decrease by half) of the material (in hrs.)

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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 7+ 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).

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