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Mathematics · JEE

Differential Equations Previous Year Questions for JEE

7+ syllabus-aligned questions available

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Goodmarks offers 7+ 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 7+ exam-pattern MCQs modelled on JEE Main and Advanced, with full solutions for every question.

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

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.

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