JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let

y=y(x)

be the solution of the differential equation

\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx

-1<x<1

, and

y(0)=0

. If

\int_{-\frac{1}{2}}^{\frac{1}{2}}\sqrt{1-x^2}\,y(x)dx=k

, then

k^{-1}

is equal to ___________.

Official answer

320

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factors with Trigonometric Functions

Same idea in other shifts

Asked 7× in all

2 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution curve of the differential equation $(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ , $y(0)=0$ . If the curve $y=y(x)$ …MediumSingle correct
2 Apr 2025, Shift 2 · Q25Let $y = y(x)$ be the solution of the differential equation…MediumNumerical value
3 Apr 2025, Shift 2 · Q20Let $y = y(x)$ be the solution of the differential equation…MediumSingle correct
29 Jan 2024, Shift 1 · Q13A function $y=f(x)$ satisfies $f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0$ with condition $f(0)=0$ . Then, $f\left(\frac{\pi}{2}\right)$ is…MediumSingle correct
31 Jan 2024, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation…HardSingle correct
28 Jul 2022, Shift 1 · Q10If $y=y(x),\ x\in(0,\pi/2)$ be the solution curve of the differential equation…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.