JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

y=y(x),\ x\in(0,\pi/2)

be the solution curve of the differential equation

(\sin^2 2x)\frac{dy}{dx}+(8\sin^2 2x+2\sin 4x)y=2e^{-4x}(2\sin 2x+\cos 2x)

, with

y(\pi/4)=e^{-\pi}

, then

y(\pi/6)

is equal to :

(1) $\frac{2}{\sqrt{3}}e^{-2\pi/3}$ Official answer
(2) $\frac{2}{\sqrt{3}}e^{2\pi/3}$
(3) $\frac{1}{\sqrt{3}}e^{-2\pi/3}$
(4) $\frac{1}{\sqrt{3}}e^{2\pi/3}$

Official answer

Option 1

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 6× 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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.