JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let

y = y(x)

be the solution curve of the differential equation

\sin\left(2x^2\right)\log_e\left(\tan x^2\right)dy + \left(4xy - 4\sqrt{2}\,x\sin\left(x^2 - \dfrac{\pi}{4}\right)\right)dx = 0

0 < x < \sqrt{\dfrac{\pi}{2}}

, which passes through the point

\left(\sqrt{\dfrac{\pi}{6}}, 1\right)

. Then

\left|y\left(\sqrt{\dfrac{\pi}{3}}\right)\right|

is equal to ________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Particular Solution Solving

Same idea in other shifts

Asked 11× in all

5 Apr 2026, Shift 2 · Q25Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx$ ,…HardNumerical value
8 Apr 2026, Shift 2 · Q17Let $y = y(x)$ be the solution of the differential equation $x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0$ ,…MediumSingle correct
4 Apr 2024, Shift 1 · Q26Let the solution $y=y(x)$ of the differential equation $\frac{dy}{dx}-y=1+4\sin x$ satisfy $y(\pi)=1$ . Then…MediumNumerical value
26 Jul 2022, Shift 1 · Q11If $\frac{dy}{dx} + 2y \tan x = \sin x$ , $0 < x < \frac{\pi}{2}$ and $y\left(\frac{\pi}{3}\right) = 0$ , then the maximum value of $y(x)$ …MediumSingle correct
26 Jul 2022, Shift 2 · Q10Let the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ , $x\in(-1,1)$ …HardSingle correct
29 Jul 2022, Shift 2 · Q10Let $y=y(x)$ be the solution curve of the differential equation…HardSingle correct
26 Jun 2022, Shift 1 · Q25Let the solution curve $y = y(x)$ of the differential equation $(4 + x^2)\,dy - 2x(x^2 + 3y + 4)\,dx = 0$ pass through the origin. Then…MediumNumerical value
22 Jul 2021, Shift 2 · Q70Let $y=y(x)$ be the solution of the differential equation $\mathrm{cosec}^2x\,dy+2dx=(1+y\cos2x)\,\mathrm{cosec}^2x\,dx$ , with…MediumSingle 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.