JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2024, Shift 2, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

y = y(x)

be the solution curve of the differential equation

\sec y \frac{dy}{dx} + 2x\sin y = x^3\cos y

y(1) = 0

. Then

y(\sqrt{3})

is equal to :

(1) $\frac{\pi}{12}$
(2) $\frac{\pi}{6}$
(3) $\frac{\pi}{4}$ Official answer
(4) $\frac{\pi}{3}$

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Generalized Substitution for LDEs

Same idea in other shifts

Asked 6× in all

4 Apr 2025, Shift 2 · Q20If a curve $y=y(x)$ passes through the point $\left(1,\frac{\pi}{2}\right)$ and satisfies the differential equation…HardSingle correct
6 Apr 2023, Shift 2 · Q12If the solution curve $f(x,y)=0$ of the differential equation $\left(1+\log_e x\right)\frac{dx}{dy}-x\log_e x=e^y,\ x>0$ , passes through…HardSingle correct
26 Aug 2021, Shift 2 · Q68Let $y(x)$ be the solution of the differential equation $2x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0$ , $x>0$ . If $y(\mathrm{e})=1$ ,…HardSingle correct
26 Feb 2021, Shift 1 · Q84If $y=y(x)$ is the solution of the equation $e^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x$ , $y(0)=0$ ; then…MediumNumerical value
25 Jul 2021, Shift 1 · Q85Let $y=y(x)$ be solution of the following differential equation $e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0$ ,…MediumNumerical value

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.