JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q13

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

A 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 equal to

(1) $0$
(2) $1$ Official answer
(3) $-1$
(4) $2$

Official answer

Option 2

NTA final key.

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