JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2026, Shift 1, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let

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)

passes through the point

\left(\alpha, \frac{-1}{2}\right)

, then a value of

\alpha

is :

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

Official answer

Option 4

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