JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 16 March 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

y=y(x)

is the solution of the differential equation

\frac{dy}{dx}+(\tan x)\,y=\sin x

0\le x\le\frac{\pi}{3}

, with

y(0)=0

, then

y\left(\frac{\pi}{4}\right)

equal to :

(1) $\left(\frac{1}{2\sqrt2}\right)\log_e 2$ Official answer
(2) $\frac12\log_e 2$
(3) $\log_e 2$
(4) $\frac14\log_e 2$

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 3× 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

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.