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Friday, 9 October

JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2026, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

Let y=y(x)y = y(x) be the solution of the differential equation x1−x2 dy+(y1−x2−xcos⁡−1x)dx=0x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0, x∈(0,1)x \in (0, 1), lim⁡x→1−y(x)=1\lim_{x \to 1^-} y(x) = 1. Then y(12)y\left(\frac{1}{2}\right) equals :
  1. (1)3−π33 - \frac{\pi}{\sqrt{3}}Official answer
  2. (2)4−3 π4 - \sqrt{3}\,\pi
  3. (3)4−2π34 - \frac{2\pi}{\sqrt{3}}
  4. (4)3−π233 - \frac{\pi}{2\sqrt{3}}

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
  1. 5 Apr 2026, Shift 2 · Q25Let y=y(x)y=y(x) be the solution of the differential equation (tan⁡x)1/2 dy=(sec⁡3x−(tan⁡x)3/2 y)dx(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx,…HardNumerical value
  2. 16 Mar 2021, Shift 2 · Q68If y=y(x)y=y(x) is the solution of the differential equation dydx+(tan⁡x) y=sin⁡x\frac{dy}{dx}+(\tan x)\,y=\sin x, 0≤x≤π30\le x\le\frac{\pi}{3}, with y(0)=0y(0)=0, then…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.