JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

If the solution curve of the differential equation

((\tan^{-1}y)-x)\,dy=(1+y^2)\,dx

passes through the point

(1, 0)

, then the abscissa of the point on the curve whose ordinate is

\tan(1)

, is

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

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Change of Independent Variable to form LDE

Same topic in other shifts

All Linear Differential Equations questions

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6 Apr 2026, Shift 2 · Q18Let $f:\mathbf{R}\to\mathbf{R}$ be such that $f(xy)=f(x)f(y)$ , for all $x,y\in\mathbf{R}$ and $f(0)\neq0$ . Let $g:[1,\infty)\to\mathbf{R}$ …HardSingle correct
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 108 of the 174 JEE Main shifts held from 2017 to 2026.