JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 August 2021, Shift 1, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

x = x(y)

is the solution of the differential equation,

2 \cdot \sqrt{\sin x + \tan^{-1} y} \cdot \frac{dy}{dx} = \left(\cos x + \frac{1}{1 + y^2}\frac{dy}{dx}\right)

satisfying

x(0) = 0

and

x(1) = b

, then

(1) $4 \sin b + \pi = 4$ Official answer
(2) $4 \cos b + \pi = 4$
(3) $2 \sin b + \pi = 2$
(4) $2 \cos b + \pi = 2$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Exact Differential Grouping

Same topic in other shifts

All Variable Separable Form questions

2 Apr 2026, Shift 1 · Q17If the curve $y=f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$ , $x>0$ , then $f(e)$ …EasySingle correct
4 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(1+x+x^2)(1-y+y^2)$ , $y(0)=\frac12$ . Then $(2y(1)-1)$ is equal toMediumSingle correct
4 Apr 2024, Shift 1 · Q14If the solution $y=y(x)$ of the differential equation $(x^4+2x^3+3x^2+2x+2)dy-(2x^2+2x+3)dx=0$ satisfies $y(-1)=-\frac{\pi}{4}$ , then…HardSingle correct
4 Apr 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2dx=dy$ , $y(0)=-2$ . Let the maximum and minimum values of the function…HardNumerical value
6 Apr 2024, Shift 2 · Q26If the solution $y(x)$ of the given differential equation $(e^y+1)\cos x\,dx+e^y\sin x\,dy=0$ passes through the point…EasyNumerical value
8 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . 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 108 of the 174 JEE Main shifts held from 2017 to 2026.