JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 August 2021, Shift 1, Maths Q71

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

Let us consider a curve,

y=f(x)

passing through the point

(-2, 2)

and the slope of the tangent to the curve at any point

(x, f(x))

is given by

f(x)+xf'(x)=x^2

. Then :

(1) $x^3-3xf(x)-4=0$ Official answer
(2) $x^2+2xf(x)-12=0$
(3) $x^3+xf(x)+12=0$
(4) $x^2+2xf(x)+4=0$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Exact Differential Recognition in LDEs

Same idea in other shifts

Asked 3× in all

30 Jan 2024, Shift 1 · Q12Let $y=y(x)$ be the solution of the differential equation $\sec x\,dy+\{2(1-x)\tan x+x(2-x)\}dx=0$ such that $y(0)=2$ . Then $y(2)$ is…MediumSingle correct
26 Jun 2022, Shift 2 · Q9If $y = y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y = x e^x$ , $y(1) = 0$ then the local maximum value of the…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 108 of the 174 JEE Main shifts held from 2017 to 2026.