JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

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 function

z(x) = x^2 y(x) - e^x

x \in \mathbb{R}

is :

(1) $1 - e$
(2) $0$
(3) $\frac{1}{2}$
(4) $\frac{4}{e} - e$ Official answer

Official answer

Option 4

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
27 Aug 2021, Shift 1 · Q71Let 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 $(x, f(x))$ …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.