JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let

y(x)

be the solution of the differential equation

2x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0

x>0

. If

y(\mathrm{e})=1

, then

y(1)

is equal to :

(1) $2$
(2) $\log_{\mathrm{e}}(2\mathrm{e})$
(3) $\log_{\mathrm{e}}2$ Official answer
(4) $0$

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Generalized Substitution for LDEs

Same idea in other shifts

Asked 6× in all

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6 Apr 2023, Shift 2 · Q12If the solution curve $f(x,y)=0$ of the differential equation $\left(1+\log_e x\right)\frac{dx}{dy}-x\log_e x=e^y,\ x>0$ , passes through…HardSingle correct
26 Feb 2021, Shift 1 · Q84If $y=y(x)$ is the solution of the equation $e^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x$ , $y(0)=0$ ; then…MediumNumerical value
25 Jul 2021, Shift 1 · Q85Let $y=y(x)$ be solution of the following differential equation $e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0$ ,…MediumNumerical value

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.