JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

If 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 the points

(1,0)

and

(\alpha,2)

, then

\alpha^\alpha

is equal to

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

Official answer

Option 4

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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8 Apr 2024, Shift 2 · Q13Let $y = y(x)$ be the solution curve of the differential equation $\sec y \frac{dy}{dx} + 2x\sin y = x^3\cos y$ , $y(1) = 0$ . Then…MediumSingle correct
26 Aug 2021, Shift 2 · Q68Let $y(x)$ be the solution of the differential equation $2x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0$ , $x>0$ . If $y(\mathrm{e})=1$ ,…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.