JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let

f(x) = x - 1

and

g(x) = e^x

for

x \in \mathbb{R}

. If

\frac{dy}{dx} = \left(e^{-2\sqrt{x}}\, g\big(f(f(x))\big) - \frac{y}{\sqrt{x}}\right)

y(0) = 0

, then

y(1)

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

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Standard Linear Form Identification

Same idea in other shifts

Asked 4× in all

24 Feb 2021, Shift 2 · Q78If a curve $y=f(x)$ passes through the point (1, 2) and satisfies $x\frac{dy}{dx}+y=bx^4$ , then for what value of b,…MediumSingle correct
17 Mar 2021, Shift 2 · Q67If the curve $y=y(x)$ is the solution of the differential equation $2(x^2+x^{5/4})dy-y(x+x^{1/4})dx=2x^{9/4}dx$ , $x>0$ which passes…HardSingle correct
6 Sep 2020, Shift 2 · Q63If $y=\left(\frac{2}{\pi}x-1\right)\mathrm{cosec}\,x$ is the solution of the differential equation,…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.