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JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q20

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

If a curve

y=y(x)

passes through the point

\left(1,\frac{\pi}{2}\right)

and satisfies the differential equation

\left(7x^4\cot y-e^x\operatorname{cosec}y\right)\frac{dx}{dy}=x^5

,

x\ge1

, then at

x=2

, the value of

\cos y

is :

(1) $\frac{2e^2-e}{64}$
(2) $\frac{2e^2-e}{128}$ Official answer
(3) $\frac{2e^2+e}{64}$
(4) $\frac{2e^2+e}{128}$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 2× in all

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 42 of the 174 JEE Main shifts held from 2017 to 2026.