JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

Let

y=y(x)

be the solution of the differential equation

\frac{dy}{dx}=(y+1)\left((y+1)e^{x^2/2}-x\right)

0<x<2.1

, with

y(2)=0

. Then the value of

\frac{dy}{dx}

x=1

is equal to :

(1) $\frac{e^{5/2}}{(1+e^2)^2}$
(2) $-\frac{2e^2}{(1+e^2)^2}$
(3) $\frac{5e^{1/2}}{(e^2+1)^2}$
(4) $\frac{-e^{3/2}}{(e^2+1)^2}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Bernoulli Equation Reduction

Same idea in other shifts

Asked 4× in all

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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.