JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 1 February 2024, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let

y=y(x)

be the solution of the differential equation

\frac{dy}{dx}=2x(x+y)^3-x(x+y)-1

y(0)=1

. Then,

\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2

equals :

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

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Reducible to Separable

Same idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2dx=dy$ , $y(0)=-2$ . Let the maximum and minimum values of the function…HardNumerical value
25 Jul 2021, Shift 1 · Q62Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=1+xe^{y-x}$ , $-\sqrt2<x<\sqrt2$ , $y(0)=0$ then, the minimum value…HardSingle correct
4 Sep 2020, Shift 2 · Q63The solution of the differential equation $\frac{dy}{dx} - \frac{y+3x}{\log_e (y+3x)} + 3 = 0$ is : (where C is a constant of integration.)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.