JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2024, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

y=y(x)

be the solution of the differential equation

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

y(1)=0

. Then

y(0)

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

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factor Calculation

Same idea in other shifts

Asked 22× in all

4 Apr 2026, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation:…HardSingle correct
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4 Apr 2024, Shift 2 · Q12Let $y=y(x)$ be the solution of the differential equation $(x^2+4)^2dy+(2x^3y+8xy-2)dx=0$ . If $y(0)=0$ , then $y(2)$ is equal toHardSingle correct
5 Apr 2024, Shift 1 · Q12If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+2y=\sin(2x)$ , $y(0)=\frac34$ , then $y\left(\frac{\pi}{8}\right)$ …MediumSingle correct
5 Apr 2024, Shift 1 · Q26Let $f$ be a differentiable function in the interval $(0,\infty)$ such that $f(1)=1$ and $\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1$ for…HardNumerical value
1 Feb 2024, Shift 1 · Q28If $x=x(t)$ is the solution of the differential equation $(t+1)dx=(2x+(t+1)^4)dt$ , $x(0)=2$ , then, $x(1)$ equals __________.MediumNumerical value
30 Jan 2024, Shift 1 · Q26Let $y=y(x)$ be the solution of the differential equation $(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx$ , $-1<x<1$ , $y(0)=0$ . If…MediumNumerical value
6 Apr 2023, Shift 2 · Q25Let a curve $y=f(x),\ x\in(0,\infty)$ pass through the points $P\left(1,\frac{3}{2}\right)$ and $Q\left(a,\frac{1}{2}\right)$ . If the…HardNumerical 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.