JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

If the solution curve

y=y(x)

of the differential equation

(1+y^2)(1+\log_e x)dx+x\,dy=0

x>0

passes through the point

(1,1)

and

y(e)=\frac{\alpha-\tan\left(\frac{3}{2}\right)}{\beta+\tan\left(\frac{3}{2}\right)}

, then

\alpha+2\beta

is ______.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Initial Value Problem

Same idea in other shifts

Asked 7× in all

4 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(1+x+x^2)(1-y+y^2)$ , $y(0)=\frac12$ . Then $(2y(1)-1)$ is equal toMediumSingle correct
8 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . Then…MediumSingle correct
9 Apr 2024, Shift 1 · Q11The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$ , passing through the point $(0,1)$ is a conic, whose…MediumSingle correct
8 Jan 2020, Shift 1 · Q62Let $y=y(x)$ be a solution of the differential equation, $\sqrt{1-x^2}\,\dfrac{dy}{dx}+\sqrt{1-y^2}=0$ , $|x|<1$ . If…MediumSingle correct
2 Sep 2020, Shift 1 · Q63Let $y=y(x)$ be the solution of the differential equation, $\frac{2+\sin x}{y+1}\cdot\frac{dy}{dx}=-\cos x,\ y>0,\ y(0)=1$ . If $y(\pi)=a$ …MediumSingle correct
2 Apr 2017 (offline) · Q77If $(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$ , then $y\left(\frac{\pi}{2}\right)$ is equal to :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 42 of the 174 JEE Main shifts held from 2017 to 2026.