JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2024, Shift 2, Maths Q13

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

Suppose the solution of the differential equation

\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}

represents a circle passing through origin. Then the radius of this circle is :

(1) $\frac{\sqrt{17}}{2}$ Official answer
(2)2
(3) $\sqrt{17}$
(4) $\frac{1}{2}$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Shift of Origin Method for Reducible Equations

Same topic in other shifts

All Homogeneous Equations questions

2 Apr 2026, Shift 2 · Q20Let $x = x(y)$ be the solution of the differential equation $2y^2\frac{dx}{dy} - 2xy + x^2 = 0, y > 1, x(e) = e$ . Then $x(e^2)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q25Let $y = y(x)$ be the solution of the differential equation…HardNumerical value
9 Apr 2024, Shift 1 · Q10The solution of the differential equation $(x^2+y^2)dx-5xy\,dy=0$ , $y(1)=0$ , is :MediumSingle correct
31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation $y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0$ passing through the point $(e,1)$ isMediumSingle correct
25 Jul 2022, Shift 1 · Q11The general solution of the differential equation $(x-y^2)\,dx+y(5x+y^2)\,dy=0$ is :HardSingle correct
28 Jul 2022, Shift 1 · Q1Let the solution curve of the differential equation $x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0$ , intersect the line $x=1$ at $y=0$ and…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.