JEE Main 2026 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q25

Question 25 of 75 in this shift, Maths question 25 of 25, Section B.

Let

y = y(x)

be the solution of the differential equation

x\sin\left(\frac{y}{x}\right)dy = \left(y\sin\left(\frac{y}{x}\right) - x\right)dx

y(1) = \frac{\pi}{2}

, and let

\alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right)

. Then the number of integral values of

p

, for which the equation

x^2 + y^2 - 2px + 2py + \alpha + 2 = 0

represents a circle of radius

r \leq 6

, is ________.

Official answer

Any non -negative Integer

NTA final key.

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Substitution y = vx

Same idea in other shifts

Asked 10× in all

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
10 Apr 2023, Shift 1 · Q10The slope of tangent at any point $(x,y)$ on a curve $y=y(x)$ is $\frac{x^2+y^2}{2xy}$ , $x>0$ . If $y(2)=0$ , then a value of $y(8)$ isMediumSingle correct
25 Jul 2022, Shift 2 · Q25Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\ y(1)=1$ . If for some…MediumNumerical value
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
28 Jun 2022, Shift 1 · Q10Let the solution curve $y=y(x)$ of the differential equation…HardSingle correct
29 Jun 2022, Shift 1 · Q2Let the solution curve of the differential equation $x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}$ , $y(1) = 3$ be $y = y(x)$ . Then $y(2)$ is…MediumSingle correct
18 Mar 2021, Shift 2 · Q86Let $y=y(x)$ be the solution of the differential equation $x\,dy-y\,dx=\sqrt{(x^2-y^2)}\,dx$ , $x\ge1$ , with $y(1)=0$ . If the area bounded…HardNumerical value
9 Jan 2020, Shift 2 · Q64If $\frac{dy}{dx}=\frac{xy}{x^2+y^2}$ ; $y(1)=1$ ; then a value of $x$ satisfying $y(x)=e$ is :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.