JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

Let

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 by the line

x=1

x=e^{\pi}

y=0

and

y=y(x)

\alpha e^{2\pi}+\beta

, then the value of

10(\alpha+\beta)

is equal to ___________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 10× in all

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
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
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.