JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 2, Maths Q63

Question 63 of 75 in this shift, Maths question 13 of 25.

If a curve

y=f(x)

, passing through the point

(1,\,2)

, is the solution of the differential equation,

2x^2\,dy=(2xy+y^2)\,dx

, then

f\left(\frac{1}{2}\right)

is equal to :

(1) $\frac{1}{1+\log_e 2}$ Official answer
(2) $\frac{1}{1-\log_e 2}$
(3) $1+\log_e 2$
(4) $\frac{-1}{1+\log_e 2}$

Official answer

Option 1

NTA final key (Sep 2020).

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
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

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.