JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q65

Question 65 of 90 in this shift, Maths question 5 of 30, Section A.

Let slope of the tangent line to a curve at any point

P(x, y)

be given by

\frac{xy^2+y}{x}

. If the curve intersects the line

x+2y=4

x=-2

, then the value of

y

, for which the point

(3, y)

lies on the curve, is :

(1) $-\frac{4}{3}$
(2) $-\frac{18}{19}$ Official answer
(3) $\frac{18}{35}$
(4) $-\frac{18}{11}$

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Bernoulli Equation Reduction

Same idea in other shifts

Asked 4× in all

31 Jan 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0$ , $0<x<\frac{\pi}{2}$ ,…HardNumerical value
25 Feb 2021, Shift 2 · Q82If the curve, $y = y(x)$ represented by the solution of the differential equation $(2xy^2 - y)dx + x\,dy = 0$ , passes through the…HardNumerical value
18 Mar 2021, Shift 2 · Q69Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(y+1)\left((y+1)e^{x^2/2}-x\right)$ , $0<x<2.1$ , with $y(2)=0$ .…HardSingle 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.