If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^2 - 4x + y + 8}{x - 2}$, then this curve also passes through the point :

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 February 2021, Shift 1, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

If a curve passes through the origin and the slope of the tangent to it at any point

(x, y)

\frac{x^2 - 4x + y + 8}{x - 2}

, then this curve also passes through the point :

(1)(4, 5)
(2)(5, 5)Official answer
(3)(5, 4)
(4)(4, 4)

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: General Solution Formula

Same idea in other shifts

Asked 3× in all

7 Apr 2025, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation $(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x$ , $y(0)=1$ . Then $\int_{-3}^{3}y(x)\,dx$ is :MediumSingle correct
5 Apr 2024, Shift 2 · Q26Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + \frac{2x}{(1+x^2)^2}\,y = x e^{\frac{1}{(1+x^2)}}$ ;…MediumNumerical 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.