JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let a curve

y=f(x),\ x\in(0,\infty)

pass through the points

P\left(1,\frac{3}{2}\right)

and

Q\left(a,\frac{1}{2}\right)

. If the tangent at any point

R(b,f(b))

to the given curve cuts the y-axis at the point

S(0,c)

such that

bc=3

, then

(PQ)^2

is equal to ___________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factor Calculation

Same idea in other shifts

Asked 22× in all

4 Apr 2026, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation:…HardSingle correct
3 Apr 2025, Shift 1 · Q20Let $g$ be a differentiable function such that $\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt$ , $x \ge 0$ and let $y = y(x)$ satisfy the…HardSingle correct
4 Apr 2024, Shift 2 · Q12Let $y=y(x)$ be the solution of the differential equation $(x^2+4)^2dy+(2x^3y+8xy-2)dx=0$ . If $y(0)=0$ , then $y(2)$ is equal toHardSingle correct
5 Apr 2024, Shift 1 · Q12If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+2y=\sin(2x)$ , $y(0)=\frac34$ , then $y\left(\frac{\pi}{8}\right)$ …MediumSingle correct
5 Apr 2024, Shift 1 · Q26Let $f$ be a differentiable function in the interval $(0,\infty)$ such that $f(1)=1$ and $\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1$ for…HardNumerical value
6 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+x^2)\frac{dy}{dx}+y=e^{\tan^{-1}x}$ , $y(1)=0$ . Then $y(0)$ isMediumSingle correct
1 Feb 2024, Shift 1 · Q28If $x=x(t)$ is the solution of the differential equation $(t+1)dx=(2x+(t+1)^4)dt$ , $x(0)=2$ , then, $x(1)$ equals __________.MediumNumerical value
30 Jan 2024, Shift 1 · Q26Let $y=y(x)$ be the solution of the differential equation $(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx$ , $-1<x<1$ , $y(0)=0$ . If…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.