JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

Let the area enclosed by the solution curve

y = y(x)

of the differential equation

\frac{dy}{dx} + \frac{x-2}{y-b} = 2

, b > 0, y(5) = 0 is

13\pi

. Let

y = y(x)

intersect the

y

-axis at the points

P

and

Q

. If the tangents to

y = y(x)

P

and

Q

meet at

T

, then the area of

\Delta PTQ

(1)13.5Official answer
(2)13
(3)14.5
(4)15

Official answer

Option 1

NTA final key.

Chapter: Application of Integrals
Topic: Variable Separable Form
Idea tested: Implicit Solution Curve Analysis

Same topic in other shifts

All Variable Separable Form questions

2 Apr 2026, Shift 1 · Q17If the curve $y=f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$ , $x>0$ , then $f(e)$ …EasySingle correct
4 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(1+x+x^2)(1-y+y^2)$ , $y(0)=\frac12$ . Then $(2y(1)-1)$ is equal toMediumSingle correct
4 Apr 2024, Shift 1 · Q14If the solution $y=y(x)$ of the differential equation $(x^4+2x^3+3x^2+2x+2)dy-(2x^2+2x+3)dx=0$ satisfies $y(-1)=-\frac{\pi}{4}$ , then…HardSingle correct
4 Apr 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2dx=dy$ , $y(0)=-2$ . Let the maximum and minimum values of the function…HardNumerical value
6 Apr 2024, Shift 2 · Q26If the solution $y(x)$ of the given differential equation $(e^y+1)\cos x\,dx+e^y\sin x\,dy=0$ passes through the point…EasyNumerical value
8 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . Then…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.