JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q9

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

The area of the smaller region enclosed by the curves

y^2 = 8x + 4

and

x^2 + y^2 + 4\sqrt{3}x - 4 = 0

is equal to

(1) $\dfrac{1}{3}\left(2 - 12\sqrt{3} + 8\pi\right)$
(2) $\dfrac{1}{3}\left(2 - 12\sqrt{3} + 6\pi\right)$
(3) $\dfrac{1}{3}\left(4 - 12\sqrt{3} + 8\pi\right)$ Official answer
(4) $\dfrac{1}{3}\left(4 - 12\sqrt{3} + 6\pi\right)$

Official answer

Option 3

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area Between Curves

Same idea in other shifts

Asked 22× in all

2 Apr 2026, Shift 2 · Q24If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$ , then $3(A + 6\log_e(3))$ is equal toHardNumerical value
5 Apr 2026, Shift 2 · Q24Let $f:\mathbf{R}\to\mathbf{R}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x$ , $x \in \mathbf{R}$ . Let the maximum…HardNumerical value
6 Apr 2026, Shift 1 · Q20Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\to\{1,e,e^2,e^3\}$ and…HardSingle correct
6 Apr 2026, Shift 2 · Q19The area of the region $\{(x,y): x^2-8x\le y\le -x\}$ is :EasySingle correct
8 Apr 2026, Shift 2 · Q18Let $f : (1, \infty) \to \mathbf{R}$ be a function defined as $f(x) = \frac{x-1}{x+1}$ . Let $f^{i+1}(x) = f\left(f^{i}(x)\right)$ ,…HardSingle correct
7 Apr 2025, Shift 1 · Q19If the area of the region bounded by the curves $y = 4 - \frac{x^2}{4}$ and $y = \frac{x-4}{2}$ is equal to $\alpha$ , then $6\alpha$ equalsEasySingle correct
4 Apr 2024, Shift 1 · Q13One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$ . Let the area of the…HardSingle correct
6 Apr 2024, Shift 1 · Q12Let the area of the region enclosed by the curves $y=3x$ , $2y=27-3x$ and $y=3x-x\sqrt{x}$ be $A$ . Then $10A$ is equal toMediumSingle 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.