Area of the region $\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}$ is

Option 2: $2\pi - \frac{16}{3}$

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q9

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

Area of the region

\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}

(1) $\pi - \frac{8}{3}$
(2) $2\pi - \frac{16}{3}$ Official answer
(3) $\pi + \frac{8}{3}$
(4) $2\pi + \frac{16}{3}$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 10× in all

5 Apr 2026, Shift 1 · Q16The area of the region $R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\}$ is equal to:MediumSingle correct
6 Apr 2026, Shift 1 · Q19The area of the region $\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\}$ is:MediumSingle correct
3 Apr 2025, Shift 2 · Q19The area of the region $\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\}$ isMediumSingle correct
8 Apr 2025, Shift 2 · Q25Let the area of the bounded region $\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\}$ be $A$ . Then $6A$ is equal to __________MediumNumerical value
31 Jan 2024, Shift 1 · Q10The area of the region $\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\}$ isHardSingle correct
6 Apr 2023, Shift 1 · Q26If the area of the region $S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\}$ is equal to $\frac{n+2}{n+1}-\frac{\pi}{n-1}$ , then the natural…HardNumerical value
13 Apr 2023, Shift 2 · Q11The area of the region $\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\}$ isHardSingle correct
25 Jul 2021, Shift 1 · Q63The area (in sq. units) of the region, given by the set $\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^2\le y\le4-2x\}$ is :EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.