If the area of the region $\left\{(x,y): x^{\frac{2}{3}}+y^{\frac{2}{3}}\leq1,\ x+y\geq0,\ y\geq0\right\}$ is $A$, then $\frac{256A}{\pi}$ is equal to ___________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

If the area of the region

\left\{(x,y): x^{\frac{2}{3}}+y^{\frac{2}{3}}\leq1,\ x+y\geq0,\ y\geq0\right\}

A

, then

\frac{256A}{\pi}

is equal to ___________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 15× 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
27 Jan 2024, Shift 1 · Q26Let the area of the region $\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\}$ be $\dfrac{m}{n}$ , where m and n are coprime…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
11 Apr 2023, Shift 1 · Q9Area of the region $\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}$ isMediumSingle 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.