If the area of the region $\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}$ is $\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)$, $\alpha, \beta\in\mathbf{N}$, then $\alpha+\beta$ is equal to ___________.

JEE Main 2025 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 2 April 2025, Shift 1, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

If the area of the region

\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}

\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)

\alpha, \beta\in\mathbf{N}

, then

\alpha+\beta

is equal to ___________.

Official answer

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area with Modulus

Same idea in other shifts

Asked 7× in all

5 Apr 2024, Shift 2 · Q12The area enclosed between the curves $y = x|x|$ and $y = x - |x|$ is :MediumSingle correct
6 Apr 2023, Shift 2 · Q14The area bounded by the curves $y=|x-1|+|x-2|$ and $y=3$ is equal toEasySingle correct
10 Apr 2023, Shift 2 · Q26If the area of the region $\{(x, y) : |x^2 - 2| \leq y \leq x\}$ is A, then $6A + 16\sqrt{2}$ is equal to ______.MediumNumerical value
26 Jul 2022, Shift 2 · Q20The area bounded by the curves $y=|x^2-1|$ and $y=1$ isMediumSingle correct
29 Jul 2022, Shift 1 · Q16The area of the region $\{(x, y) : |x - 1| \leq y \leq \sqrt{5 - x^2}\}$ is equal to :MediumSingle correct
28 Jun 2022, Shift 2 · Q9The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x$ -axis is :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.