JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

The area of the region

\{(x, y) : |x - 1| \leq y \leq \sqrt{5 - x^2}\}

is equal to :

(1) $\frac{5}{2}\sin^{-1}\left(\frac{3}{5}\right) - \frac{1}{2}$
(2) $\frac{5\pi}{4} - \frac{3}{2}$
(3) $\frac{3\pi}{4} + \frac{3}{2}$
(4) $\frac{5\pi}{4} - \frac{1}{2}$ Official answer

Official answer

Option 4

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

2 Apr 2025, Shift 1 · Q21If the area of the region $\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}$ is…HardNumerical value
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
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.