JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let the locus of the centre

(\alpha,\beta)

\beta>0

, of the circle which touches the circle

x^2+(y-1)^2=1

externally and also touches the

x

-axis be

L

. Then the area bounded by

L

and the line

y=4

is :

(1) $\frac{32\sqrt{2}}{3}$
(2) $\frac{40\sqrt{2}}{3}$
(3) $\frac{64}{3}$ Official answer
(4) $\frac{32}{3}$

Official answer

Option 3

NTA final key (2022 Session 2).

Chapter: Conic Sections
Topic: Area Under Curves
Idea tested: Area of Locus-Defined Regions

Same topic in other shifts

All Area Under Curves questions

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4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves $x+3y^2=0$ and $x+4y^2=1$ is equal to:EasySingle correct
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
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 · Q19The area of the region $\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\}$ 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 42 of the 174 JEE Main shifts held from 2017 to 2026.