JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 9 April 2024, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

The area (in square units) of the region enclosed by the ellipse

x^2+3y^2=18

in the first quadrant below the line

y=x

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

Official answer

Option 1

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Ellipse Segment Area via Eccentric Angle

Same topic in other shifts

All Area Under Curves questions

2 Apr 2026, Shift 2 · Q24If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$ , then $3(A + 6\log_e(3))$ is equal toHardNumerical value
4 Apr 2026, Shift 1 · Q18The area of the region $\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\}$ is:HardSingle correct
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.