JEE Main 2024 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 29 January 2024, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

The area (in sq. units) of the part of the circle

x^2+y^2=169

which is below the line

5x-y=13

\frac{\pi\alpha}{2\beta}-\frac{65}{2}+\frac{\alpha}{\beta}\sin^{-1}\left(\frac{12}{13}\right)

, where

\alpha,\beta

are coprime numbers. Then

\alpha+\beta

is equal to ______.

Official answer

171

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area of Ellipse and its Segments

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.