If the area of the region $\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\}$ is $(\log_e 2)-\frac{1}{7}$ then the value of $7a-3$ is equal to :

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2024, Shift 2, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

If the area of the region

\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\}

(\log_e 2)-\frac{1}{7}

then the value of

7a-3

is equal to :

(1)-1Official answer
(2)0
(3)1
(4)2

Official answer

Option 1

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Finding Unknown Parameters from Area

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.