Let the area of the region $\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\}$ be $\dfrac{m}{n}$, where m and n are coprime numbers. Then $m+n$ is equal to ________.

JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

Let the area of the region

\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\}

\dfrac{m}{n}

, where m and n are coprime numbers. Then

m+n

is equal to ________.

Official answer

119

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area of Inequalities

Same idea in other shifts

Asked 15× in all

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3 Apr 2025, Shift 2 · Q19The area of the region $\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\}$ isMediumSingle correct
8 Apr 2025, Shift 2 · Q25Let the area of the bounded region $\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\}$ be $A$ . Then $6A$ is equal to __________MediumNumerical value
31 Jan 2024, Shift 1 · Q10The area of the region $\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\}$ isHardSingle correct
6 Apr 2023, Shift 1 · Q26If the area of the region $S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\}$ is equal to $\frac{n+2}{n+1}-\frac{\pi}{n-1}$ , then the natural…HardNumerical value
11 Apr 2023, Shift 1 · Q9Area of the region $\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}$ isMediumSingle correct
13 Apr 2023, Shift 2 · Q11The area of the region $\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\}$ isHardSingle 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.