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Friday, 9 October

JEE Main Maths · Application of Integrals

Area of Inequalities

Area of Inequalities (Application of Integrals) was asked 10 times in 10 JEE Main shifts, 2017–2026, out of the 42 shifts Lumi analysed. 2 of the 10 had a numerical answer.

Times asked
10
in 10 shifts
Years
2017–2026
Usual format
Single correct
Multi-step
Pattern
Asked most years
repeats across shifts

How it is asked

  • Area of region defined by inequalities
  • Area of region from system of inequalities

Difficulty

Easy 1Medium 5Hard 4

Where it sits

Chapter: Application of Integrals. Topic: Area Under Curves, 41 questions over 15 ideas.

Other repeat ideas in this topic

Every time it came

All 10 questions

Newest first, each with its options and official answer.

  1. 5 Apr 2026, Shift 1 · Q16The area of the region R={(x,y):xy≤27, 1≤y≤x2}R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\} is equal to:MediumSingle correct
  2. 6 Apr 2026, Shift 1 · Q19The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\} is:MediumSingle correct
  3. 3 Apr 2025, Shift 2 · Q19The area of the region {(x,y):∣x−y∣≤y≤4x}\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\} isMediumSingle correct
  4. 8 Apr 2025, Shift 2 · Q25Let the area of the bounded region {(x,y):0≤9x≤y2,y≥3x−6}\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\} be AA. Then 6A6A is equal to __________MediumNumerical value
  5. 31 Jan 2024, Shift 1 · Q10The area of the region {(x,y):y2≤4x, x<4, xy(x−1)(x−2)(x−3)(x−4)>0, x≠3}\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. 6 Apr 2023, Shift 1 · Q26If the area of the region S={(x,y):2y−y2≤x2≤2y, x≥y}S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\} is equal to n+2n+1−πn−1\frac{n+2}{n+1}-\frac{\pi}{n-1}, then the natural…HardNumerical value
  7. 11 Apr 2023, Shift 1 · Q9Area of the region {(x,y):x2+(y−2)2≤4, x2≥2y}\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\} isMediumSingle correct
  8. 13 Apr 2023, Shift 2 · Q11The area of the region {(x,y):x2≤y≤∣x2−4∣, y≥1}\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\} isHardSingle correct
  9. 25 Jul 2021, Shift 1 · Q63The area (in sq. units) of the region, given by the set {(x,y)∈R×R∣x≥0, 2x2≤y≤4−2x}\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^2\le y\le4-2x\} is :EasySingle correct
  10. 2 Apr 2017 (offline) · Q76The area (in sq. units) of the region {(x,y):x≥0, x+y≤3, x2≤4y and y≤1+x}\{(x,y):x\geq0,\ x+y\leq3,\ x^2\leq4y\ \text{and}\ y\leq1+\sqrt{x}\} is :HardSingle correct