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Saturday, 31 October

JEE Main · Maths · Application of Integrals

Area of Inequalities

JEE Main asked Area of Inequalities 15 times in 15 of the 108 shifts Lumi analysed, in 2017, 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Area Under Curves, in Application of Integrals (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2022, 2023, 2024, 2025 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 15 shifts
Years
8 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.510.86’170.08’200.03’210.11’220.21’230.09’240.25’250.22’26

Raw count: 2017: 1 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 3 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20262 of 9
  • 20252 of 8
  • 20242 of 18
  • 20233 of 12
  • 20223 of 24
  • 20211 of 24
  • 20201 of 12
  • 20171 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

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

Difficulty

Easy 1Medium 8Hard 6

5 of the 15 questions had a numerical answer.

Every question

All 15 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 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
  2. 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
  3. 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
  4. 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
  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. 27 Jan 2024, Shift 1 · Q26Let the area of the region {(x,y):x−2y+4≥0, x+2y2≥0, x+4y2≤8, y≥0}\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\} be mn\dfrac{m}{n}, where m and n are coprime…MediumNumerical value
  7. 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
  8. 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
  9. 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
  10. 28 Jun 2022, Shift 1 · Q9The area of the region S={(x,y):y2≤8x, y≥2x, x≥1}S=\{(x, y): y^2\le8x,\ y\ge\sqrt{2}x,\ x\ge1\} isMediumSingle correct
  11. 27 Jun 2022, Shift 2 · Q27If the area of the region {(x,y):x23+y23≤1, x+y≥0, y≥0}\left\{(x,y): x^{\frac{2}{3}}+y^{\frac{2}{3}}\leq1,\ x+y\geq0,\ y\geq0\right\} is AA, then 256Aπ\frac{256A}{\pi}…HardNumerical value
  12. 27 Jun 2022, Shift 1 · Q26Let A1={(x,y):∣x∣⩽y2,∣x∣+2y⩽8}A_1 = \{(x, y) : |x| \leqslant y^2, |x|+2y \leqslant 8\} and A2={(x,y):∣x∣+∣y∣⩽k}A_2 = \{(x, y) : |x|+|y| \leqslant k\}. If…HardNumerical value
  13. 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
  14. 3 Sep 2020, Shift 1 · Q61The area (in sq. units) of the region {(x,y):0≤y≤x2+1, 0≤y≤x+1,\{(x,y):0\le y\le x^2+1,\ 0\le y\le x+1, 12≤x≤2}\frac{1}{2}\le x\le2\} is :MediumSingle correct
  15. 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

Shifts: 2 Apr 2017 (offline), 3 Sep 2020, Shift 1, 25 Jul 2021, Shift 1, 27 Jun 2022, Shift 2, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 1, 6 Apr 2023, Shift 1, 11 Apr 2023, Shift 1, 13 Apr 2023, Shift 2, 27 Jan 2024, Shift 1, 31 Jan 2024, Shift 1, 3 Apr 2025, Shift 2, 8 Apr 2025, Shift 2, 5 Apr 2026, Shift 1, 6 Apr 2026, Shift 1.

Same topic

Other ideas in Area Under Curves

Area Under Curves has 24 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas