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Saturday, 31 October

JEE Main · Maths · Application of Integrals

Area Involving Tangents and Normals

JEE Main asked Area Involving Tangents and Normals 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2023 and 2025. It belongs to Area Under Curves, in Application of Integrals (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210’220.07’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20251 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 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 bounded by tangent, parabola and axis
  • Area bounded by curve tangent and line

Difficulty

Easy 0Medium 3Hard 0

1 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 4 Apr 2025, Shift 2 · Q19A line passing through the point A(−2,0)A(-2,0), touches the parabola P:y2=x−2P:y^2=x-2 at the point B in the first quadrant. The area, of the region…MediumSingle correct
  2. 11 Apr 2023, Shift 2 · Q25If AA is the area in the first quadrant enclosed by the curve C:2x2−y+1=0C : 2x^2 - y + 1 = 0, the tangent to CC at the point (1,3)(1, 3) and the…MediumNumerical value
  3. 27 Aug 2021, Shift 2 · Q71The area of the region bounded by the parabola (y−2)2=(x−1)(y-2)^2 = (x-1), the tangent to it at the point whose ordinate is 3 and the xx-axis is :MediumSingle correct

Shifts: 27 Aug 2021, Shift 2, 11 Apr 2023, Shift 2, 4 Apr 2025, Shift 2.

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