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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

L'Hopital with Inverse Trigonometric Functions

JEE Main asked L'Hopital with Inverse Trigonometric Functions 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Left and right limits with fractional part
  • Limit with inverse trig substitution

Difficulty

Easy 0Medium 1Hard 1

1 of the 2 questions had a numerical answer.

Every question

All 2 questions

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

  1. 1 Feb 2024, Shift 1 · Q26Let {x}\{x\} denote the fractional part of xx and f(x)=cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3f(x)=\frac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x≠0x\neq0. If L and…HardNumerical value
  2. 26 Jun 2022, Shift 1 · Q6lim⁡x→12sin⁡(cos⁡−1x)−x1−tan⁡(cos⁡−1x)\lim_{x \to \frac{1}{\sqrt{2}}} \frac{\sin(\cos^{-1}x) - x}{1 - \tan(\cos^{-1}x)} is equal to :MediumSingle correct

Shifts: 26 Jun 2022, Shift 1, 1 Feb 2024, Shift 1.

Same topic

Other ideas in L'Hopital's Rule

L'Hopital's Rule has 18 ideas JEE Main has asked; 9 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas