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Saturday, 31 October

JEE Main · Maths · Relations and Functions

Inverse Trig Function Domain

JEE Main asked Inverse Trig Function Domain 6 times in 6 of the 108 shifts Lumi analysed, in 2022, 2023, 2024 and 2025. It belongs to Functions and Domain, in Relations and Functions (Maths). The longest wait between two years asking it was 1 year. In 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2022
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.150.30’170’200’210.04’220.07’230.09’240.25’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 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
  • 20252 of 8
  • 20242 of 18
  • 20231 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

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

  • Domain endpoints of inverse trig and log
  • Domain of log plus inverse trig function

Difficulty

Easy 0Medium 5Hard 1

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 8 Apr 2025, Shift 2 · Q21Let the domain of the function f(x)=cos⁡−1(4x+53x−7)f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right) be [α,β][\alpha, \beta] and the domain of…MediumNumerical value
  2. 3 Apr 2025, Shift 1 · Q2If the domain of the function f(x)=log⁡e(2x−35+4x)+sin⁡−1(4+3x2−x)f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right) is [α,β)[\alpha, \beta),…MediumSingle correct
  3. 30 Jan 2024, Shift 1 · Q1If the domain of the function f(x)=cos⁡−1(2−∣x∣4)+{log⁡e(3−x)}−1f(x)=\cos^{-1}\left(\frac{2-|x|}{4}\right)+\{\log_e(3-x)\}^{-1} is [−α,β)−{γ}[-\alpha,\beta)-\{\gamma\}, then…MediumSingle correct
  4. 4 Apr 2024, Shift 1 · Q1If the domain of the function sin⁡−1(3x−222x−19)+log⁡e(3x2−8x+5x2−3x−10)\sin^{-1}\left(\frac{3x-22}{2x-19}\right)+\log_e\left(\frac{3x^2-8x+5}{x^2-3x-10}\right) is…MediumSingle correct
  5. 15 Apr 2023, Shift 1 · Q1If the domain of the function f(x)=log⁡e(4x2+11x+6)+sin⁡−1(4x+3)+cos⁡−1(10x+63)f(x)=\log_e\left(4x^2+11x+6\right)+\sin^{-1}(4x+3)+\cos^{-1}\left(\frac{10x+6}{3}\right) is…MediumSingle correct
  6. 27 Jul 2022, Shift 2 · Q1The domain of the function f(x)=sin⁡−1[2x2−3]+log⁡2(log⁡12(x2−5x+5))f(x) = \sin^{-1}[2x^2 - 3] + \log_2\left(\log_{\frac{1}{2}}(x^2 - 5x + 5)\right), where [t] is the greatest…HardSingle correct

Shifts: 27 Jul 2022, Shift 2, 15 Apr 2023, Shift 1, 30 Jan 2024, Shift 1, 4 Apr 2024, Shift 1, 3 Apr 2025, Shift 1, 8 Apr 2025, Shift 2.

Same topic

Other ideas in Functions and Domain

Functions and Domain has 20 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas