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Friday, 9 October

JEE Main Maths · Class 12

Inverse Trigonometric Functions: JEE Main previous year questions

Inverse Trigonometric Functions had 25 questions in the 42 JEE Main shifts Lumi analysed, about 0.5 a shift, asked in 20 of 42 shifts. It ranks 20 of 22 Maths chapters by questions; 32% of its questions were hard.

Questions
25
in 20 of 42 shifts
A shift, on average
0.5
of 25 Maths questions
Since 2024
+0.1
0.5 a shift in 2017–23, 0.5 in 2024–26
Numerical answer
5
20% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
0360’172’202’215’222’233’245’256’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 2017
  • 20202
  • 20212
  • 20225
  • 20232
  • 20243
  • 20255
  • 20266
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

3 topics and 20 distinct ideas; 4 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions
Ideas asked most
4 repeat

Study it on Lumi

Inverse Trigonometric Functions: the interactive lesson

Every question

All 25 Inverse Trigonometric Functions questions

Newest first. Each opens with its options and the official answer.

2026 6 questions

  1. 4 Apr 2026, Shift 1 · Q1Let [⋅][\cdot] denote the greatest integer function. If the domain of the function f(x)=cos⁡−1(4x+2[x]3)f(x)=\cos^{-1}\left(\frac{4x+2[x]}{3}\right) is…MediumSingle correct
  2. 5 Apr 2026, Shift 1 · Q24If π4+∑p=111tan⁡−1(2p−11+22p−1)=α\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha, then tan⁡α\tan\alpha is equal to ________.MediumNumerical value
  3. 6 Apr 2026, Shift 1 · Q1Let [⋅][\cdot] denote the greatest integer function. If the domain of the function f(x)=sin⁡−1(x+[x]3)f(x)=\sin^{-1}\left(\frac{x+[x]}{3}\right) is…MediumSingle correct
  4. 6 Apr 2026, Shift 1 · Q13Let 0<α<10<\alpha<1, β=13α\beta=\frac{1}{3\alpha} and tan⁡−1(1−α)+tan⁡−1(1−β)=π4\tan^{-1}(1-\alpha)+\tan^{-1}(1-\beta)=\frac{\pi}{4}. Then 6(α+β)6(\alpha+\beta) is equal to:MediumSingle correct
  5. 6 Apr 2026, Shift 2 · Q13If sin⁡(tan⁡−1(x2))=cot⁡(sin⁡−11−x2)\sin\left(\tan^{-1}\left(x\sqrt{2}\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right), x∈(0,1)x\in(0,1), then the value of xx is :MediumSingle correct
  6. 8 Apr 2026, Shift 2 · Q12Let α=3sin⁡−1(611)\alpha = 3\sin^{-1}\left(\frac{6}{11}\right) and β=3cos⁡−1(49)\beta = 3\cos^{-1}\left(\frac{4}{9}\right), where inverse trigonometric functions…HardTwo statements

2025 5 questions

  1. 2 Apr 2025, Shift 2 · Q23If y=cos⁡(π3+cos⁡−1x2)y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right), then (x−y)2+3y2(x-y)^2 + 3y^2 is equal to __________.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. 4 Apr 2025, Shift 2 · Q1Let the domains of the functions f(x)=log⁡4log⁡3log⁡7(8−log⁡2(x2+4x+5))f(x)=\log_4\log_3\log_7(8-\log_2(x^2+4x+5)) and g(x)=sin⁡−1(7x+10x−2)g(x)=\sin^{-1}\left(\frac{7x+10}{x-2}\right) be…MediumSingle correct
  4. 4 Apr 2025, Shift 2 · Q13The sum of the infinite series…HardSingle correct
  5. 8 Apr 2025, Shift 2 · Q13The value of…HardSingle correct

2024 3 questions

  1. 9 Apr 2024, Shift 2 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
  2. 31 Jan 2024, Shift 1 · Q20For α,β,γ≠0\alpha,\beta,\gamma\neq0, if sin⁡−1α+sin⁡−1β+sin⁡−1γ=π\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi and…HardSingle correct
  3. 31 Jan 2024, Shift 2 · Q20If a=sin⁡−1(sin⁡(5))a=\sin^{-1}(\sin(5)) and b=cos⁡−1(cos⁡(5))b=\cos^{-1}(\cos(5)), then a2+b2a^2+b^2 is equal toMediumSingle correct

2023 2 questions

  1. 13 Apr 2023, Shift 2 · Q1The range of f(x)=4sin⁡−1(x2x2+1)f(x)=4\sin^{-1}\left(\frac{x^2}{x^2+1}\right) isMediumSingle correct
  2. 13 Apr 2023, Shift 2 · Q30For x∈(−1,1]x\in(-1,1], the number of solutions of the equation sin⁡−1x=2tan⁡−1x\sin^{-1}x=2\tan^{-1}x is equal to ______.HardNumerical value

2022 5 questions

  1. 28 Jul 2022, Shift 1 · Q2Considering only the principal values of the inverse trigonometric functions, the domain of the function…EasySingle correct
  2. 28 Jul 2022, Shift 1 · Q4Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation…HardSingle correct
  3. 24 Jun 2022, Shift 1 · Q8The set of all values of k for which (tan⁡−1x)3+(cot⁡−1x)3=kπ3, x∈R(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}, is the interval :HardSingle correct
  4. 29 Jun 2022, Shift 1 · Q15The domain of the function cos⁡−1(2sin⁡−1(14x2−1)π)\cos^{-1}\left(\frac{2\sin^{-1}\left(\frac{1}{4x^2 - 1}\right)}{\pi}\right) is :MediumSingle correct
  5. 29 Jun 2022, Shift 1 · Q26…MediumNumerical value

2021 2 questions

  1. 16 Mar 2021, Shift 2 · Q78Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xx which satisfy…MediumSingle correct
  2. 18 Mar 2021, Shift 1 · Q71The real valued function f(x)=cosec−1xx−[x]f(x)=\dfrac{\mathrm{cosec}^{-1}x}{\sqrt{x-[x]}}, where [x][x] denotes the greatest integer less than or equal to…MediumSingle correct

2020 2 questions

  1. 8 Jan 2020, Shift 1 · Q69Let f(x)=(sin⁡(tan⁡−1x)+sin⁡(cot⁡−1x))2−1f(x)=\left(\sin(\tan^{-1}x)+\sin(\cot^{-1}x)\right)^2-1, ∣x∣>1|x|>1. If…HardSingle correct
  2. 2 Sep 2020, Shift 1 · Q69The domain of the function f(x)=sin⁡−1(∣x∣+5x2+1)f(x)=\sin^{-1}\left(\frac{|x|+5}{x^{2}+1}\right) is (−∞,−a]∪[a,∞)(-\infty, -a]\cup[a, \infty). Then a is equal to :MediumSingle correct

Pattern: Asked most years.