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Sunday, 25 October

JEE Main · Maths · Class 12

Inverse Trigonometric Functions: JEE Main previous year questions

60 questions in 52 of the 108 JEE Main shifts Lumi analysed, asked in 7 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
60
in 52 of 108 shifts · 7 of 8 years
Average a shift
0.4
of 25 Maths · 0.5 since 2024 0.2
Typical range
0.3–0.7
questions a shift; fewest 0.0, most 0.7
Weighted estimate
0.5
model, recent years count more · about 2 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Inverse Trigonometric Functions

Priority

Lower priority

One of the 7 Maths chapters that shared the last fifth of Maths questions in the 108 shifts analysed. How bands are set

Past questions
60in 52 of 108 shifts
Study plan gives it
10 hover 12 months; 8 h over 6
Study this chapter →

Ideas asked most often

  1. Complementary Identities7×
  2. Telescoping Inverse Trig Series5×
  3. Tan-1 Sum and Difference4×
  4. Trig of Sum of Inverse Trig Functions4×
  5. Evaluating Trig of Inverse Trig3×

81 of the 126 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 24% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Inverse Trigonometric Functions at a glance

  1. 01

    76%

    of its 17 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    64%

    of the 126 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    20%

    of its questions asked for a numerical answer, 0.7 times the Maths average.

  4. 04

    27%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240’170.3’200.6’210.7’220.3’230.3’240.6’250.7’26

Raw count: 2017: 0 in 1 shift · 2020: 4 in 12 shifts · 2021: 16 in 24 shifts · 2022: 19 in 24 shifts · 2023: 4 in 12 shifts · 2024: 6 in 18 shifts · 2025: 5 in 8 shifts · 2026: 6 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step55%
  • Numerical answer20%
  • Application13%
  • Calculation10%
  • Two statements2%

Most common asks: count solutions of inverse trig equation (5); sum of telescoping inverse trig series (5); sum of solutions of inverse trig equation (3).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#66
of 70 by weighted estimate
Rank in Maths
#21
of 21 chapters
Share of Maths
1.7%
of its questions, all shifts analysed
Busiest year
2022
0.7 questions a shift
Year to year
Swings a lot
varies by about 0.2 questions a shift
Long-run direction
+0.06
questions a shift, per year
Easy questions
8%
27% rated hard
Numerical answer
20%
0.7× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
10 h
8 h on a 6-month plan
Marks per study hour
0.20
#67 of 70 chapters
Foundation for others
16%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 2017
  • 20204
  • 202116
  • 202219
  • 20234
  • 20246
  • 20255
  • 20266
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step68%
  • Calculation17%
  • Application15%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 126 ideas. In the 108 shifts analysed, JEE Main built a question around 33 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
33
Touched on in a question
12
Never asked
81

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker.

’17’20’21’22’23’24’25’26
016+questions in that year’s analysed shifts, shaded per shift

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open45 · 75%311162634

    22 ideas inside

    • OpenRepeated7 · 16%232
    • OpenRepeated5 · 11%2
    • OpenRepeated4 · 9%2
    • OpenRepeated4 · 9%2
    • OpenRepeated3 · 7%2
    • OpenRepeated3 · 7%
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
  • Open11 · 18%432
  • Open4 · 7%2

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 29 different ideas were tested; 13 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 60 Inverse Trigonometric Functions questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 20266 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

JEE Main 20255 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

JEE Main 20246 questions

  1. 4 Apr 2024, Shift 2 · Q20Given that the inverse trigonometric function assumes principal values only. Let xx, yy be any two real numbers in [−1,1][-1,1] such that…HardSingle correct
  2. 6 Apr 2024, Shift 1 · Q30For n∈Nn \in \mathbb{N}, if cot⁡−13+cot⁡−14+cot⁡−15+cot⁡−1n=π4\cot^{-1}3+\cot^{-1}4+\cot^{-1}5+\cot^{-1}n=\frac{\pi}{4}, then nn is equal to __________.MediumNumerical value
  3. 9 Apr 2024, Shift 2 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
  4. 1 Feb 2024, Shift 1 · Q20If tan⁡A=1x(x2+x+1)\tan A=\frac{1}{\sqrt{x(x^2+x+1)}}, tan⁡B=xx2+x+1\tan B=\frac{\sqrt{x}}{\sqrt{x^2+x+1}} and tan⁡C=(x−3+x−2+x−1)1/2\tan C=\left(x^{-3}+x^{-2}+x^{-1}\right)^{1/2},…MediumSingle correct
  5. 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
  6. 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

JEE Main 20234 questions

  1. 10 Apr 2023, Shift 2 · Q21If the domain of the function f(x)=sec⁡−1(2x5x+3)f(x) = \sec^{-1}\left(\frac{2x}{5x+3}\right) is [α,β)∪(γ,δ][\alpha, \beta) \cup (\gamma, \delta], then…MediumNumerical value
  2. 13 Apr 2023, Shift 1 · Q30If…HardNumerical value
  3. 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
  4. 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

JEE Main 202219 questions

  1. 25 Jul 2022, Shift 2 · Q30Let x=sin⁡(2tan⁡−1α)x=\sin\left(2\tan^{-1}\alpha\right) and y=sin⁡(12tan⁡−143)y=\sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right). If…MediumNumerical value
  2. 26 Jul 2022, Shift 1 · Q19tan⁡(2tan⁡−115+sec⁡−152+2tan⁡−118)\tan\left(2\tan^{-1}\frac{1}{5} + \sec^{-1}\frac{\sqrt{5}}{2} + 2\tan^{-1}\frac{1}{8}\right) is equal to :MediumSingle correct
  3. 26 Jul 2022, Shift 2 · Q16If 0<x<120<x<\frac{1}{\sqrt{2}} and sin⁡−1xα=cos⁡−1xβ\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}, then a value of…MediumSingle correct
  4. 27 Jul 2022, Shift 1 · Q21For k∈Rk \in \mathbb{R}, let the solutions of the equation…HardNumerical value
  5. 28 Jul 2022, Shift 1 · Q2Considering only the principal values of the inverse trigonometric functions, the domain of the function…EasySingle correct
  6. 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
  7. 30 Jul 2022, Shift 2 · Q90Let…HardNumerical value
  8. 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
  9. 24 Jun 2022, Shift 2 · Q1Let x∗y=x2+y3x*y = x^2 + y^3 and (x∗1)∗1=x∗(1∗1)(x*1)*1 = x*(1*1). Then a value of 2sin⁡−1(x4+x2−2x4+x2+2)2\sin^{-1}\left(\frac{x^4+x^2-2}{x^4+x^2+2}\right) isMediumSingle correct
  10. 25 Jun 2022, Shift 2 · Q19The value of tan⁡−1(cos⁡(15π4)−1sin⁡(π4))\tan^{-1}\left(\frac{\cos\left(\frac{15\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right) is equal to :EasySingle correct
  11. 26 Jun 2022, Shift 1 · Q19Let f(x)=2cos⁡−1x+4cot⁡−1x−3x2−2x+10f(x) = 2\cos^{-1}x + 4\cot^{-1}x - 3x^2 - 2x + 10, x∈[−1,1]x \in [-1, 1]. If [a,b][a, b] is the range of the function ff, then 4a−b4a - b is…MediumSingle correct
  12. 26 Jun 2022, Shift 2 · Q19If the inverse trigonometric functions take principal values, then…EasySingle correct
  13. 27 Jun 2022, Shift 1 · Q19sin⁡−1(sin⁡2π3)+cos⁡−1(cos⁡7π6)+tan⁡−1(tan⁡3π4)\sin^{-1}\left(\sin\frac{2\pi}{3}\right)+\cos^{-1}\left(\cos\frac{7\pi}{6}\right)+\tan^{-1}\left(\tan\frac{3\pi}{4}\right) is equal to :EasySingle correct
  14. 27 Jun 2022, Shift 2 · Q18The value of cot⁡(∑n=150tan⁡−1(11+n+n2))\cot\left(\sum_{n=1}^{50}\tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right) isMediumSingle correct
  15. 28 Jun 2022, Shift 2 · Q18The value of lim⁡n→∞6tan⁡{∑r=1ntan⁡−1(1r2+3r+3)}\lim_{n\to\infty} 6\tan\left\{\sum_{r=1}^{n}\tan^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\} is equal to :MediumSingle correct
  16. 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
  17. 29 Jun 2022, Shift 1 · Q26…MediumNumerical value
  18. 30 Jun 2022, Shift 1 · Q10Let m and M respectively be the minimum and the maximum values of f(x)=sin⁡−12x+sin⁡2x+cos⁡−12x+cos⁡2xf(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x,…MediumSingle correct
  19. 30 Jun 2022, Shift 1 · Q19Let α=tan⁡(5π16sin⁡(2cos⁡−1(15)))\alpha = \tan\left(\frac{5\pi}{16}\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right) and…MediumSingle correct

JEE Main 202116 questions

  1. 26 Aug 2021, Shift 1 · Q68Multiple Angle Inverse ID · Hard · Single correct
  2. 26 Aug 2021, Shift 2 · Q61Sec-1 and Csc-1 Domains · Easy · Single correct
  3. 26 Aug 2021, Shift 2 · Q77Telescoping Inverse Trig Series · Medium · Single correct
  4. 27 Aug 2021, Shift 1 · Q76Complementary Identities · Medium · Single correct
  5. 31 Aug 2021, Shift 2 · Q79Domain Intersection of Multiple Inverse Trig Functions · Hard · Single correct
  6. 24 Feb 2021, Shift 1 · Q90Telescoping Inverse Trig Series · Medium · Numerical value
  7. 24 Feb 2021, Shift 2 · Q74Half-Angle Inverse Trig Evaluations · Medium · Single correct
  8. 25 Feb 2021, Shift 2 · Q79Trig of Sum of Inverse Trig Functions · Medium · Single correct
  9. 26 Feb 2021, Shift 1 · Q76Complementary Identities · Medium · Single correct
  10. 26 Feb 2021, Shift 2 · Q64Tan-1 Sum and Difference · Medium · Single correct
  11. 22 Jul 2021, Shift 2 · Q61Domain Intersection of Multiple Inverse Trig Functions · Medium · Single correct
  12. 16 Mar 2021, Shift 2 · Q78Sine Inverse Sum and Difference · Medium · Single correct
  13. 17 Mar 2021, Shift 1 · Q68Telescoping Series with cot-1 · Medium · Single correct
  14. 17 Mar 2021, Shift 1 · Q80Tan-1 Sum and Difference · Hard · Single correct
  15. 17 Mar 2021, Shift 2 · Q61Inverse Trig with GIF and Fractional Part · Hard · Single correct
  16. 18 Mar 2021, Shift 1 · Q71Domain of Inverse Secant and Cosecant · Medium · Single correct

JEE Main 20204 questions

  1. 8 Jan 2020, Shift 1 · Q69sin^-1(2x/(1+x^2)) Piecewise Conversion · Hard · Single correct
  2. 2 Sep 2020, Shift 1 · Q69Domain of Inverse Trig with Modulus Arguments · Medium · Single correct
  3. 3 Sep 2020, Shift 1 · Q69Sine Inverse Sum and Difference · Medium · Single correct
  4. 5 Sep 2020, Shift 1 · Q69Telescoping Inverse Trig Series · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

More Maths, Class 12

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