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Saturday, 31 October

JEE Main · Maths · Inverse Trigonometric Functions

Telescoping Inverse Trig Series

JEE Main asked Telescoping Inverse Trig Series 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2026. It belongs to Inverse Trig Identities, in Inverse Trigonometric Functions (Maths). The longest wait between two years asking it was 4 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2020
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210.04’220’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 of 24
  • 20201 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.

  • Sum of telescoping inverse trig series
  • Sum of inverse tangent series

Difficulty

Easy 0Medium 5Hard 0

2 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 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
  2. 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
  3. 24 Feb 2021, Shift 1 · Q90lim⁡n→∞tan⁡{∑r=1ntan⁡−1(11+r+r2)}\lim_{n \to \infty} \tan\left\{\sum_{r=1}^{n} \tan^{-1}\left(\frac{1}{1 + r + r^2}\right)\right\} is equal to ___________.MediumNumerical value
  4. 26 Aug 2021, Shift 2 · Q77If ∑r=150tan⁡−112r2=p\sum_{\mathrm{r}=1}^{50}\tan^{-1}\frac{1}{2\mathrm{r}^2}=\mathrm{p}, then the value of tan⁡p\tan\mathrm{p} is :MediumSingle correct
  5. 5 Sep 2020, Shift 1 · Q69If S is the sum of the first 10 terms of the series…MediumSingle correct

Shifts: 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 1, 26 Aug 2021, Shift 2, 28 Jun 2022, Shift 2, 5 Apr 2026, Shift 1.

Same topic

Other ideas in Inverse Trig Identities

Inverse Trig Identities has 25 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas