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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Pre-simplification via Trig Substitution

JEE Main asked Pre-simplification via Trig Substitution 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2021. It belongs to Chain Rule, in Continuity and Differentiability (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2020
last in 2021
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200.03’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 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: multi-step.

  • Derivative of composite inverse trig function
  • Derivative of sum of inverse trig terms

Difficulty

Easy 0Medium 0Hard 2

2 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. 17 Mar 2021, Shift 1 · Q89If f(x)=sin⁡(cos⁡−1(1−22x1+22x))f(x)=\sin\left(\cos^{-1}\left(\frac{1-2^{2x}}{1+2^{2x}}\right)\right) and its first derivative with respect to xx is…HardNumerical value
  2. 2 Sep 2020, Shift 2 · Q72If y=∑k=16kcos⁡−1{35cos⁡kx−45sin⁡kx}y=\sum_{k=1}^{6} k\cos^{-1}\left\{\frac{3}{5}\cos kx-\frac{4}{5}\sin kx\right\}, then dydx\frac{dy}{dx} at x=0x=0 is ________.HardNumerical value

Shifts: 2 Sep 2020, Shift 2, 17 Mar 2021, Shift 1.

Same topic

Other ideas in Chain Rule

Chain Rule has 15 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