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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Second Derivative of Composite Functions

JEE Main asked Second Derivative of Composite Functions 2 times in 2 of the 108 shifts Lumi analysed, in 2023 and 2024. 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
2023
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200’210’220.07’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20231 of 12
  • 20220 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.

  • Derivatives of trig quotient at a point
  • Second derivative of trigonometric function value

Difficulty

Easy 0Medium 0Hard 2

Every question was multiple choice.

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. 5 Apr 2024, Shift 2 · Q20If y(θ)=2cos⁡θ+cos⁡2θcos⁡3θ+4cos⁡2θ+5cos⁡θ+2y(\theta) = \frac{2\cos\theta + \cos 2\theta}{\cos 3\theta + 4\cos 2\theta + 5\cos\theta + 2}, then at θ=π2\theta = \frac{\pi}{2},…HardSingle correct
  2. 8 Apr 2023, Shift 1 · Q19Let f(x)=sin⁡x+cos⁡x−2sin⁡x−cos⁡xf(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x∈[0,π]−{π4}x\in[0,\pi]-\left\{\frac{\pi}{4}\right\}. Then…HardSingle correct

Shifts: 8 Apr 2023, Shift 1, 5 Apr 2024, Shift 2.

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