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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Existence of Higher Order Derivatives

JEE Main asked Existence of Higher Order Derivatives 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2022 and 2024. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 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
  • 20230 of 12
  • 20221 of 24
  • 20210 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.

  • Higher-order derivative of oscillating piecewise function
  • Derivative relation for inverse trig function

Difficulty

Easy 0Medium 2Hard 1

Every question was multiple choice.

Every question

All 3 questions

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

  1. 6 Apr 2024, Shift 1 · Q8If f(x)={x3sin⁡(1x),x≠00,x=0f(x)=\begin{cases} x^3\sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}, thenMediumSingle correct
  2. 24 Jun 2022, Shift 2 · Q17If y=tan⁡−1(sec⁡x3−tan⁡x3)y = \tan^{-1}\left(\sec x^3 - \tan x^3\right), π2<x3<3π2\frac{\pi}{2} < x^3 < \frac{3\pi}{2}, thenHardSingle correct
  3. 5 Sep 2020, Shift 1 · Q59If the function f(x)={k1(x−π)2−1,x≤πk2cos⁡x,x>πf(x)=\begin{cases}k_1(x-\pi)^2-1, & x\le\pi\\ k_2\cos x, & x>\pi\end{cases} is twice differentiable, then the ordered…MediumSingle correct

Shifts: 5 Sep 2020, Shift 1, 24 Jun 2022, Shift 2, 6 Apr 2024, Shift 1.

Same topic

Other ideas in Continuity and Differentiability

Continuity and Differentiability has 18 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas