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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Differentiability of Modulus Functions

JEE Main asked Differentiability of Modulus Functions 9 times in 9 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024 and 2026. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
5 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210.07’220.07’230.09’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20231 of 12
  • 20222 of 24
  • 20213 of 24
  • 20200 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: application.

  • Count non-differentiable points of modulus function
  • Count points of non-differentiability of composite modulus function

Difficulty

Easy 0Medium 7Hard 2

4 of the 9 questions had a numerical answer.

Every question

All 9 questions

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

  1. 4 Apr 2026, Shift 2 · Q22Let f(x)={ex−1,x<0x2−5x+6,x≥0f(x)=\begin{cases}e^{x-1}, & x<0\\ x^2-5x+6, & x\ge0\end{cases} and g(x)=f(∣x∣)+∣f(x)∣g(x)=f(|x|)+|f(x)|. If the number of points where gg is not…MediumNumerical value
  2. 31 Jan 2024, Shift 2 · Q8Consider the function f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} defined by f(x)=e−∣log⁡ex∣f(x)=e^{-|\log_e x|}. If mm and nn be respectively the number of points…MediumSingle correct
  3. 1 Feb 2024, Shift 2 · Q8Let f(x)=∣2x2+5∣x∣−3∣f(x)=|2x^2+5|x|-3|, x∈Rx\in\mathbf{R}. If mm and nn denote the number of points where ff is not continuous and not differentiable…MediumSingle correct
  4. 10 Apr 2023, Shift 1 · Q27Let f:(−2,2)→Rf:(-2,2)\to\mathbb{R} be defined by f(x)={x[x],−2<x<0(x−1)[x],0≤x<2f(x)=\begin{cases}x[x], & -2<x<0\\ (x-1)[x], & 0\le x<2\end{cases} where [x][x] denotes the…HardNumerical value
  5. 29 Jul 2022, Shift 1 · Q18The number of points, where the function f:R→Rf : \mathbf{R} \to \mathbf{R}, f(x)=∣x−1∣cos⁡∣x−2∣sin⁡∣x−1∣+(x−3)∣x2−5x+4∣f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|,…HardSingle correct
  6. 27 Jul 2022, Shift 2 · Q6Let f(x)=2+∣x∣−∣x−1∣+∣x+1∣f(x) = 2 + |x| - |x - 1| + |x + 1|, x∈Rx \in \mathbf{R}. Consider (S1) :…MediumTwo statements
  7. 25 Feb 2021, Shift 1 · Q86The number of points, at which the function f(x)=∣2x+1∣−3∣x+2∣+∣x2+x−2∣f(x) = |2x+1| - 3|x+2| + |x^2 + x - 2|, x∈Rx \in \mathrm{R} is not differentiable, is…MediumNumerical value
  8. 31 Aug 2021, Shift 1 · Q69The function f(x)=∣x2−2x−3∣⋅e∣9x2−12x+4∣f(x)=|x^2-2x-3|\cdot\mathrm{e}^{|9x^2-12x+4|} is not differentiable at exactly :MediumSingle correct
  9. 4 Aug 2021, Shift 1 · Q89The number of points in (0,2π)(0, 2\pi), where the function f:R→Rf:\mathbb{R}\to\mathbb{R} given by f(x)=∣sin⁡x∣+∣cos⁡x∣f(x)=|\sin x|+|\cos x| is NOT…MediumNumerical value

Shifts: 25 Feb 2021, Shift 1, 4 Aug 2021, Shift 1, 31 Aug 2021, Shift 1, 27 Jul 2022, Shift 2, 29 Jul 2022, Shift 1, 10 Apr 2023, Shift 1, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 2, 4 Apr 2026, Shift 2.

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