Learn

Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Continuity and Differentiability of Composite Functions

JEE Main asked Continuity and Differentiability of Composite Functions 7 times in 7 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 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 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.

00.10.20’170’200.03’210.11’220.07’230.05’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20231 of 12
  • 20223 of 24
  • 20211 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.

  • Count discontinuities of composite piecewise function
  • Unknown constants for continuity of composite

Difficulty

Easy 0Medium 3Hard 4

3 of the 7 questions had a numerical answer.

Every question

All 7 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 2026, Shift 2 · Q25Let f(x)={x3+8;x<0,x2−4;x≥0,f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases} and g(x)={(x−8)1/3;x<0,(x+4)1/2;x≥0.g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}…HardNumerical value
  2. 6 Apr 2024, Shift 2 · Q10Suppose for a differentiable function hh, h(0)=0h(0)=0, h(1)=1h(1)=1 and h′(0)=h′(1)=2h'(0)=h'(1)=2. If g(x)=h(ex)eh(x)g(x)=h(e^x)e^{h(x)}, then g′(0)g'(0) is equal to :MediumSingle correct
  3. 11 Apr 2023, Shift 2 · Q10Let ff and gg be two functions defined by f(x)={x+1,x<0∣x−1∣,x≥0f(x) = \begin{cases} x+1, & x<0 \\ |x-1|, & x \ge 0 \end{cases} and…MediumSingle correct
  4. 28 Jun 2022, Shift 2 · Q6Let f,g:R→Rf, g : \mathbf{R} \to \mathbf{R} be functions defined by f(x)={[x],x<0∣1−x∣,x≥0f(x) = \begin{cases} [x] , & x < 0 \\ |1-x| , & x \geq 0 \end{cases} and…HardSingle correct
  5. 26 Jun 2022, Shift 1 · Q7Let f,g:R→Rf, g : \mathbf{R} \to \mathbf{R} be two real valued functions defined as…HardSingle correct
  6. 25 Jun 2022, Shift 2 · Q22Let f(x)=[2x2+1]f(x) = \left[2x^2 + 1\right] and g(x)={2x−3,x<02x+3,x≥0g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}, where [t][t] is the…HardNumerical value
  7. 16 Mar 2021, Shift 2 · Q85Let f:R→Rf:\mathbf R\to\mathbf R and g:R→Rg:\mathbf R\to\mathbf R be defined as f(x)={x+a,x<0∣x−1∣,x≥0f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases} and…MediumNumerical value

Shifts: 16 Mar 2021, Shift 2, 25 Jun 2022, Shift 2, 26 Jun 2022, Shift 1, 28 Jun 2022, Shift 2, 11 Apr 2023, Shift 2, 6 Apr 2024, Shift 2, 6 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