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Friday, 9 October

JEE Main Maths · Continuity and Differentiability

Continuity and Differentiability of Composite Functions

Continuity and Differentiability of Composite Functions (Continuity and Differentiability) was asked 3 times in 3 JEE Main shifts, 2021–2026, out of the 42 shifts Lumi analysed. 2 of the 3 had a numerical answer.

Times asked
3
in 3 shifts
Years
2021–2026
Usual format
Numerical value
Multi-step
Pattern
Frequent
repeats across shifts

How it is asked

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

Difficulty

Easy 0Medium 2Hard 1

Where it sits

Chapter: Continuity and Differentiability. Topic: Continuity and Differentiability, 33 questions over 14 ideas.

Other repeat ideas in this topic

Every time it came

All 3 questions

Newest first, each with its options and 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. 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