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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Differentiability via Functional Equations

JEE Main asked Differentiability via Functional Equations 10 times in 10 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2024, 2025 and 2026. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years. In 2020, 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.17’200.10’210.07’220’230.05’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20230 of 12
  • 20222 of 24
  • 20213 of 24
  • 20202 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.

  • Derivative from functional equation
  • Minimum value after solving functional equation

Difficulty

Easy 1Medium 6Hard 3

3 of the 10 questions had a numerical answer.

Every question

All 10 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 2026, Shift 1 · Q19Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3} for all…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q14Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a twice differentiable function such that…HardSingle correct
  3. 30 Jan 2024, Shift 2 · Q7Let f:R−{0}→Rf: \mathbb{R} - \{0\} \to \mathbb{R} be a function satisfying f(xy)=f(x)f(y)f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)} for all…MediumSingle correct
  4. 26 Jun 2022, Shift 2 · Q21Let f:R→Rf : \mathbb{R} \rightarrow \mathbb{R} satisfy f(x+y)=2xf(y)+4yf(x)f(x + y) = 2^x f(y) + 4^y f(x), ∀x,y∈R\forall x, y \in \mathbb{R}. If f(2)=3f(2) = 3, then…HardNumerical value
  5. 26 Jul 2022, Shift 1 · Q1Let f:R→Rf : \mathbf{R} \rightarrow \mathbf{R} be a continuous function such that f (3x)−f (x)=xf\,(3x) - f\,(x) = x. If f (8)=7f\,(8) = 7, then f (14)f\,(14) is…MediumSingle correct
  6. 18 Mar 2021, Shift 2 · Q90Let f:R→Rf:\mathbb{R}\to\mathbb{R} satisfy the equation f(x+y)=f(x)⋅f(y)f(x+y)=f(x)\cdot f(y) for all x,y∈Rx, y\in\mathbb{R} and f(x)≠0f(x)\neq0 for any…MediumNumerical value
  7. 26 Feb 2021, Shift 1 · Q74Let ff be any function defined on R\mathbf{R} and let it satisfy the condition :…MediumSingle correct
  8. 4 Aug 2021, Shift 2 · Q67Let f:R→Rf:\mathbb{R}\to\mathbb{R} be twice differentiable and satisfy f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y). If f′(0)=1f'(0)=1, then which of the following is true?EasySingle correct
  9. 4 Sep 2020, Shift 2 · Q58Let f:(0,∞)→(0,∞)f : (0, \infty) \to (0, \infty) be a differentiable function such that f(1)=ef(1) = e and…HardSingle correct
  10. 4 Sep 2020, Shift 1 · Q73Suppose a differentiable function f(x)f(x) satisfies the identity f(x+y)=f(x)+f(y)+xy2+x2yf(x+y) = f(x) + f(y) + xy^2 + x^2y, for all real xx and yy. If…MediumNumerical value

Shifts: 4 Sep 2020, Shift 2, 4 Sep 2020, Shift 1, 26 Feb 2021, Shift 1, 18 Mar 2021, Shift 2, 4 Aug 2021, Shift 2, 26 Jun 2022, Shift 2, 26 Jul 2022, Shift 1, 30 Jan 2024, Shift 2, 2 Apr 2025, Shift 1, 5 Apr 2026, 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