Learn

Saturday, 31 October

JEE Main · Maths · Relations and Functions

Total Number of Functions

JEE Main asked Total Number of Functions 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022, 2023 and 2024. It belongs to Permutations and Combinations, in Relations and Functions (Maths). The longest wait between two years asking it was 1 year. In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.03’210.07’220.07’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 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
  • 20231 of 12
  • 20222 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

Numerical value is the usual form. Skill tested: multi-step.

  • Count functions with a constraint
  • Count functions with membership condition

Difficulty

Easy 0Medium 4Hard 1

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 30 Jan 2024, Shift 1 · Q21Let A={1,2,3,…,7}A=\{1,2,3,\ldots,7\} and let P(A)P(A) denote the power set of AA. If the number of functions f:A→P(A)f:A\to P(A) such that…HardNumerical value
  2. 11 Apr 2023, Shift 2 · Q22Let A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\} and B={1,2,3,4,5,6}B = \{1, 2, 3, 4, 5, 6\}. Then the number of functions f:A→Bf : A \to B satisfying f(1)+f(2)=f(4)−1f(1) + f(2) = f(4) - 1…MediumNumerical value
  3. 27 Jul 2022, Shift 2 · Q22The number of functions f, from the set A={x∈N:x2−10x+9≤0}A = \{x \in \mathbf{N} : x^2 - 10x + 9 \leq 0\} to the set B={n2:n∈N}B = \{n^2 : n \in \mathbf{N}\} such…MediumNumerical value
  4. 25 Jul 2022, Shift 1 · Q1The total number of functions, f:{1,2,3,4}→{1,2,3,4,5,6}f:\{1,2,3,4\}\rightarrow\{1,2,3,4,5,6\} such that f(1)+f(2)=f(3)f(1)+f(2)=f(3), is equal to :MediumSingle correct
  5. 26 Feb 2021, Shift 2 · Q62Let A={1,2,3,…,10}A=\{1, 2, 3, \ldots, 10\} and f:A→Af : A \to A be defined as…MediumSingle correct

Shifts: 26 Feb 2021, Shift 2, 25 Jul 2022, Shift 1, 27 Jul 2022, Shift 2, 11 Apr 2023, Shift 2, 30 Jan 2024, Shift 1.

Same topic

Other ideas in Permutations and Combinations

Permutations and Combinations has 33 ideas JEE Main has asked; 20 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas