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Saturday, 31 October

JEE Main · Maths · Relations and Functions

Number of Injective Functions

JEE Main asked Number of Injective Functions 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2026. It belongs to Permutations and Combinations, in Relations and Functions (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
7
in 7 shifts
Years
4 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.07’210.07’220’230.09’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 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
  • 20230 of 12
  • 20222 of 24
  • 20212 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 injective functions with constraints
  • Count of one-one functions

Difficulty

Easy 1Medium 4Hard 2

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. 5 Apr 2026, Shift 1 · Q21Let A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}. The number of one-one functions f:A→Af: A \to A such that f(1)≥3f(1) \geq 3, f(3)≤4f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5,…MediumNumerical value
  2. 8 Apr 2024, Shift 1 · Q1Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \to \mathbb{Z} be…MediumSingle correct
  3. 5 Apr 2024, Shift 1 · Q1Let A={1,3,7,9,11}A=\{1,3,7,9,11\} and B={2,4,5,7,8,10,12}B=\{2,4,5,7,8,10,12\}. Then the total number of one-one maps f:A→Bf:A\to B, such that f(1)+f(3)=14f(1)+f(3)=14, is :MediumSingle correct
  4. 28 Jun 2022, Shift 2 · Q17The probability that a randomly chosen one-one function from the set {a,b,c,d}\{a, b, c, d\} to the set {1,2,3,4,5}\{1, 2, 3, 4, 5\} satisfies…HardSingle correct
  5. 24 Jun 2022, Shift 1 · Q21The number of one-one functions f:{a,b,c,d}→{0,1,2,…,10}f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\} such that 2f(a)−f(b)+3f(c)+f(d)=02f(a)-f(b)+3f(c)+f(d)=0 is ______.HardNumerical value
  6. 22 Jul 2021, Shift 2 · Q81Let A={0,1,2,3,4,5,6,7}\mathrm{A}=\{0, 1, 2, 3, 4, 5, 6, 7\}. Then the number of bijective functions f:A→Af:\mathrm{A}\to\mathrm{A} such that…MediumNumerical value
  7. 25 Feb 2021, Shift 2 · Q78Let xx denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and yy denote the total…EasySingle correct

Shifts: 25 Feb 2021, Shift 2, 22 Jul 2021, Shift 2, 24 Jun 2022, Shift 1, 28 Jun 2022, Shift 2, 5 Apr 2024, Shift 1, 8 Apr 2024, Shift 1, 5 Apr 2026, 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