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Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Number of Surjective (Onto) Functions

JEE Main asked Number of Surjective (Onto) Functions 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022, 2023 and 2026. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 3 years. In 2021 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 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, 2023 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.07’210.04’220.07’230’240’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20262 of 9
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20221 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 digit strings using every given digit
  • Count functions that are not onto

Difficulty

Easy 1Medium 3Hard 2

2 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 4 Apr 2026, Shift 1 · Q4The number of functions f:{1,2,3,4}→{a,b,c}f:\{1,2,3,4\}\to\{a,b,c\}, which are not onto, is:EasySingle correct
  2. 2 Apr 2026, Shift 1 · Q6The number of seven-digit numbers, that can be formed by using the digits 1,2,3,51, 2, 3, 5 and 77 such that each digit is used at least once,…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q23The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ____________MediumNumerical value
  4. 28 Jun 2022, Shift 2 · Q29Let S={1,2,3,4}S=\{1, 2, 3, 4\}. Then the number of elements in the set…HardNumerical value
  5. 31 Aug 2021, Shift 2 · Q76Let S={1,2,3,4,5,6}\mathrm{S} = \{1, 2, 3, 4, 5, 6\}. Then the probability that a randomly chosen onto function g\mathrm{g} from S to S satisfies…MediumSingle correct
  6. 3 Aug 2021, Shift 1 · Q78Let A={0,1,2,3,4,5}A = \{0, 1, 2, 3, 4, 5\}. Then the probability that a randomly selected onto function ff from A to A satisfies f(1)+f(2)=f(3)f(1) + f(2) = f(3)…HardSingle correct

Shifts: 3 Aug 2021, Shift 1, 31 Aug 2021, Shift 2, 28 Jun 2022, Shift 2, 6 Apr 2023, Shift 1, 2 Apr 2026, Shift 1, 4 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