Learn

Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Fundamental Counting Principle

JEE Main asked Fundamental Counting Principle 13 times in 12 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024 and 2025. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
13
in 12 shifts
Years
5 of 8
First asked
2021
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.10’210.21’220.07’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 6 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 202225 of 24
  • 20213 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 numbers with even digit sum
  • Count numbers with digit constraints

Difficulty

Easy 1Medium 7Hard 5

11 of the 13 questions had a numerical answer.

Every question

All 13 questions

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

  1. 3 Apr 2025, Shift 1 · Q21If the number of seven-digit numbers, such that the sum of their digits is even, is m⋅n⋅10nm \cdot n \cdot 10^n;…MediumNumerical value
  2. 1 Feb 2024, Shift 2 · Q22The lines L1,L2,…,L20L_1, L_2, \ldots, L_{20} are distinct. For n=1,2,3,…,10n=1,2,3,\ldots,10 all the lines L2n−1L_{2n-1} are parallel to each other and all the…MediumNumerical value
  3. 8 Apr 2024, Shift 1 · Q23The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not…MediumNumerical value
  4. 13 Apr 2023, Shift 2 · Q22Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______MediumNumerical value
  5. 28 Jun 2022, Shift 1 · Q5The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, isMediumSingle correct
  6. 25 Jun 2022, Shift 1 · Q22The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is __________.HardNumerical value
  7. 25 Jun 2022, Shift 1 · Q29Let A be a 3×33\times3 matrix having entries from the set {−1,0,1}\{-1,0,1\}. The number of all such matrices A having sum of all the entries…HardNumerical value
  8. 28 Jul 2022, Shift 1 · Q21Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A,B,C,D,E}\{A,B,C,D,E\}…MediumNumerical value
  9. 27 Jul 2022, Shift 1 · Q28Let SS be the set containing all 3×33 \times 3 matrices with entries from {−1,0,1}\{-1, 0, 1\}. The total number of matrices A∈SA \in S such that…HardNumerical value
  10. 26 Jul 2022, Shift 2 · Q23Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of…MediumNumerical value
  11. 22 Jul 2021, Shift 2 · Q84If the digits are not allowed to repeat in any number formed by using the digits 0,2,4,6,80, 2, 4, 6, 8, then the number of all numbers greater…EasyNumerical value
  12. 25 Feb 2021, Shift 2 · Q76Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A…HardSingle correct
  13. 27 Aug 2021, Shift 1 · Q83A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number…HardNumerical value

Shifts: 25 Feb 2021, Shift 2, 22 Jul 2021, Shift 2, 27 Aug 2021, Shift 1, 25 Jun 2022, Shift 1, 28 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 27 Jul 2022, Shift 1, 28 Jul 2022, Shift 1, 13 Apr 2023, Shift 2, 1 Feb 2024, Shift 2, 8 Apr 2024, Shift 1, 3 Apr 2025, 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