Learn

Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Combinations of Distinct Objects

JEE Main asked Combinations of Distinct Objects 16 times in 16 of the 108 shifts Lumi analysed, in 2017, 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2020, 2021, 2022 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
16
in 16 shifts
Years
8 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.510.86’170.17’200.10’210.14’220.07’230.05’240.13’250.33’26

Raw count: 2017: 1 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 in 8 shifts · 2026: 3 in 9 shifts.

Shift by shift

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

  • 20263 of 9
  • 20251 of 8
  • 20241 of 18
  • 20231 of 12
  • 20224 of 24
  • 20213 of 24
  • 20202 of 12
  • 20171 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Ways to win a series
  • Count words with letter-type restrictions

Difficulty

Easy 5Medium 9Hard 2

9 of the 16 questions had a numerical answer.

Every question

All 16 questions

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

  1. 6 Apr 2026, Shift 1 · Q7The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the…MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q9A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :MediumSingle correct
  3. 5 Apr 2026, Shift 1 · Q22Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends…MediumNumerical value
  4. 7 Apr 2025, Shift 1 · Q8From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4…MediumSingle correct
  5. 4 Apr 2024, Shift 2 · Q24There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of…MediumNumerical value
  6. 10 Apr 2023, Shift 1 · Q24Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match,…MediumNumerical value
  7. 27 Jun 2022, Shift 1 · Q16Five numbers x1,x2,x3,x4,x5x_1, x_2, x_3, x_4, x_5 are randomly selected from the numbers 1,2,3,……,181, 2, 3, \ldots\ldots, 18 and are arranged in the…MediumSingle correct
  8. 26 Jun 2022, Shift 1 · Q22There are ten boys B1,B2,…,B10B_1, B_2, \ldots, B_{10} and five girls G1,G2,…,G5G_1, G_2, \ldots, G_5 in a class. Then the number of ways of forming a…EasyNumerical value
  9. 29 Jul 2022, Shift 1 · Q26The number of matrices of order 3×33 \times 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is…MediumNumerical value
  10. 28 Jul 2022, Shift 2 · Q82A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g is equal to…EasyNumerical value
  11. 17 Mar 2021, Shift 1 · Q65Team ‘A’ consists of 7 boys and n girls and Team ‘B’ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these…EasySingle correct
  12. 25 Jul 2021, Shift 1 · Q89There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be…HardNumerical value
  13. 24 Feb 2021, Shift 1 · Q68A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of…MediumSingle correct
  14. 4 Sep 2020, Shift 2 · Q72A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in…EasyNumerical value
  15. 8 Jan 2020, Shift 1 · Q75An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the…EasyNumerical value
  16. 2 Apr 2017 (offline) · Q66A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and…HardSingle correct

Shifts: 2 Apr 2017 (offline), 8 Jan 2020, Shift 1, 4 Sep 2020, Shift 2, 24 Feb 2021, Shift 1, 17 Mar 2021, Shift 1, 25 Jul 2021, Shift 1, 26 Jun 2022, Shift 1, 27 Jun 2022, Shift 1, 28 Jul 2022, Shift 2, 29 Jul 2022, Shift 1, 10 Apr 2023, Shift 1, 4 Apr 2024, Shift 2, 7 Apr 2025, Shift 1, 5 Apr 2026, Shift 2, 5 Apr 2026, Shift 1, 6 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