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Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Distribution of Identical Objects

JEE Main asked Distribution of Identical Objects 11 times in 11 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Permutations and Combinations (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
11
in 11 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.07’210.07’220.07’230.19’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 4 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
  • 20244 of 18
  • 20231 of 12
  • 20222 of 24
  • 20212 of 24
  • 20201 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: calculation.

  • Count solutions of linear equation
  • Distribution of identical objects with minimum

Difficulty

Easy 1Medium 9Hard 1

5 of the 11 questions had a numerical answer.

Every question

All 11 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 2 · Q17Let A={(a,b,c):a,b,cA=\{(a,b,c):a,b,c are non-negative integers and a+b+2c=22}a+b+2c=22\}. Then n(A)n(A) is equal to:MediumSingle correct
  2. 31 Jan 2024, Shift 2 · Q5The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isEasySingle correct
  3. 1 Feb 2024, Shift 1 · Q24The number of elements in the set S={(x,y,z):x,y,z∈Z,x+2y+3z=42,x,y,z≥0}S=\{(x,y,z): x,y,z\in\mathbb{Z}, x+2y+3z=42, x,y,z\geq0\} equals __________.MediumNumerical value
  4. 9 Apr 2024, Shift 2 · Q23The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ______________.MediumNumerical value
  5. 5 Apr 2024, Shift 1 · Q23The number of ways of getting a sum 16 on throwing a dice four times is ________.MediumNumerical value
  6. 11 Apr 2023, Shift 1 · Q4The number of triplets (x,y,z)(x, y, z), where x,y,zx, y, z are distinct non negative integers satisfying x+y+z=15x + y + z = 15, isMediumSingle correct
  7. 28 Jun 2022, Shift 2 · Q3The number of ways to distribute 30 identical candies among four children C1,C2,C3C_1, C_2, C_3 and C4C_4 so that C2C_2 receives atleast 4 and…MediumSingle correct
  8. 27 Jun 2022, Shift 2 · Q23Let AA be a matrix of order 2×22\times2, whose entries are from the set {0,1,2,3,4,5}\{0, 1, 2, 3, 4, 5\}. If the sum of all the entries of AA is a…HardNumerical value
  9. 26 Feb 2021, Shift 1 · Q70The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :MediumSingle correct
  10. 25 Feb 2021, Shift 1 · Q78The total number of positive integral solutions (x,y,z)(x, y, z) such that xyz=24xyz = 24 is :MediumSingle correct
  11. 3 Sep 2020, Shift 2 · Q72The total number of 3 - digit numbers, whose sum of digits is 10, is __________.MediumNumerical value

Shifts: 3 Sep 2020, Shift 2, 25 Feb 2021, Shift 1, 26 Feb 2021, Shift 1, 27 Jun 2022, Shift 2, 28 Jun 2022, Shift 2, 11 Apr 2023, Shift 1, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 1, 5 Apr 2024, Shift 1, 9 Apr 2024, Shift 2, 4 Apr 2026, Shift 2.

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