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Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Multinomial Theorem in Counting

JEE Main asked Multinomial Theorem in Counting 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2023. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.03’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20211 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: calculation.

  • Count digit strings with fixed digit sum
  • Coefficient in multinomial expansion

Difficulty

Easy 0Medium 1Hard 1

2 of the 2 questions had a numerical answer.

Every question

All 2 questions

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

  1. 13 Apr 2023, Shift 1 · Q22The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is ________.HardNumerical value
  2. 31 Aug 2021, Shift 2 · Q83If the coefficient of a7b8\mathrm{a}^7\mathrm{b}^8 in the expansion of (a+2b+4ab)10(\mathrm{a}+2\mathrm{b}+4\mathrm{ab})^{10} is…MediumNumerical value

Shifts: 31 Aug 2021, Shift 2, 13 Apr 2023, 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