Learn

Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Principle of Inclusion-Exclusion in Counting

JEE Main asked Principle of Inclusion-Exclusion in Counting 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 1 year. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.07’210.04’220.07’230’240’250’26

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: 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
  • 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

Numerical value is the usual form. Skill tested: multi-step.

  • Count digit arrangements with consecutive ap condition
  • Count integers with given gcd condition

Difficulty

Easy 0Medium 2Hard 2

4 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 12 Apr 2023, Shift 1 · Q23Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive…HardNumerical value
  2. 26 Jun 2022, Shift 2 · Q25The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ______.HardNumerical value
  3. 26 Feb 2021, Shift 2 · Q88The total number of 4-digit numbers whose greatest common divisor with 1818 is 33, is __________.MediumNumerical value
  4. 31 Aug 2021, Shift 2 · Q82The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ______________.MediumNumerical value

Shifts: 26 Feb 2021, Shift 2, 31 Aug 2021, Shift 2, 26 Jun 2022, Shift 2, 12 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