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Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Pascal's Rule and nCr Properties

JEE Main asked Pascal's Rule and nCr Properties 3 times in 3 of the 108 shifts Lumi analysed, all in 2024. It belongs to Permutations and Combinations (Maths). In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
1 of 8
First asked
2024
the only year
Pattern
New since 2024
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210’220’230.14’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 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
  • 20243 of 18
  • 20230 of 12
  • 20220 of 24
  • 20210 of 24
  • 20200 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.

  • Combinatorial inequality and permutation ratio equations
  • Find n and r from ratio of ncr

Difficulty

Easy 0Medium 3Hard 0

Every question was multiple choice.

Every question

All 3 questions

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

  1. 31 Jan 2024, Shift 2 · Q6If for some m,nm,n; 6Cm+2(6Cm+1)+6Cm+2>8C3{}^6C_m+2\left({}^6C_{m+1}\right)+{}^6C_{m+2}>{}^8C_3 and n−1P3:nP4=1:8{}^{n-1}P_3:{}^nP_4=1:8, then nPm+1+n+1Cm{}^nP_{m+1}+{}^{n+1}C_m…MediumSingle correct
  2. 27 Jan 2024, Shift 1 · Q5n−1Cr=(k2−8) nCr+1{}^{n-1}\mathrm{C}_r=(k^2-8)\,{}^{n}\mathrm{C}_{r+1} if and only if :MediumSingle correct
  3. 6 Apr 2024, Shift 2 · Q6Let 0≤r≤n0\le r\le n. If n+1Cr+1:nCr:n−1Cr−1=55:35:21^{n+1}C_{r+1}:{}^{n}C_r:{}^{n-1}C_{r-1}=55:35:21, then 2n+5r2n+5r is equal to :MediumSingle correct

Shifts: 27 Jan 2024, Shift 1, 31 Jan 2024, Shift 2, 6 Apr 2024, 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