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Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Binomial Coefficients with AP Multiplier

JEE Main asked Binomial Coefficients with AP Multiplier 3 times in 3 of the 108 shifts Lumi analysed, in 2021 and 2025. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). The longest wait between two years asking it was 4 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
2 of 8
First asked
2021
last in 2025
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.07’210’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 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: calculation.

  • Sum of binomial series with multiplier
  • Sum of binomial coefficients with ap multiplier

Difficulty

Easy 0Medium 3Hard 0

2 of the 3 questions had a numerical answer.

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. 3 Apr 2025, Shift 1 · Q8If ∑r=19(r+32r)⋅9Cr=α(32)9−β\sum_{r=1}^{9}\left(\frac{r+3}{2^r}\right)\cdot {}^9C_r = \alpha\left(\frac{3}{2}\right)^9 - \beta, α,β∈N\alpha, \beta \in \mathbb{N},…MediumSingle correct
  2. 18 Mar 2021, Shift 2 · Q89Let nCr{}^nC_r denote the binomial coefficient of xrx^r in the expansion of (1+x)n(1+x)^n. If…MediumNumerical value
  3. 25 Jul 2021, Shift 2 · Q83Let n ϵ Nn\,\epsilon\,\mathbf{N} and [x][x] denote the greatest integer less than or equal to xx. If the sum of (n+1)(n+1) terms…MediumNumerical value

Shifts: 18 Mar 2021, Shift 2, 25 Jul 2021, Shift 2, 3 Apr 2025, Shift 1.

Same topic

Other ideas in Binomial Coefficients

Binomial Coefficients has 28 ideas JEE Main has asked; 15 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas