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Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Geometric Progression of Expansions

JEE Main asked Geometric Progression of Expansions 3 times in 3 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). The longest wait between two years asking it was 2 years. In 2022 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
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200’210.07’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20222 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: multi-step.

  • Coefficient in geometric series of binomial expansions
  • Coefficient in sum of binomial expansions in gp

Difficulty

Easy 0Medium 2Hard 1

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. 9 Apr 2024, Shift 1 · Q4The coefficient of x70x^{70} in x2(1+x)98+x3(1+x)97+x4(1+x)96+…+x54(1+x)46x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46} is 99Cp−46Cq{}^{99}C_p-{}^{46}C_q. Then a…HardSingle correct
  2. 25 Jun 2022, Shift 2 · Q7The coefficient of x101x^{101} in the expression (5+x)500+x(5+x)499+x2(5+x)498+.......+x500(5+x)^{500} + x(5+x)^{499} + x^2(5+x)^{498} + ....... + x^{500}, x>0x > 0, isMediumSingle correct
  3. 30 Jul 2022, Shift 2 · Q66The coefficient of x1011x^{1011} in the expression (1+2x)2022+2x (1+2x)2021+(2x)2 (1+2x)2020+...+(2x)2022(1+2x)^{2022} + 2x\,(1+2x)^{2021} + (2x)^2\,(1+2x)^{2020} + ... + (2x)^{2022} isMediumSingle correct

Shifts: 25 Jun 2022, Shift 2, 30 Jul 2022, Shift 2, 9 Apr 2024, 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