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Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Coefficient Extraction from Products

JEE Main asked Coefficient Extraction from Products 6 times in 6 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 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 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.

00.10.20’170’200’210.11’220’230.14’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 3 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
  • 20223 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

Numerical value is the usual form. Skill tested: calculation.

  • Term independent of x in expansion
  • Coefficients in product expansion

Difficulty

Easy 0Medium 4Hard 2

5 of the 6 questions had a numerical answer.

Every question

All 6 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 1 · Q24In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5, x≠0(1+x)(1-x^2)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5,\ x\neq0, the sum of the coefficients of x3x^3…MediumNumerical value
  2. 1 Feb 2024, Shift 1 · Q23If the Coefficient of x30x^{30} in the expansion of (1+1x)6(1+x2)7(1−x3)8\left(1+\frac{1}{x}\right)^6(1+x^2)^7(1-x^3)^8 ; x≠0x\neq0 is α\alpha, then…HardNumerical value
  3. 5 Apr 2024, Shift 1 · Q24If the constant term in the expansion of (1+2x−3x3)(32x2−13x)9(1+2x-3x^3)\left(\frac{3}{2}x^2-\frac{1}{3x}\right)^9 is pp, then 108p108p is equal to ________.MediumNumerical value
  4. 28 Jun 2022, Shift 2 · Q4The term independent of xx in the expansion of (1−x2+3x3)(52x3−15x2)11(1-x^2+3x^3)\left(\frac{5}{2}x^3-\frac{1}{5x^2}\right)^{11}, x≠0x \neq 0 is :MediumSingle correct
  5. 30 Jul 2022, Shift 2 · Q82If p1p_1 and p2p_2, respectively, are the second largest and the fourth largest prime numbers in the factorization of the coefficient of…HardNumerical value
  6. 26 Jul 2022, Shift 1 · Q25If the coefficients of xx and x2x^2 in the expansion of (1+x)p (1−x)q(1 + x)^{\mathrm{p}}\ (1 - x)^{\mathrm{q}}, p, q≤15\mathrm{p},\ \mathrm{q} \leq 15,…MediumNumerical value

Shifts: 28 Jun 2022, Shift 2, 26 Jul 2022, Shift 1, 30 Jul 2022, Shift 2, 31 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 5 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