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Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Sum of all Coefficients

JEE Main asked Sum of all Coefficients 6 times in 6 of the 108 shifts Lumi analysed, in 2017, 2022, 2023 and 2024. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). The longest wait between two years asking it was 5 years, across 2018 and 2019, which Lumi has no shifts for. In 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2017
last in 2024
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 2022, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.510.86’170’200’210.04’220.14’230.09’240’250’26

Raw count: 2017: 1 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 2 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20232 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20171 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.

  • Sum of coefficients of binomial-type series
  • Mean of selected binomial coefficients

Difficulty

Easy 1Medium 3Hard 2

4 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 2 · Q23Let the coefficient of xrx^r in the expansion of (x+3)n−1+(x+3)n−2(x+2)+(x+3)n−3(x+2)2+…+(x+2)n−1(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1} be αr\alpha_r. If…HardNumerical value
  2. 27 Jan 2024, Shift 1 · Q6If A denotes the sum of all the coefficients in the expansion of (1−3x+10x2)n(1-3x+10x^2)^n and B denotes the sum of all the coefficients in the…EasySingle correct
  3. 13 Apr 2023, Shift 1 · Q23Let α\alpha be the constant term in the binomial expansion of (x−6x3/2)n\left(\sqrt{x}-\frac{6}{x^{3/2}}\right)^n, n≤15n\leq15. If the sum of the…HardNumerical value
  4. 11 Apr 2023, Shift 1 · Q21The mean of the coefficients of x,x2,…,x7x, x^2, \ldots, x^7 in the binomial expansion of (2+x)9(2+x)^9 is ______________.MediumNumerical value
  5. 28 Jul 2022, Shift 2 · Q84If 1+(2+49C1+49C2+...+49C49)(50C2+50C4+...+50C50)1+(2+{}^{49}C_1+{}^{49}C_2+...+{}^{49}C_{49})({}^{50}C_2+{}^{50}C_4+...+{}^{50}C_{50}) is equal to 2n⋅m2^n\cdot m, where m is odd, then…MediumNumerical value
  6. 2 Apr 2017 (offline) · Q67The value of (21C1−10C1)+(21C2−10C2)+(21C3−10C3)+(21C4−10C4)+…+(21C10−10C10)(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})…MediumSingle correct

Shifts: 2 Apr 2017 (offline), 28 Jul 2022, Shift 2, 11 Apr 2023, Shift 1, 13 Apr 2023, Shift 1, 27 Jan 2024, Shift 1, 31 Jan 2024, Shift 2.

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