Learn

Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Sum of Even and Odd Coefficients

JEE Main asked Sum of Even and Odd Coefficients 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2025. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210.04’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 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
  • 20221 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: multi-step.

  • Odd-coefficient sum in trinomial expansion
  • Sum of odd-indexed coefficients of expansion

Difficulty

Easy 0Medium 1Hard 3

2 of the 4 questions had a numerical answer.

Every question

All 4 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 2 · Q21Let (1+x+x2)10=a0+a1x+a2x2+…+a20x20(1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \ldots + a_{20} x^{20}. If (a1+a3+a5+…+a19)−11a2=121k(a_1 + a_3 + a_5 + \ldots + a_{19}) - 11a_2 = 121k, then…HardNumerical value
  2. 25 Jun 2022, Shift 2 · Q24If the sum of the co-efficients of all the positive even powers of xx in the binomial expansion of (2x3+3x)10\left(2x^3 + \frac{3}{x}\right)^{10}…HardNumerical value
  3. 18 Mar 2021, Shift 1 · Q66Let (1+x+2x2)20=a0+a1x+a2x2+…+a40x40(1+x+2x^2)^{20} = a_0 + a_1x + a_2x^2 + \ldots + a_{40}x^{40}. Then, a1+a3+a5+…+a37a_1 + a_3 + a_5 + \ldots + a_{37} is equal to :HardSingle correct
  4. 4 Aug 2021, Shift 1 · Q65If (1+x+x2)4=a0+a1x+a2x2+……+a8x8(1+x+x^2)^4=a_0+a_1x+a_2x^2+\ldots\ldots+a_8x^8, then the value of a0+4a2+16a4+….+28a8a_0+4a_2+16a_4+\ldots.+2^8a_8 is equal toMediumSingle correct

Shifts: 18 Mar 2021, Shift 1, 4 Aug 2021, Shift 1, 25 Jun 2022, Shift 2, 3 Apr 2025, 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