Learn

Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Sum of Squares of Binomial Coefficients

JEE Main asked Sum of Squares of Binomial Coefficients 2 times in 2 of the 108 shifts Lumi analysed, all in 2021. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
1 of 8
First asked
2021
the only year
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.07’210’220’230’240’250’26

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: 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
  • 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

Single correct is the usual form. Skill tested: calculation.

  • Sum of squares of binomial coefficients
  • Sum of products of binomial coefficients

Difficulty

Easy 2Medium 0Hard 0

Every question was multiple choice.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 17 Mar 2021, Shift 2 · Q76The value of ∑r=06(6Cr⋅6C6−r)\sum_{r=0}^{6}\left({}^6C_r\cdot{}^6C_{6-r}\right) is equal to :EasySingle correct
  2. 27 Aug 2021, Shift 1 · Q80∑k=020(20Ck)2\sum_{k=0}^{20}\left({}^{20}C_k\right)^2 is equal to :EasySingle correct

Shifts: 17 Mar 2021, Shift 2, 27 Aug 2021, 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