/

Learn

Saturday, 31 October

/

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

\sum_{\substack{i,j=0\\ i\neq j}}^{n}{}^nC_i\,{}^nC_j

is equal to

(1) $2^{2n}-{}^{2n}C_n$ Official answer
(2) $2^{2n-1}-{}^{2n-1}C_{n-1}$
(3) $2^{2n}-\frac{1}{2}\,{}^{2n}C_n$
(4) $2^{n-1}+{}^{2n-1}C_n$

Official answer

Option 1

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Double Summation of Coefficients

Same idea in other shifts

Asked 2× in all

4 Aug 2021, Shift 2 · Q64If $C_r$ ( $r=0,1,2,\ldots,11$ ) are the Binomial coefficients in the expansion of $(1+x)^{11}$ , then the value of…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.