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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 26 February 2021, Shift 1, Maths Q90

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

Let m,n∈Nm, n\in\mathbf{N} and gcd⁡(2,n)=1\gcd(2, n)=1. If 30(300)+29(301)+…..+2(3028)+1(3029)=n⋅2m30\binom{30}{0}+29\binom{30}{1}+\ldots..+2\binom{30}{28}+1\binom{30}{29}=n\cdot 2^m, then n+mn+m is equal to _________. (Here (nk)=nCk\binom{n}{k}={}^nC_k)

Official answer

45

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
AP-Weighted Coefficient Sums

Same idea in other shifts

Asked 2× in all
  1. 25 Jun 2022, Shift 1 · Q21Let CrC_r denote the binomial coefficient of xrx^r in the expansion of (1+x)10(1+x)^{10}. If for α,β∈R\alpha,\beta\in\mathbf{R},…HardNumerical value

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.