Learn

Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let 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}, C1+3⋅2 C2+5⋅3 C3+…C_1+3\cdot2\,C_2+5\cdot3\,C_3+\ldots upto 10 terms =α×2112β−1(C0+C12+C23+… upto 10 terms)=\frac{\alpha\times2^{11}}{2^\beta-1}\left(C_0+\frac{C_1}{2}+\frac{C_2}{3}+\ldots\text{ upto 10 terms}\right) then the value of α+β\alpha+\beta is equal to __________.

Official answer

286

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. 26 Feb 2021, Shift 1 · Q90Let 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…MediumNumerical 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.