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JEE Main 202127 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Morning Shift
Subject
Mathematics
Chapter
Binomial Theorem

JEE Main 2021 · 27 August · Morning Shift · Mathematics · Binomial Theorem

∑ _ k = 0 ^ 20 (Ck 20) ^ 2 is equal to

∑k=020(Ck20)2isequalto\mathop{∑}_{k = 0}^{20}{\left(Ck 20\right)}^{2} is equal to

Options

  1. AC2140C21 40
  2. BC2041C20 41
  3. CC2040C20 40
  4. DC1940C19 40

Correct answer

C. C2040C20 40

Step-by-step solution

∑k=020(Ck20)2=∑k=020Ck20.C20−k20\mathop{∑}_{k = 0}^{20}{\left(Ck 20\right)}^{2} = \mathop{∑}_{k = 0}^{20} Ck 20 . C20 - k 20

Sum of suffix is constant so summation will be C2040C20 40

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