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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The value of ∑ r = 0 7 7 C r r + 2 C 2 is equal to

Options

  1. A128
  2. B251 18
  3. C128 3
  4. D11 7

Correct answer

B. 251 18

Step-by-step solution

∑ r = 0 7 7 C r r + 2 r + 1 2 = 2 ∑ r = 0 7 7 C r r + 1 r + 2 = 2 ∑ r = 0 7 9 C r 8 × 9 = 2 8 × 9 2 9 - 9 C 0 - 9 C 1 = 512 - 1 - 9 36 = 502 36 = 251 18

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