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If the value of the sum 29 C 30 0 + 28 C 30 1 + 27 C 30 2 + . … … . + 1 C 30 28 + 0 ⋅ C 30 29 - C 30 30 is equal to K ⋅ 2 32 , then the value of K is equal to

Options

  1. A7
  2. B14
  3. C5 2
  4. D7 2

Correct answer

D. 7 2

Step-by-step solution

S = 29 C 30 0 + 28 C 30 1 + 27 C 30 2 + . … … . + 1 C 30 28 + 0 ⋅ C 30 29 - C 30 30 Also, S = - C 30 0 + 0 ⋅ C 30 1 + 1 C 30 2 + . … … . + 27 C 30 28 + 28 C 30 29 + 29 C 30 30 Adding we get, 2 S = 28 C 30 0 + C 30 1 + C 30 2 + . … . . + C 30 28 + C 30 29 + C 30 30 ⇒ S = 14 ⋅ 2 30 = 14 4 2 32 = 7 2 ⋅ 2 32 ⇒ K = 7 2

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