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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

If 1 1 ! 11 ! + 1 3 ! 9 ! + 1 5 ! 7 ! = 2 n m ! , then the value of m + n is

Options

  1. A18
  2. B23
  3. C12
  4. D22

Correct answer

D. 22

Step-by-step solution

1 12 ! 12 ! 1 ! 11 ! + 12 ! 3 ! 9 ! + 12 ! 5 ! 7 ! = 2 n m ! ⇒ 1 12 ! 12 C 1 + 12 C 3 + 12 C 5 = 2 n m ! ⇒ 1 12 ! 12 C 1 + 12 C 1 + 12 C 3 + 12 C 3 + 12 C 5 + 12 C 5 = 2 n + 1 m ! ⇒ 1 12 ! 12 C 1 + 12 C 11 + 12 C 3 + 12 C 9 + 12 C 5 + 12 C 7 = 2 n + 1 m ! ⇒ 1 12 ! 12 C 1 + 12 C 3 + 12 C 5 + 12 C 7 + 12 C 9 + 12 C 11 = 2 n + 1 m ! ⇒ 2 11 12 ! = 2 n + 1 m ! ⇒ n = 10 , m = 1 2 ⇒ m + n = 2 2

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