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JEE Main2017MathematicsBinomial TheoremActual

The value of 21 C 1 - 10 C 1 + 21 C 2 - 10 C 2 + 21 C 3 - 10 C 3 + 21 C 4 - 10 C 4 + … + 21 C 10 - 10 C 10 is

Options

  1. A2 21 - 2 11
  2. B2 21 - 2 10
  3. C2 20 - 2 9
  4. D2 20 - 2 10

Correct answer

D. 2 20 - 2 10

Step-by-step solution

We have, 21 C 1 - 10 C 1 + 21 C 2 - 10 C 2 + 21 C 3 - 10 C 3 + 21 C 4 - 10 C 4 + … + 21 C 10 - 10 C 10   = 21 C 1 +   21 C 2 +   21 C 3 + … +   21 C 10 - 10 C 1 + 10 C 2 + 10 C 3 + … + 10 C 10   = 1 2 21 C 1 + 21 C 2 + 21 C 3 + … + 21 C 10 + 21 C 11 + … + 21 C 20 - 2 10 - 1 = 1 2 2 21 - 2 - 2 10 - 1 = 2 20 - 1 - 2 10 + 1 = 2 20 - 2 10 .

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