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JEE Main2007MathematicsBinomial TheoremActual

The sum of the series ²⁰ C ₀- ²⁰ C ₁+ ²⁰ C ₂- ²⁰ C ₃+ - + ²⁰ C ₁₀ is

Options

  1. A- ²⁰ C ₁₀
  2. B1 2 ²⁰ C ₁₀
  3. C0
  4. D²⁰ C ₁₀

Correct answer

B. 1 2 ²⁰ C ₁₀

Step-by-step solution

(1+ x )²⁰= ²⁰ C ₀+ ²⁰ C ₁ x + + ²⁰ C ₁₀ x ¹⁰+ + ²⁰ C ₂₀ x ²⁰ put x =-1 , 0= ²⁰ C ₀- ²⁰ C ₁+ - ²⁰ C ₉+ ²⁰ C ₁₀- ²⁰ C ₁₁+ + ²⁰ C ₂₀0=2 ( ²⁰ C ₀- ²⁰ C ₁+ - ²⁰ C ₉ )+ ²⁰ C ₁₀ ²⁰ C ₀- ²⁰ C ₁+ + ²⁰ C ₁₀= 1 2 ²⁰ C ₁₀ .

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