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KCET2012MathematicsBinomial Theorem

The value of ¹⁰ C ₁+ ¹⁰ C ₂+ ¹⁰ C ₃+ + ¹⁰ C ₉ is

Options

  1. A2¹⁰
  2. B2¹¹
  3. C2¹⁰-2
  4. D2¹⁰-1

Correct answer

C. 2¹⁰-2

Step-by-step solution

Since, (1+x)^ n = n 0 + n 1 x+ n 2 x²+ + n n x^ n Put x=1 and n=10 , we get aligned &2¹⁰= ¹⁰ C ₀+ ¹⁰ C ₁+ ¹⁰ C ₂+ + ¹⁰ C ₁₀ &2¹⁰=1+ ¹⁰ C ₁+ ¹⁰ C ₂+ + ¹⁰ C ₉+1 &2¹⁰-2= ¹⁰ C ₁+ ¹⁰ C ₂+ + ¹⁰ C ₉ aligned

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