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KVPY2012MathematicsBinomial Theorem

The coefficient of x²⁰¹² in 1+x (1+x² )(1-x) is -

Options

  1. A2010
  2. B2011
  3. C2012
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Coeff. Of x²⁰¹² (1+x)² (1+x² ) (1-x² ) =(1+x)² (1-x⁴ )⁻¹= (1+2 x+x² ) (1-x⁴ )⁻¹ Coeff. Of x²⁰¹²+2 Coeff of x²⁰¹¹+ Coeff of x²⁰¹⁰ in the expansion of (1-x⁴ )⁻¹x²⁰¹¹ and x²⁰¹⁰ not possible in (1-x⁴ )⁻¹= only coeff. Of x²⁰¹² in the expassion of (1-x⁴ )⁻¹ 1+503-1 503 =1

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