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BITSAT2012MathematicsBinomial TheoremActual

The coefficient of x²⁰ in the expansion of (1+x² )⁴⁰ (x²+2+ 1 x² )⁻⁵ is

Options

  1. A³⁰ C ₁₀
  2. B³⁰ C ₂₅
  3. C1
  4. DNone of these

Correct answer

B. ³⁰ C ₂₅

Step-by-step solution

Expression = (1+x² )⁴⁰ (x+ 1 x )⁻¹⁰= (1+x² )³⁰ x¹⁰ The coefficient of x²⁰ in x¹⁰ (1+x² )³⁰= the coefficient of x ¹⁰ in (1+ x ² )³⁰= ³⁰ C ₅= ³⁰ C _ 30-5 = ³⁰ C ₂₅

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