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COMEDK2024MathematicsBinomial Theorem

The coefficient of x^6 in the expansion of (1+x^2+2 x )¹⁰ is

Options

  1. A¹⁰ C₆
  2. B¹⁰ C₅^6
  3. C¹⁰ C₃
  4. D²⁰ C₆

Correct answer

D. ²⁰ C₆

Step-by-step solution

We have, (1+x^2+2 x )¹⁰= [(1+x)^2 ]^0=(1+x)²⁰ General term of (x+y)^n= ^" C_r(x)^ n-r (y)^r T_ r+1 = ²⁰ C_r(1)^ 20-r (x)^r= ²⁰ C_r(x)^r To find coefficient of x^6 we need to put r=6 Coefficient of x^6= ²⁰ C₆

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