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AP EAMCET2003MathematicsBinomial Theorem

The coefficient of x^5 in the expansion of (1+x^2 )^5(1+x)^4 , is :

Options

  1. A60
  2. B50
  3. C40
  4. D56

Correct answer

A. 60

Step-by-step solution

We have, (1+x^2 )^5(1+x)^4= [1+ ^5 C₁ x^2+ ^5 C₂ x^4+ + (x^2 )^5 ] [1+ ^4 C₁ x+ ^4 c₂ x^2+ ^4 C₃ x^3+x^4 ] Coefficient of x^5= ^5 C₁ ^4 C₃+ ^5 C₂ ^4 C₁=5 4+10 4=20+40=60

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