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NDA2021MathematicsBinomial TheoremActual

What is the coefficient of the middle term in the expansion of (1+4 x+4 x^2 )^5 ?

Options

  1. A8064
  2. B4032
  3. C2016
  4. D1008

Correct answer

A. 8064

Step-by-step solution

aligned & (1+4 x+4 x^2 )^5=(1+2 x)^ 2 5 =(1+2 x)¹⁰ & Middle term = ¹⁰ C₅(2 x)^5= 10! 5!5! 2^5 x^5 aligned Co-efficient of middle term =8064 .

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