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NDA2018MathematicsBinomial TheoremActual

What is the coefficient of the middle term in the binomial expansion of (2+3 x )^4 ?

Options

  1. A6
  2. B12
  3. C108
  4. D216

Correct answer

D. 216

Step-by-step solution

Middle term in the expansion of (x+y)^n= ( n+1 2 )^ th term, if n is odd = ( n 2 +1 )^ th term, if n is even Here n=4 Middle term is ( 4 2 +1 )^ th =3^ rd term aligned 4 c₂ 2^2 3^2 & =6 4 9 & =216 aligned

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