Binomial TheoremHard

Question

The sum , where = 0 if p ? q, is maximum when m is

Options

A.5
B.10
C.15
D.20

Solution

is the coefficient of xm in the expansion of
     (1 + x)10 (x + 1)20
⇒     is the coefficient of xm in the expansion of (1+ x)30
ie,     = 30Cm =
and we know is maximum, when
= 30Cm =
      is maximum when m = 15.

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