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Q.

The middle term in the expansion of ${(1 + 3 x + 3 x^{2} + x^{3})}^{50}$ is

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a

$156 x^{156}$

b

none

c

$150 x^{150}$

d

$149 x$

answer is C.

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Detailed Solution

${(1 + 3 x + 3 x^{2} + x^{3})}^{50} = {[{(1 + x)}^{3}]}^{50} = {(1 + x)}^{150}$

Middle term $= T_{\frac{n}{2} + 1} = T_{\frac{150}{2} + 1} = T_{75 + 1}$

$= 150_{C_{75}} x^{75}$

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