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The co-efficient of $x^{50}$ in ${(1 + x^{7})}^{100}$ is

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100_{c 50}

1

100_{c_{7}}

0

answer is D.

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Detailed Solution

Co-efficient of

x^{50}

{(1 + x^{7})}^{100}

$T_{r + 1} = 100_{c_{r}} {(x^{7})}^{r}$

$= 100_{c_{r}} x^{7 r}$

$7 r = 50$

$r = \frac{50}{7} \notin I$

$∴$ The co – efficient $x^{50}$ is $0$

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