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

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$100_{c_{7}}$

$100_{c_{50}}$

answer is D.

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Detailed Solution

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

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

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

$7 r = 50$

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

∴ The co – efficient $x^{50}$ is 0

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