Coefficient of $x^{5}$ in $(1 + x^{2})^{5} (1 + x)^{4}$ is

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100

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Solution

The correct option is A 60
$(1 + x)^{4} (1 + x^{2})^{5}$
$(1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}) (1 + 5 x^{2} + 10 x^{4} + 10 x^{6} + 5 x^{8} + x^{10})$
Hence coefficient of $x^{5}$ will be
$4 (10) + 4 (5)$
$= 40 + 20$
$= 60$

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