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Q.
Coefficient of $x^{12}$ in $\left(1+x^{3}\right)^{5}\left(1+x^{4}\right)^{8}\left(1+x^{5}\right)^{11}$ is
Binomial Theorem
Solution:
Possible powers of $x$
in $\left(1+x^{3}\right)^{5}=0,3,6,9,12, \ldots\left(1+x^{4}\right)^{8}$
$=0,4,8,12, \ldots$ and in $\left(1+x^{5}\right)^{11}=0,5,10, \ldots$
Possibilities for $x^{12}$ is
$\Rightarrow 501$
