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  4. The coefficient of t7 in (1+t)6(1+t2)(1+t4)(1+t8) is divisible by

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Q. The coefficient of $t^7$ in $(1+t)^6\left(1+t^2\right)\left(1+t^4\right)\left(1+t^8\right)$ is divisible by

Binomial Theorem

Solution:

Coefficient of $t ^7 \text { in }\left(1+ t ^6\left[1+ t ^2+ t ^4+ t ^6+ t ^8+\ldots .\right]\right.$
$={ }^6 C _5+{ }^6 C _3+{ }^6 C _1=32$