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  4. The coefficient of t4 in (1-t)6(1+t2)5 is equal to

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Q. The coefficient of $t^4$ in $(1-t)^6\left(1+t^2\right)^5$ is equal to

Binomial Theorem

Solution:

The coefficient of $ t^4 \text { in }(1-t)^6\left(1+t^2\right)^5$
$={ }^6 C _0{ }^5 C _2+{ }^6 C _2 \cdot{ }^5 C _1+{ }^6 C _4 \cdot{ }^5 C _0=(1)(10)+(15)(5)+(15)(1)=10+75+15=100$