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Q. The last two digits of the number $3^{400}$ are

Binomial Theorem

Solution:

$\left[\right.3^{400}=81^{100}=(1+80)^{100}$
$={ }^{100} C_{0}+{ }^{100} C_{1} 80+\ldots$ $+{ }^{100} C_{100} 80^{100}$
$\Rightarrow$ Last two digits are $01$