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  4. If (27)999 is divided by 7, then the remainder is :

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Q. If $(27)^{999}$ is divided by $7$, then the remainder is :

JEE MainJEE Main 2017Binomial Theorem

Solution:

$\frac{\left(28-1\right)^{999}}{7} = \frac{28\lambda-1}{7} \Rightarrow \frac{28\lambda-7+1-1}{7} = \frac{7\left(4\lambda-1\right)+6}{7}$
$\therefore $ Rem = 6