If 27 999 is divided by 7 , then the remainder is

If

{(27)}^{999}

is divided by

7

, then the remainder is

$3$
$1$
$6$
$2$

Solution

Given, $(27)^{999}$

$= \frac{{(28 - 1)}^{999}}{7}$

$= \frac{28 λ - 1}{7}$

$= \frac{28 λ - 7 + 7 - 1}{7}$

$= \frac{7 (4 λ - 1) + 6}{7}$

$∴$ Remainder $= 6$

Asked in: JEE Main 2017 (08 Apr Online)

Practice more Binomial Theorem questions on Aicharya