The remainder when 3 2022 is divided by 5 is

The remainder when

3^{2022}

is divided by

5

is

$1$
$2$
$3$
$4$

Solution

${(3^{2})}^{1011}$ $= {(10 - 1)}^{1011}$ $= - {(1 - 10)}^{1011}$

$= - [1 - {{}^{1011}C}_{1} 10 + {}^{1011}C_{2} 10^{2} \dots] = 10 q - 1$

So, here the remainder will be $5 - 1 = 4$

Asked in: JEE Main 2022 (24 Jun Shift 1)

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