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JEE Main 202224 JuneMorning Shift

Exam: JEE Main
Year: 2022
Date: 24 June
Shift: Morning Shift
Subject: Mathematics
Chapter: Binomial Theorem

JEE Main 2022 · 24 June · Morning Shift · Mathematics · Binomial Theorem

The remainder when 3 ^ 2022 is divided by 5 is

The remainder when

{3}^{2022}

is divided by

5

is

Options

A $1$
B $2$
C $3$
D $4$

Correct answer

D. $4$

Step-by-step solution

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

$= - \left[1 - {C 1011}_{1}10 + C2 1011 {10}^{2} \ldots\right] = 10q - 1$

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

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