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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Induction

NTA Abhyas 2020 · Mathematics · Mathematical Induction

If (27) ^ 999 is divided by 7, then the remainder is

If

{\left(27\right)}^{999} is divided by

7, then the remainder is

Options

A $\text{1}$
B $\text{2}$
C $\text{3}$
D $\text{6}$

Correct answer

D. $\text{6}$

Step-by-step solution

Express the given number

{27}^{999}

as

{\left(28 - 1\right)}^{999}

Now, divide by

7,\dfrac{{( 28 - 1 )}^{999}}{7}

and apply the formula of binomial expansion.
We get the reminder as

- 1 ⇒ 7 + ( - 1 ) = 6

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