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2^60 when divided by 7 leaves the remain...

`2^60` when divided by 7 leaves the remainder

A

1

B

6

C

5

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`2^(60) = (1 + 7)^(20)`
`rArr 2^(60) = ""^(20)C_(0) + ""^(20) C_(1)xx 7 + ""^(20)C_(2)xx7^(2) + …+ ""^(20)C_(20) xx7^(20)`
`rArr 2^(60) =7( ""^(20)C_(1) + ""^(20) C_(2)xx 7 +...+ ""^(20)C_(2)xx7^(19))+1`.
`2^(60)` when divided by 7 leaves the remainder 1. .
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