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nCr Definitions and Properties

If 540 is div...

Question

If $5^{40}$ is divided by 11 then the remainder is

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Solution

The correct option is D
1

$5^{40}$ = $625^{10}$ = $(56 \times 11 + 9)^{10}$

= multiple of 11 + $9^{10}$

Now = $9^{10} = (11 - 2)^{10}$ = multiple of $11 + 2^{10}$

$2^{10}$ = 1024 = 93 × 11 + 1

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