$9^6$ – 11 when divided by 8 would leave a remainder of :

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Question

$9^6$ – 11 when divided by 8 would leave a remainder of :

Options:

A . 2

B . 0

C . 6

D . 4

Answer: Option C
Answer: (c)If $(x ±1)^n$ is divided by x, the remainder is $(±1)^n$ , Now, $9^6$ – 11 == $(8 + 1)^6$ –11 When it is divided by 8, remainder = + 1 – 11 = – 10 When – 10 is divided by 8, remainder = – 2 i.e. – 2 + 8 = 6

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