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What is the remainder when is divided by 216?

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214

answer is B.

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Detailed Solution

We need to find the remainder when

is divided by 216.
We can write 216 as

We know that

Now, let us write

Now let us divide this by 126 . We will get

Now, let us find the remainder of this.
Question Image

Now, let us consider a term x. When we divide x by x we will get the remainder 0 and quotient 1.
When we divide by

by x, quotient will be x and remainder will be 0.
In general, when we divide

by x , where n=1,2,3,... , the remainder will always be 0.
Hence, we can write
Question Image

That is,

Hence, we can write
Question Image

Thus, the remainder when

is divided by 216 is 36.
So, the correct Ans is “Option 2”.

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