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Q.



What is the remainder when Question Imageis divided by 216?


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a

1

b

36

c

5

d

214
 

answer is B.

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Detailed Solution

We need to find the remainder when Question Image  is divided by 216.
We can write 216 as
Question Image
We know that Question Image
Now, let us write Question Imageas
Question Image
Now let us divide this by 126 . We will get
Question Image
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 Question Image by x, quotient will be x and remainder will be 0.
In general, when we divide Question Image by  x , where n=1,2,3,... , the remainder will always be 0.
Hence, we can write
Question Image
Question Image
That is,
Question Image
Hence, we can write
Question Image
Thus, the remainder when Question Image is divided by 216 is 36.
So, the correct Ans is “Option 2”.
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