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Question

When 27 is divided by 4, the unique integers q and r as per Euclid's division lemma are and respectively.

A
3
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B
6
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C
7
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D
-1
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E
5
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Solution

The correct options are
A 3
B 6
According to Euclid's division lemma, for positive a and b, there exist unique integers q and r such that
a=bq+r, where 0r<b.
We have 27=4(6)+3.
Thus, on comparison, we get the quotient q=6 and the remainder r=3.

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