Are fragments with the same number of base pairs always the same exact fragment?

No, the fragments with same number of base pairs  do not always the same exact fragments.

Lets take an example, There are two fragments of DNA, having 20 number of base pair each. But the one fragment contains a sequence in which there are 12 GC base pairs.

The second fragment contains sequence with only 5 GC pairs.

Hence the same number of base pairs in fragments does not assure Exact fragments.

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