Hii , Nano-Passion !!
This is a very interesting question.
0/0 is neither ∞ nor 0. It is what is "Indeterminate".
For example we can say that 1/0 = ∞ because 0x1 = 0 , 0x10100000000000000000
= 0. So we assume that somehow at an undefined place that is ∞ 0 will become 1.
But in case of 0/0 , every equation is satisfied !
0/0 = x , where x can be any number. So this is kinda indeterminable.
Here is the best explanation of 0/0 by Doctor Math : http://mathforum.org/library/drmath/view/55722.html
Read it , it is very interesting.