Can I pursue B.Sc degree and D.Pharmacy diploma simultaneously?

As per the guidelines, you cannot continue two courses at a same time, unless other is a distance course. If both are regular courses, then it is not legal.

No, as per the rules and regulations, one cannot complete two degrees at a time.

I don't think you can pursue two-degree programmes simultaneously. Please follow the link to understand the UGC instructions:- http://www.ugc.ac.in/ugc_notices.aspx?id=1275 All the best.