If i trade one day on BSE and another day on NSE, is there any prohibition in doing that thing?
It is absolutely fine and legal thing to do in context of Equities.
You can do trading in any exchange.
In equities if you want to do intraday, then you have to close your positions on the same exchange before close of day.
In F&O you open and close your positions on same exchange.
Otherwise you can do any set of trading on BSE, NSE or MCX and no prohibitions of any such kind.