HELLO ANIRUDH
In karnataka the 11th and 12th are considered as PUC1st year(Pre university) and 2nd year respectively this just for the karnataka state board.

Now coming to your question if you want to study your 11th in karnataka board then mainly you get two choices either BIology or computer science in most of the colleges and yes there is a option between kannada and hindi subjects too>
NOw you want maths as an optional subject then you can choose CBSE board since they have varieties there are good CBSE colleges or schools in karnataka where you can take admission. Hope it helps!!
BEST OF LUCK FOR YOUR BOARDS!!