BCA

My college IIEST does not offer BCA, but yes many colleges in Kolkata does. You need to collect their application form and enter your marks details and get a call.

Yes, Maths is compulsory. And, a sufficient marks is also required in order to get a chance in BCA in any good college. So, best of luck.

B.Tech was introduced before BCA.

Yes, of course. Mainly, PCM is required for BCA and you have that already. Also you have Biology. The combination you are having is Excellent. You can't even imagine how many opportunities are there for your career building.
Do not worry you can choose BCA with this combination.
Best of luck.
For any other queries please feel free to ask.

You can get admission in good college. All the best.

Hello,
Every place is good to study as it depends on how much you learn. And please go with following link for BCA colleges with all details. https://www.shiksha.com/it-software/colleges/bca-colleges-Patna
Thank you.