Science

It's totally depend upon you if you like math physics, chemistry, go for B.Sc. Otherwise, you can move in B.A. It will help out to come over from Political Science sociology. All these subjects will help you as IPS Aspirants.

A candidate who has passed any undergraduate degree examination with 50 % aggregate marks and 50% of marks in the cognate subject (Mathematics) from any recognised University in India or abroad recognised by UGC / AIU are eligible to apply.

The students who wish to continue with the traditional Science field can go for the B.Sc. Or B.Sc. (Hons) degree after 12th (Science). Once you have done your graduation, you may choose the career in scientific research, banking, teaching, chemist, analyst, biologist, zoologist and management

Refer HC VERMA books for physics preparation if you want to score high in Mains exam.
Regards.

Yes, it includes maths but I am not sure about Science.

Yes, obviously, you have to study very hard for admission in USA and UK.

No, Kolkata University doesn't have B.Sc Geography, you can choose presidency University.

No, you can't join Andhra university without AUCET.