Lawyer

Internship:
After completing the classroom courses, you will have to do a mandatory internship as per the norms set by the specific institution.
Enrolment with State Bar Council:
The final step to becoming a lawyer is to enrol yourself as an advocate in any of the state bar councils regulated by the Advocates Act 1961. The State Bar Councils do not have a uniform process of registration. After registration, you must clearAll India Bar Examination (AIBE). The exam is conducted by Bar Council of India, and once you clear it, you get a certificate of practice. The test assesses your basic analytical capabilities and your knowledge of the law. After completing LLB, you can either choose to start practising, or you can continue with studies. You can opt for an LLM course to get in-depth knowledge in your area of interest. Difference between a Lawyer and an Advocate
We often use the terms lawyer and advocate interchangeably, however, there is a difference between the two. After completing your LLB course, you become a lawyer. However, you are still not an advocate. To become an advocate, you will have to enrol yourself with any State Bar Council and clear the India Bar Examination (AIBE)as explained above.

While it is a personal choice, it would be best to seek career counselling and guidance professionally. Also, because the choice of subjects is pretty fluid, it may change over a few months, so take an informed decision. For example, you may have grade 10th maths, but grade 12th maths is very different. In science stream, you may like biology but not physics or chemistry).
However, I can elaborate on the meeting points of law and science and likewise for law and maths.
Law and Science:
Patent-related work requires knowledge of science for the description of patents and other details. Knowledge of biology comes handy when doing environmental law also. Law and Maths (with commerce stream, or inclination towards accountancy):
Taxation laws essentially.

Yes, you can. Although, it would be very difficult and demanding. Study hard and party harder should be the goal of the college. But, if you work little harder in your graduation than you can cover up to 70% of the syllabus of the UPSC Exam. The UPSC Exams cycle consist of three stages Prelims, Mains and Interview, which normally has a fixed schedule in August (for Prelims), Nov/Dec (for Mains) and March/April (for Interviews). The IAS is the perfect harmony of social and personal good, an opportunity, that only few can careers can provide. Be inspired. The 3 golden tips for IAS preparation is to aspire for this golden service you need to prepare smartly, persistently, and patiently. Remember one thing that if you want to clear UPSC Exam than you should keep your basics clear because if your basics are clear than you can think about the problem and can try to find the solution for the same.