Hey.

LLM is masters in law. So you can pursue this course only if you have completed a bachelors degree in law- 5 year integrated law course or 3 year LLb. As per your question, if you have already done any graduation degree in any stream, and now you want to puruse law then you will have to go for LLB degree which is for 3 years and not for LLM. Admission process for LLb degree is  different for each college. Here is a list of law entrances for 3 year LLB course -

 DU LLB - Delhi University  

MH CET- GLC mumbai, ILS Pune and other colleges in Maharashtra

SLAT- Symbiosis Law school

PU LLB- Panjab University, Chandigarh

LSAT- Jindal global Law school, IIT Kharagpur and other private law colleges

BHU LLB- Banaras Hindu University 

BVP LLB- Bharatiya Vidyapeeth

TS LAWCET Etc

Best of luck!