Dear Deepak, 

To pursue LLB you need to qualify the Common Law Aptitude Test (CLAT). As you have completed B.Sc. in Computer Science you can appear the CLAT exam now. Regarding the state of domicile you need to provide the resident certificate which will determine to which state you belong.Once submitted means you can't change your category. If you want to get admission in UP produce your Resident certificate indicating UP.