Dear Jatin,  irrespective of the graduation stream, you can pursue 3year LLB course. The top institutions offering 3year LLB are Faculty of Law DU, Faculty of Law BHU and Jindal Global School. Few Universities take admissions based on their Entrance Examinations. Here are the Entrance Examinations of the Universities along with their official websites. Please check their websites for information on minimum aggregate, eligibility criteria and important dates: 

1. University of Delhi, Faculty of Law, DU LLB Entrance Test: www.du.ac.in

2. BHU-UET: Faculty of Law, Banaras Hindu University: www.bhu.ac.in

3. LSAT India, Jindal Global School: www.pearsonvue.com/lsatindia/

4. Punjab University, Chandigarh: www.puchd.ac.in

5. LAWCET of Andhra Pradesh: www.apsche.org

6. CEE Kerala: www.cee-kerala.org

7.Kurukshetra University: www.kuk.ac.in

8.MD University: www.mdurohtak.ac.in

9. IIT Kharagpur: www.iitkgp.ac.in