Hey.

BA LLB is a 5 year integrated law course which combines an Undergraduate degree with Law. There are various different law colleges that offer this course. So, If you are interested in  5 year Integrated course of Law after 12th then the forms to be filled are-

CLAT- This is the most sought after entrance exam for Law as from it you can get admission to All National Law Universities. The top ranked law colleges like National Law School, Bangalore, NALSAR Hyderabad, WBNUJS, Kolkata, NLU Jodhpur, NLIU Bhopal, GNLU Gandhinagar and all other NLUs offer admission through CLAT.

Eligibility criteria- You need to score a minimum aggregate of 45% marks in your 12th board exams from any recognised boards tp be eligible to take CLAT.

Admission process- The applications for CLAT 2019 are already out.  The application process wil end in March.

AILET- This is an entrance test for admission to National Law University Delhi. Admission to all NLUs is through CLAT expect for NLU Delhi which is through AILET.

Eligibility criteria- You need to score a minimum aggregate of 50% marks in your 12th board exams from any recognised boards to be eligible to take AILET.

Admission process- The applications for AILET 2019 are already out.  The application process wil end on April 8th.

SLAT- This is an entrance test for  admission Symbiosis Law School all campuses- Pune, Noida, Hyderabad. SLS Pune is considered one of the good law colleges in India.

Eligibility criteria- You need to score a minimum aggregate of 45% marks in your 12th board exams from any recognised boards tp be eligible to take SLAT

Admission process- The applications for SLAT 2019 are already out.  The application process wil end in April second week.

LSAT-  This is for admission to all All Private Law colleges in India like Jindal Global Law School etc

Eligibility criteria- You need to pass your 12th board exams from any recognised boards tp be eligible to take LSAT

Admission process- The applications for LSAT 2019 are already out.  The application process wil end in May.

MHCET-  This is an entrance test for admission to a few top colleges of India like GLC Mumbai, ILS Pune, and other law colleges in Maharashtra 

Eligibility criteria- You need to score a minimum aggregate of 45% marks atleast in your 12th board exams from any recognised boards tp be eligible to take MHCET 

Admission process- The applications for 2019 session are not out yet. The application process will end in March.

PU BA/BCOM LLb- This is for admission to UILS, Panjab University, Chandigarh. The applications will commence from March. You need to score a minimum aggregate of 50% marks in your 12th boards to be eligible.

Other law exams for admission to BA LLB courses are- 

IPU CET- IP University

Christ University 

TS LAWCET- Law Colleges in Tamil Nadu

AIL LET- Army law school, Mohali.

Etc

Best of luck.