Dear Neelam,

Yes , there are several law entrance exam for getting admission in BA llb , conducted by different universities/instituites.

Most of the exam names are given below:

1. Common Law admission Test (Conducted by 18 national law universities)
2. Symbiosis Entrance test (Conducted by Symbiosis University, Pune)
3. Delhi University Law entrance exam
4. Law School Admission Test
5. All India Law Entrance Test(Conducted by National law university ,Delhi)

to know more details about these exams, please refer to this link:

https://law.careers360.com/exams?level=1

Hope this helps !!

Best wishes !!