Yes you can apply for admission to LLB course after completing Bachelor of Arts and without giving any entrance examination. There are various colleges and universities in India which provide admission to the LLB course on the basis of merits course achieved in the graduation course examinations:

1. Bhai Gurdas group of institutions Punjab
2. Doctor KN Modi University Rajasthan
3. Teerthankar mahaveer University Uttar Pradesh
4. Sandeep University Maharashtra
5. Amity University
6. Sage University Indore
7. Alliance University Bangalore

Read more about LLB:

https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.careers360.com/courses/llb-bachelor-of-legislative-law/amp&ved=2ahUKEwjKt5j99Z_5AhULGogKHT8mB6gQFnoECBYQAQ&usg=AOvVaw0b6DacVZKawZAB6StucJtI