Hi,

1. Yes, you are eligible to persue BA because the eligibility criteria for BA is to passed intermediate in any stream with an recognised board.

2. There are several universities which conduct there own entrance exam for BA and some universities take admission on the basis of their state level examination or national level examination for ug courses.

Most of the state/national level entrance exam form has already been closed but there are some exam remain you can go through them.

Hope this will help you.