I passed my class 10 from cbse with 60% and class 12 with 47.8 mark but if i will pass my B.A. with 50 could iligible for cat exam

Hello Kuja. The basic necessity to write the cat exam, is that, you should have at least 50% in your graduation. If you are in the final year, you should have at least 50% marks, till you apply for cat, i.e., for a 3 year graduation course,  if you are in final year, and are applying for cat, then you should have at least 50% marks till 2nd year.
So yes, with 50% in graduation, you can apply for cat. So prepare well, and score high.
All the best.