See through the AILET only Integrated LLB courses are provided. Now as there are no age limit for the examination and as you have passed 10+2 so you can apply for it. But you will have to get into a course of BA LLB which isn't relevant because you have already completed your BA. I would recommend you that CLAT will be a better option for you than AILET. Now you have to decide what you want to do.

To know more about AILET visit the link below:

https://law.careers360.com/exams/ailet

To know more about CLAT visit the link below:

https://law.careers360.com/exams/clat

I hope this answer helps. All the very best for your future endeavors!