Hey Aspirant, yes you can apply for B.A. course as the eligibility criteria is just that the candidate must have passed its 10+2 from a recognised board like UP board/C.B.S.E/ICSE.

For admission in B.A., you will have to give an admission test called UGAT(Under Graduate admission test).

Registration for UGAT will start in the second week of April.

For more information about admission in Allahabad University please visit the link below:

https://university.careers360.com/articles/allahabad-university-admission

Hope this helps.