Hi aspirant,
Based on the information from the official website of the st.Xavier's college, there is no specific entrance exams for the BA courses. So you can apply if you have passed your 12th standard with minimum 45% marks from a recognized institution.
For more details, http://xaviers.edu/main/index.php/admissions-and-courses?showall=&limitstart=
Hope it helps.
Application | Eligibility | Exam Pattern | Dates | FAQs
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile