Hello aspirant,

Hope you are doing absolutely great.

So with regard to your query, YES there is an entrance exam conducted by the St. Xavier's College, Mumbai. You can apply for the exam by getting into the official site of the college and should apply online. Based upon the merit in the exam, candidates will be shortlisted for the purpose of admissions. The process is same for the UG and PG courses.

Checkout the following link for any information regarding the admissions process in St. Xavier's Mumbai: https://www.careers360.com/colleges/st-xaviers-college-mumbai/admission

Hope this helps you!!