Hello aspirant,
St.Xavier college in Mumbai will conduct the entrance exam and  the admissions will be given based on the qualifying marks in the entrance exam.
The clear information about St.Xavier college and the important dates  which are required for the admissions are  provided in our careers 360 website.
Here I will provide you the link please go through the link once and if you have any queries please drop a comment.
http://www.careers360.com/exams/st-xaviers-college-entrance-test
Hope you understood.
Thank you!!!!

Admission process will start just after the declaration of results of 12th of all the central or state boards. It probably starts in the month of June where students first have to submit their 12th marksheet along with entrance form and accordingly selection process takes place.