Hi , 

There is no entrance exam for BSc in st.Xavier's college. Also , st. Xavier's College doesn't conduct any entrance exam for any BSc degrees. 

Xavier's autonomus college mumbai conduscts entrance test only for BMS and BMM courses. 
other than these two courses admission will be based on aggregate of qualifying examination marks. 
For admissions into st. Xavier's college for any UG or PG excluding the above mentioned courses, the marks in qualifying examination is  taken as aggregate. 

You need to apply online for all UG and PG courses through the website only. 

You will need Maths compulsory for applying into BSc (IT). Based on math class 12th aggregate, admissions for this particular course is done. So there is no entrance exam for BSc (IT) as well. 

The actual admissions for course will be on the announced dates and it will be through the interveiw of candidate and Parent or guardian. and the selected students' name will be published in the website. You will need to check the websites for regular updates. 

For St. Xaviers Mumbai, students who passed class 12 other than maharashtra state board and seeking admissions, you need to give provisional eligibility certificate. 

They have not given any deadline for applying or they have not opened any site to apply for the said course either. You will have to call them or mail them in order to get the exact dates to submit forms. But the entrance exam dates are announced for BBM and BMM courses . It is on 15th as well as 16th june. so the admission procedure for BSc will also be around that month only. You can confirm the actual dates by mailing them. 

If you keep regular checking with the website, you will get the application form. Their first year ends around april mid week, hence they would release forms may be around april end or may first week. 

You can keep updated with the website regularly. And there is no such compulsory mentioned. It depends on which subject you want to do B.Sc which matters whether Maths is required or not. They take overall aggregate in +2 in order to get you admitted in one of these courses. 

Hope this helped with your query,

For any further informations, You can contact anytime. 

All the Best.