Hello Navjot, 

Mumbai University does not conduct any entrance examination for UG and PG courses other than LLB. Admission to engineering courses occur through JEE Mains and medical courses through NEET. 

The university will release its application form on the last week of May and it will available till the 2nd week of June.  After this they will release the pre admission enrollment form on the first or second week of June which needs to be submitted with the application form by the second week of June. The merit list will be out by the 4th week of June. 

Various universities come under Mumbai University and cut off varies according to subject so I cannot give you a specific answer about the cut off here. But you can check out subject wise and institution wise cut off/merit list of Mumbai University for the year 2018, here:  https://university.careers360.com/articles/mumbai-university-second-merit-list

Hope this helps :)