Hey Nandita!

There are less chances to get a seat through MH CET. You can check your chances through MHCET PREDICTOR TOOL 2019. 

Here is the link for same:

http://www.engineering.careers360.com/mhcet-college-predictor

You can take admission in private colleges through JEE MAINS.  To check the name of colleges , refer the given link :

http://www.engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India-accepting-jee-main-score

Hope it helps!