Mumbai

You can prefer HM by Taj Group in Mumbai. Placements are also very good and you will also earn some income during your college life.

https://www.shiksha.com/science/ranking/top-science-colleges-in-Mumbai-all/101-2-0-10224-0
This link will help you find your dream college.
Hope it helps.
All the best.

You can consider following colleges:
Kishinchand Chellaram College of Arts, Commerce & Science, [KCCACS] Mumbai
Kirti M. Doongursee College of Arts, Science and Commerce, [KMDCASC] Mumbai
GN Khalsa College of Arts Science and Commerce, [GNKCASC] Mumbai
SIES College of Arts Science and Commerce, [SIES] Mumbai
Maharshi Dayanand College of Arts, Science and Commerce, [MDCASC] Mumbai
St Xaviers College, Mumbai
Lala Lajpat Rai College of Commerce and Economics, [LLRCCE] Mumbai
Bhavan's College, Mumbai
Royal College of Science, Arts and Commerce, Mumbai
Good luck Pranay

IHM Mumbai is obviously the best choice. IHM Mumbai comes at second place only behind IHM Pusa.

Yes, you can get the admission. But for the further procedures please contact the relevant person of the institute and ask for all the details needed. Also, if possible do visit the place and get the exposure of the same and only then decide whether to join or not.

Check the list of BBA colleges in colleges/institutes in Mumbai (All) listed on Shiksha at the link provided below. Get all information related to admissions, fees, courses, placements, reviews and more on BBA colleges in colleges in Mumbai (All) to help you decide which college you should be targeting for BBA colleges in admissions in Mumbai (All).
https://www.shiksha.com/bba/colleges/bba-colleges-mumbai-all

Top computer science engineering colleges in Mumbai (All) at the link provided below:
The ranking is based on engineering ranking 2015 published by The Week.
https://www.shiksha.com/b-tech/ranking/top-computer-science-engineering-colleges-in-mumbai-all/46-2-0-10224-0