Colleges in Mumbai

No, there are no government colleges for MBA in Hospital and Healthcare Management in Mumbai. You can check private known universities and colleges that offer MBA in Hospital and Healthcare.

Hello Sejal,
Admission is through counselling based on the rank obtained in Maharashtra State Common Entrance Test (MHTCET). Vacant seats will be filled by the institute based on the rank obtained in JEE-Mains.
For more information please visit the link below:
https://www.shiksha.com/college/thakur-college-of-engineering-and-technology-kandivali-east-Mumbai-47539/admission

You have a good score in mentioned exams but the admission will be made through CAP-based score obtained in National Aptitude Test in Architecture (NATA).
For more information, please visit the link given below:
https://www.shiksha.com/college/rizvi-college-of-architecture-bandra-west-mumbai-22909/admission

You have very good marks but for admission, you have to appear in counselling procedures.
Admission is through counselling conducted by Directorate of Technical Education, Maharashtra based on marks obtained in 10+2/ Diploma and score obtained in National Aptitude Test in Architecture(NATA).
Selection parameter and weightages:
10+2/ Diploma marks - 50%
NATA score - 50%

For admission in Manav Rachna University in engineering, you have JEE marks.
And in architecture, you have NATA, so don't worry. You have lots of choices for admission in various colleges.
For more information, please visit the link below:
https://www.shiksha.com/b-tech/articles/list-of-popular-colleges-accepting-nata-scores-blogId-10681

Yes, you can get admission.

You need to give the NATA exam (preferably before the end of May) and then in the month of June-July apply for the admission process of DTE. If your NATA score and 12th percentage are really good then you might get into Sir J.J. college of Architecturing.
Admission to B.Arch. is done on the basis of valid score obtained in NATA/ JEE Main 2018.