Maharashtra

Wilson, Andrews, Bhavans, etc. are the colleges I can think of. Try in various quotas according to the colleges.

You can give CAT, CMAT, GMAT, MAT CET and according to the colleges there are many more entrance tests.

Following are some of the good options:
Rizvi College Mumbai
AISSMS Pune
IHM Mumbai

Hi, You can refer the link for college comparison:
https://www.shiksha.com/resources/college-comparison-236567-244785-128271

Hi, You may refer to following link for list of top MBA B-Schools in Pune accepting MAT score:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-pune-accepting-mat/2-2-0-174-306

Hi, You haven't mentioned the course in which you are interested in. Therefore you can refer the link for complete information:
https://www.shiksha.com/university/flame-university-pune-47736

It does not matter if you are from UP. You can appear for the MH-CET even if you are from UP.
You should be able to determine if you are eligible for the MH-CET from the eligibility criteria mentioned below.
The MH-CET eligibility criteria are mentioned below:
Engineering/Technology, Pharmacy & Pharm.D Courses.
Nationality: Candidates must be an Indian citizen.
Age Limit: There is no age limit to apply.
Qualifying Exam: Candidates must pass their HSC/12th or its equivalent examination from a recognised board.
Regards.

Annual fee structure of B.Tech in marine engineering from IMU, Mumbai is listed below:
1) Yearly fees: 2.25 Lacs
2) Total fees: 9 Lacs
Regards.