Maharashtra

As per students reviews, and my own opinion, IIAEIT is not an up to mark college either for education or placements.
If doing graduation in aviation field is your interest then its fine but if you are opting for aeronautical engineering just because you are having a misconception regarding highly paid jobs (after completion of graduation in aero.) then let me clarify few things.
There is a huge misconception in students (especially who seeks a career in engineering field) that after doing BE/B.Tech in aeronautical/aerospace, they will get highly paid jobs in aero core companies or airlines. But the reality is very much different. Requirements of aero engineers in private firms are negligible. Moreover, there are just countable Private aero firms in India. In most of the aero firms, whether it's a production firm or an R&D, 90% of mechanical people are given preference. Even though you get a job into a private firm (aero organization) your starting salary will not be more than 15K.
There are only a few government organisations, Like ISRO, DRDO, NAL & HAL which gives chance to aero graduates. But getting jobs in these organisations is also not that easy. They individually have their own sets of assessment methods for the job candidates.
No institution takes guaranty of placements for aeronautical/aerospace, not even IIT's since the field is very narrow in our country. But this scenario will change in few years as Indian aviation sector is developing rapidly.

If you want to get an admission into any of the reputed business school in Maharashtra, it is very important to crack an entrance. Also, it is not the waste of time, as it enables the college to judge your basic skills, whether you are fit for the college or not. For example, If you want to take admission into Symbiosis School of Banking & Finance (SSBF), which is one of the reputed Business School that comes under Symbiosis International University. It is mandatory to pass SNAP test, which consists of questions from the background of:1) General English: Reading Comprehension, Verbal Reasoning, Verbal Ability
2) Quantitative, Data Interpretation & Data Sufficiency
3) Current Affairs
4) Analytical & Logical Reasoning

That depends entirely on what you want to do. You could pursue M.Sc. in Physics from Mumbai University. Please refer to the link provided below for details on Mumbai University. You should be able to decide whether you want to take admission in Mumbai University. I have also provided you the scope for M.Sc. Physics. You should be able to decide whether you want to pursue M.Sc. Physics.
Link1: https://www.shiksha.com/university/university-of-mumbai-fort-campus-856
Scope:
There are wide opportunities available for M.Sc Physics graduates in foreign countries. They can work in several health care, manufacturing and electronics companies in foreign countries. Students having high percentage during their post graduation can apply for jobs in National Aeronautics and Space Administration (NASA), one of most famous space research organization in the world.