CAT

For logistics and SCM, symbiosis has a college in SCM in Nasik but it would be better if you prepare for MH CET and keep it as back up. I hope this answer will help you.

All top MBA colleges require that you take at least one competitive exam like CAT, XAT, SNAP, MAT, GMAT, etc. There may be some courses which accept students without any of these exams but then they may not be competitive.

Dear Indraja Naik,
CAT normally got three stages of preparation: first, you should start your own preparation first by getting material that is available in the market. Second, you should go for some excellent coaching center, third stage is to solve old papers.
All the best.

Yes, you can get admission. Have you applied to other colleges? You can also get admission in better colleges

Dear Aayu Patel,
Hyderabad and Jaipur are the best locations for CAT preparation. Prefer famous coaching centres like TIME, IMS, Career Launcher etc. along with other institutions. All the best.

Yes, its worth every penny. The level of faculty, interaction with peer group and learning is unparalleled in India. Hence, its worth it.
Do understand that unlike other government institutes (read IITs/NITs), IIM's do not take any form of monetary support from government. Hence, the complete expense of the education is born by the students itself rather than the tax-payers of India.

You can start preparing diligently for CAT. If you do not have much idea about CAT, I would suggest you to join a coaching institute with good faculty to help you get the basics right in DILR/Verbal/Quant. After the basics the next challenge is to solve the said question within a stipulated time. Hence, second stage of your preparation should deal with giving mocks and analyzing your mistake repeatedly till CAT.

Good chances, you are a good candidate for MBA in finance. Prepare well.

Since you have completed a 3-year degree in 5 years, I am assuming you have not-that-great academics. If that's the case then getting admission to IIM-A will be difficult even after getting a high percentile as IIM-A gives substantial weightage to academics.