Exam

Yes, you are eligible for MITSOB, Pune if you score valid score in MAT exam also.

CAT is a test of how active, hardworking and techniques knowing you are.
To learn techniques you may join a coaching institute and try solving every type of questions. Don't go into detail, try variety of questions. Keep watch on the pattern of the exam.
Do mock papers and keep working.

I will keep this answer as short and accurate as possible.
It depends on how you define decent college but 90+ overall and in both sections should suffice.

You have scored well in graduation but your high school and intermediate scores are much less for IIMs, especially in case of top 6 IIMs this will act as your negative point so you need to get above 80 percentile in CAT according to me.

I was a student of VMC. I would suggest you to join VMC if your basics are not clear or you are an average student. If you are a good student and know various things of 11th and 12th then go for FIIT-JEE.

I think you are eligible because I know about the last year’s condition of BSEB. I'm 97% sure that you are eligible. You can check the top 20 percentile list at the website of BSEB.

Hello Rinku,
You have indeed scored quite well in your graduation as well as IELTS but you have not raised any query. What is it that you want to ask?

No, check their website xime.org. Admissions are currently open for PGDM 2018-20. Kindly go through their webpage.

For MBA (PGDM) you can apply in IES, MET, Thakur, Saraf, Welingkar, etc. You need to perform well in GD/PI to make it through these colleges.