Exam

For business management studies you need to apply for BBA and then MBA. I guess there are no exams in BBA but yes, MBA has the entrance exams. You can appear for the same by preparing it yourself from reference books available or can join the coaching classes for the same which would always be a bet

You can get a seat in NIT-Kozhikode, NIT-Trichy (less likely), RV College of Engineering, Modi University and BMS College of Engineering.

Refer the following schedule:
1. )
Registration & Choice Filling Process
Third week of June 2018
2. )
Mock Allotment Round 1
Third week of June 2018
3. )
Mock Allotment Round 2
Third week of June 2018
4. )
First Round of Seat allotment
Fourth week of June 2018
5. )
Seat allotment acceptance and reporting to help-

IITians Pace, Resonance and Catalyser and Motion Classes are the best coaching institutes in Nashik. Though, IITians Pace is the best among them.

I would prefer you to thoroughly study your 11th and 12th syllabus. Prefer NCERT books for study solve their whole questions. Go for the link below to know about JEE Mains and list of books for preparation for JEE Mains:
https://www.askiitians.com/iit-jee/main/preparation-tips/

It depends on the entrance exam though for most of them you can refer NCERTs.

BA means Bachelors in arts. Jobs opportunities after BA are:
Government entrance exams like SSC CGL, CDS, Bank PO position, jobs in BPO, UPSC examination, etc.

Yes, you can get the admission but only in private colleges.

No, NITs take admission only through JEE Mains.