Colleges in Tiruchirappalli

Here are the fee structures of B.Tech in NIT-Trichy:
https://www.nitt.edu/home/academics/fee_details/

Here are the cut-offs for you:-
1. General: 90.
2. NC-OBC: 81.
3. SC:75.
4. ST:65.
5. DAP:65.
While institute says they have this criteria, but shortlisted students always have the greater percentile than this criteria.

You have to score 250+ in JEE Mains to be on the safer side to get your desired branch. The score can differ according to the branch you need and your category.

Hi,
Dhanalakshmi Srinivasan Engineering College offers the most focused MBA specialization like Marketing, Human Resource, and Finance & System. It doesn't offer MBA with logistics and supply chain management.
https://www.shiksha.com/mba/course/master-of-business-administration-dhanalakshmi-srinivasan-engineering-college-tamil-nadu-other-55157

NIT-Trichy takes admission on the basis of JEE Mains paper-1 given by B.Tech aspirants.

Yes, it is worth it. But if you are taking a drop year, your main aim should be the top IITs. After that, NIT-Trichy and Warangal are good.

Go for IIT-Guwahati. IIT-Guwahati is ranked 7 while NIT-Trichy is ranked 11th. Also IIT tag is more valuable than NIT tag.

No, only PGDM and EMBA courses are available in IIMs and there is no such correspondence course available.

Few exams which can open the gate for MBA from a premier college are CAT,XAT,SNAP,NMAT, GMAT and few more. So better start preparing for these exams before 6 months of the exam dates. Buy Arun Sharma books, start watching videos of CAT preparation coaching classes. For example: Takshila youtube channel. Start preparing as your undergraduate marks seems good & also you are a quant person you won't face much difficulty in preparing. You need to focus more on the verbal part because this makes a huge difference in CAT scores.