IIM Trichy - Indian Institute of Management

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.

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.

Yes, you are eligible to get admission for PG in IIM-Trichy or Bangalore after completing your graduation through the exam of CAT.

Exam to get into an IIM is CAT & GMAT (for NRI students).

Yes, it is required to clear the sectional cut off. Every institutions have there different sectional cut-offs.

you need to score >99% ile.