Greetings of the day mate

Firstly, I would like to congratulate you on successful completion of your MET exam. It's really hard to predict rank and cut-off as it depends on the number of students attempting, difficulty level of the exam, number of seats available, etc. Based on the previous year cut-off's your rank must be in the range of 10,000-12,000. This is a rough calculation and can vary accordingly.

With this rank you may be able to secure a Mechanical seat but not EEE seat in thier main campus Manipal. This is entirely based on previous year cut-off's. Just participate in their counselling process and as it has many rounds, the chances of securing a seat increases too.

https://engineering.careers360.com/articles/met-cutoff

You can have a look at the cut-off trends from the above link

Hope this helps!!

Wishing you luck for the counselling process