Engineering Eligibility

If your rank belongs to KCET, then you can get the following in BITM under the general category of Karnataka.
1. ECE
2. EEE
3. Civil.

In order to teach at school levels, you will have to pursue at least graduation (in any field) followed by Bachelors in Education (B.Ed. ) degree. Since you are interested in teaching online in any tuition class or any school. It completely depends upon the requirement. However, as per my knowledge you can teach Science and maths in private tuition classes with having some sound knowledge of particular subjects.

I am also an aspirant. If you are a keralite and had appeared for KEAM then its easy. You have to secure minimum of 60% in your 12th exams and secure a rank (around14,000-17,000) in KEAM. If you appeared for JEE Main then you have to secure a rank between 10,000-1,50,000 (to 3 colleges). Sorry that I can't provide further information (since I know much only).

Please check the admission guidelines of UEM Kolkata to know your query from here https://www.shiksha.com/university/uem-kolkata-university-of-engineering-and-management-47398/admission.