Science

Yes, you are eligible to apply for M.Sc. in Counselling Psychology from Institute of Distance Education, University of Madras. Basic eligibility for this course requires its candidates to be a graduate from a recognized college /university. Admission is based on the marks obtained in graduation. Interested candidates can apply online/ offline with the required information.
Regards.

If you are good in the logical part of Maths I. e Permutations and Combinations and probability, choose CSE. If you are good with algebra and Geometry, choose Civil or Mechanical.

For B.Tech, you need to give EAMCET. For B.Sc, AUCET should do.

As IIM is one of the finest and most renowned institutes. They prefer candidates with very good academic results. It is very difficult to get a call from IIM-A, you have to score very well in your B.Com and in the entrance exam.
Best of luck.

If your maths is good then you can choose computer field like CSE/IT. That will help you to use your logic of maths in the programming. On the other hand, there is a nice scope for all the engineers related to the computer field.
Regards.