Teacher

Amity Institute of Education
Army Institute of Education
AURA Institutions
B. K. Institute of Education & Technology
C E S College of Educational Research and Training
Central Institute of Education Delhi University
College Of Education, Delhi University S
Department of Education Shri Lal Bahadur Shastri Rashtriya Sanskrit Vidyapeetha
Excel Institute of Management & Technology
Faculty of Education - University of Delhi
Guru Gobind Singh Indraprastha University
Guru Nanak College of Education
Guru Ram Dass College of Education
Indira Gandhi National Open University
International Women Polytechnic
Jamia Millia Islamia

In school teaching engineering is not a subject therefore it is not included in the list

Dear Subrata,
A year loss for MAT exam will affect because for clearing MAT exam it takes less than a month preparation, but if you are graduating this year and targeting admissions in next year I suggest you to prepare for CAT/XAT/SNAP/IIFT because these exams carries value.and if you manages to score anything above 85% then you will be getting in top 20' business schools.
All the very best.

You can become a Teacher with any subject that you have.

You can apply for TGT on completion of BEd in Government school. You may able to apply in private schools even without BEd degree.

Professorship has a great deal of Research orientation. The Publications, Ph.D and guidance for Research and the number of Seminars and Text Books written are taken into account, at the time of Interview. The Seniority as Associate Professor is an important criterion.