Indore

Hi,
There are many Top MBA Colleges offering MBA / PGDM Admission without Entrance Exams. These colleges granting admission on the bases of personal Interview and Group Discussion. Most of all Private Universities and Colleges all across India. It may be really tough, in fact next to impossible to get Admission in Top 50 MBA Colleges in India without Entrance Exams.

Hi,
You have not mentioned the course for which you are seeking admission. Hence review your question, please.

Yes, they provide good placements. Rest depends on your hard work.

Yes, maths is considered there, you should get 60% minimum to do BBA there.

NMIMS-Navi Mumbai is better and reasonably good to study at.

You can again give JEE and apply for a new college via lateral entry. This way you will get admission directly into 2nd year and no year will be wasted.

Several universities all across India provide distance learning Courses in psychology. You can apply.

Prestige Institute and Jaipuria Institute are good Institutes in Indore, In Pune Singhad, D. Y. Patil, check the below link for the list of colleges in Indore and Pune accepting CMAT score-
https://www.shiksha.com/mba/colleges/mba-colleges-accepting-cmat-india?rf=filters&ct[]=174&ct[]=106&ex[]=5822&ed[]=et_20&uaf[]=location&uaf[]=et_dm&uaf[]=exam.

Yes, you are eligible to give second year exams.