MAT

Yes, you are eligible to apply.

No, KJ SIMSR doesn't consider MAT score for admissions.

Hello! If you want to pursue MBA full-time then you need to appear for at least one of the several entrance exams whose scores are considered by the colleges for their respective admission processes. There is no other way one can get admission in a reputed college apart from it.
https://www.shiksha.com/mba/articles/20-mba-entrance-exams-you-can-take-this-year-blogId-11473
Kindly visit this link to know about the various MBA exams conducted in India every year.

Below are some suggestions. The best book for the preparation of MAT exam.
1. English/verbal ability S. P. Bakashi
2. Mathematics - R. S. Agarwal
Good luck for exam and your efforts. You can also follow the books of Arihant Publications.

Keep it as second option if you can't make before it. As admission is important and just for one semester you need to take little more efforts as most of the syllabus will be covered before your joining. However, many colleges do support in such situations for exams and they will help you to cover the syllabus as early as possible.

Hi, List of colleges with your score:
VJIM Hyderabad: Vignana Jyothi Institute of Management
IES MCRC Mumbai: IES Management College And Research Centre
SCMS Cochin: SCMS Cochin School of Business
AIMIT Bangalore: Adarsh Institute of Management And Information Technology, Bangalore
MSRIM Bangalore: MS Ramaiah Institute of Management
FIIB New Delhi
JBS Noida: Jaypee Business School
IIMS Pune: International Institute of Management Studies
EMPI New Delhi: EMPI Business School
Calcutta Business School, Kolkata
GLBIMR Greater Noida: GL Bajaj Institute of Management And Research.