Exam

Yes, you can. You can fill form for colleges like:
BIMM
ISBS
ITM Navi Mumbai
RIIM. etc. I am currently studying in BIMM Executive (marketing)
For more queries, or discount in form filling, comment below.

Earlier if you want to study in NIT for general category student 160 to 200 marks was okay. In the current scenario, it is still valid for getting an NIT.

Rather than MAT score, your personal interview is important. Average score is good enough. But, focus on GD and communication skills. Being good in aptitude is a plus too. Because, there is an aptitude training for placements and most of the placement selections have aptitude round. So, utilize the

No, you can not apply for these government exams, you should qualified your graduation degree, then only you can apply for this exam.