Birla Institute of Technology, Mesra Eligibility

Yes, you can easily get any of the college in above list, but in the last round of the counselling.

No, you can't get admission. You have to clear both the exam, and if you are not qualified in one, then you can't be able to take admission in this college.

You will hardly get good colleges/top ten colleges through MAT, as those colleges are participating in September/December MAT. Your score is good, but not up to the mark to get a top tier I colleges like SIMSREE Mumbai, Pumba Pune, XIME Banglore, BIMTECH, Noida, NIBM, Pune, IFMR, Great lake, Chennai, Christ Banglore.
However, you can try XIME Kochi, IPE Hyderabad (Banking finance), IIRM Hyderabad (Rusk management, Business analytics) etc.
Best option is try for September/December MAT to get a top tier I college, which can give you a secured and sustainable job not just a degree and 100% placement.