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Hello Pratik,
Admissions abroad follow a totally different pattern as compared to Indian universities. Hence, there is a bright chance that you may get admission in petroleum engineering abroad for MS even after completing your graduation in pharmaceutical. However there are many nuances in the whole process & hence I would advise you to approach an agency dealing with sending students abroad.

For MBA, it is mandatory to write any of these entrance exam - CAT, CMAT, MAT, XAT, SNAP etc.
It depends on institute as to which exam they prefer and what is the cut-off score.

Please refer to the link provided to know about the eligibility: https://cbsenet.nic.in/CMS/Public/View.aspx?page=80.

No, it won't be valid for 2019.
2017 CAT Percentile will be valid for 2018 admissions only.

These days, it's almost impossible to take admission in an Engineering College in any state, unless you are domicile of that state. It is more pronounced for lateral admission after the diploma. For fresh admission, some states do allow admissions under national quota

I passed class 12th from commerce stream with a of 182cm.

NMIMS-Mumbai is a Tier-1 college. So, in terms of placements, their statistics are better than NMIMS-Bangalore.