Nagpur

Apologies for the late reply! My preference will be: IIT-D &get; IIM-A or IIM-N. The reason being IIT-D is already a well-established brand and placements would not be a big issue there unlike these baby IIMs. I agree one cannot ignore the IIM tag, but there is still lot of time before these IIMs establish themselves properly(it's been only 2 years since their existence). You may contact the current students and alumni for more insights.

If this 19k is your general rank, then you will easily get IIIT
but if 19k is your OBC rank, then I am sorry to say but it will not help you to get into IIITs because your rank in OBC category is 19k, so your general rank is somewhere in 1 lakhs.

Tough chances for MMS. You can apply for PGDM AIMA if you haven't applied for core PGDM.

Hey there,
As you mentioned that you got 65 marks in JEE Mains 2017 and yo belong to SC category, there are fair chances of you to get admission into VNIT, Nagpur.
Branch? I can't predict which branch you will get, but I am sure that you will definitely get admission there.

Here is a link. You can check the expected cut off of the college on the basis of MH-CET score and check if you can get it:
https://www.shiksha.com/b-tech/resources/mhcet-cut-off-predictor

In Pune
1.Paradigm IAS Academy Pvt Ltd Pune
Civil Services Entrance Coaching Center 3rd Floor, Chandrasheel Building, Near Hotel Surya, Ghole Road, Shivajinagar
2.RBA Civil Services Academy
Civil Services Entrance Coaching Center 19, Camp
In Nagpur
1.Pre IAS Training Center, Nagpur
Civil Services Entrance Coaching Center Old Morris College Building
2.Rahul Sir's IAS Academy
Civil Services Entrance Coaching Center 92, Income Tax Colony, Opp. Durga Mandir,

Admission in KDKCE is through counselling based on the rank obtained in Maharashtra Health and Technical Common Entrance Test (MHTCET).
Total seats in college are 120.
Vacant seats will be filled by the institute based on the rank obtained in JEE-Mains.