NIT

Definitely, NIT Nagpur. If you are looking for good faculty members and placements.

Yes definitely, if you want, you can pursue MCA from NIT since, you have done B.Sc in maths. But the condition is that you have to qualify NIMCET examination to pursue MCA from any of the 11 NITs providing the same. The NIMCET is a National Level Entrance Test conducted by NITs for admission to the MCA course offered by NITs. Only if you are capable of qualifying the exam with a good rank, you will be able to get an admission in the NITs.

Hello Dear,
Here is an article by Shiksha authors about top engineering colleges along with their rankings, fee structure and placements. Apply the filter to get desired results.
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0

You can try your luck in DTU counselling. IIITs and NITs seem to be tough with this rank but anything is possible. You just need to have patience and wait for all the counselling till spot round. GFTIs are not as much better option as the above two are, so keep that as a back up plan. All the best.

GFTI is possible. You can also apply to your state level entrance counselling with your JEE Mains rank. NIT is also possible if you have enough patience to wait till the spot round counselling of JEE.

As per recent news, there were no announcement regarding one course for engineering.
So, the chances for MHCET to be happen in 2019 is more.
Wait for the further announcements.

Yes of course, you can join preparatory course in IIT if you qualified under preparatory course in JEE Advanced in your very first attempt.
Generally, the cut-off for preparatory course is less than general cut-off.
Thanks.

Hello Akash,
Please refer to this link to get more insights of your probable colleges and branches.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.
However, as per your rank, you may not get allocated any seat in the first round but as the counseling process, you will get good branches at lower NITs.

Hello Dear,
Here is a tool called college comparison app by Shiksha. You can compare any two colleges. Here is the link:
https://www.shiksha.com/resources/college-comparison

Hello Dear,
Here is a tool called college comparison app by Shiksha. You can compare any of two colleges. Here is the link:
https://www.shiksha.com/resources/college-comparison
Hope this will resolve your query.