BITS Pilani - Birla Institute of Technology and Science

BITS is a better option than NIT.

Kindly refer to the link mentioned below:
http://bitsadmission.com/cutoffscores.aspx

Kindly refer to the link mentioned below:
http://www.bitsadmission.com/

It comes around 7 lakhs.

You should solve as many numericals as you can. Take mock tests and practice well.

BITS, Dubai is a good option.

If this is your rank in JEE Advanced under general category then you can get mechanical engineering in an IIT. You may not get IIT Bombay, Madras, etc. but you may get Mandi, Jammu, etc.
These are also good IITs and they are better to study.
BITS Pilani is really costly so if you get any IIT then drop BITS Pilani. If you can take loan and if you don't want an average IIT then go for BITS Pilani.
For previous year opening and closing ranks refer:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx

Hello,
I am sorry to inform your score is not enough to get you an admission to any of the BITS campuses. The admission is provided only on the basis of your BITSAT score and the cutoff for last year for any branch in any campuses was at least 270+.

You can consider following colleges:
Thapar University
SRM
VIT
Manipal University
Amrita University
Amity University
Chandigarh University
Chitkara University
Lovely Professional University
UPES
SASTRA University

Yes, BITS Pilani offers ME programmes for BE graduates. But for that, you need to clear an entrance exam conducted for higher degree programmes.
For more details refer:
https://www.bitsadmission.com/hdmain.aspx