Allahabad

List of MBA colleges in Delhi:
Guru Gobind Singh Indraprastha University, Delhi
Department of Management Studies, Indian Institute of Technology
Jamia Hamdard, New Delhi
Indian Institute of Foreign Trade, DelhiMaharaja Agrasen Institute of Technology, Delhi
Colleges in Allahabad are:
IIIT Allahabad
Govind Ballabh Pant Social Science Institute
IIBM International, Allahabad
Shambhunath Institute of Engineering & Technology
United Institute of Management

Dear Avi,
Yes, it is a good option to apply for BJMC in SHIATS, Allahabad. For necessary information please visit the official website: http://shiatsdde.edu.in/

You can check placement stats here:
http://www.mnnit.ac.in/tnp/placement/placementarchive.php
http://www.nitkkr.ac.in/sub_courses.php?id=371&id3=115
and I think MNNIT is the best, in terms of placement as well as learning.

You are in general category, so your chance is very low.

If you are getting chemical at old iits I would say go for it. Old IITs (Delhi, Mumbai, Chennai, Kanpur, Roorkee, Kharagpur, Guwahati), else compare each IIT placement and MNNIT placement then choose accordingly.

Everything depends on category, and the cutoff which varies from year to year. For general category, 15k rank may be the last at which you can get admission in MNNIT.
For mechanical engineering, it can be 7k approx