Patna

Bangalore is slightly a better option here.

Recruiting Companies:
Cadbury
Cipla
Coca-Cola
ICICI
Airtel
Vodafone
Total Fees
(INR)-1,60,000
https://www.shiksha.com/mba/course/master-business-administration-lalit-narayan-mishra-institute-economic-development-social-change/10099

Depends on the college

Hi Aditya,
Kindly refer the link below:
http://goo.gl/eJgH2g
Hope this information helps. Please feel free to revert.
Wish you luck.

Fee structure is within 3lacs all Inclusive for two year program and placement ratio is at 80% with avg salary around 5lacs.
https://www.shiksha.com/Agbs-Amity-Amity-Global-Business-School-Patna-Patna-institute-college-listingoverviewtab-36847

Take admission in St. Xavier's College of Management and Technology.

Amity Patna Total Fees for MBA - (INR)-4,45,000
MCA - INR 391050
https://www.shiksha.com/Agbs-Amity-Amity-Global-Business-School-Patna-Indore-institute-college-listingoverviewtab-36849
https://www.shiksha.com/Mca-Lateral-Entry-course-in-Noida-Au-Amity-University-Noida-course-information-listingcourse-232116

very few companies hav visited for jobs and max salary offered is 5lacs. You can apply through CAT/CMAT,XAT/MAT following by GDPI. Form can be submitted till 15june. Coll starts frm 15july.
https://www.shiksha.com/mba/course/post-graduate-diploma-management-international-school-management-patna/151461

You may first try in chandragupt institute of management(patna).It's in top 50 b school in india.Just search once on wikipedia.You may secondly try in lalit narayan mishra(patna) but first one is a level of iim.