Operations Management

You can check out IGNOU, NMIMS, Welingkar and Amity as they offer good curriculum into distance management studies. Even Symbiosis is good option for you.

Yes MBA in systems or MBA in operations are very relevant streams in MBA for engineering graduates. Management gives you exposure to management roles with technical knowledge.

Manufacturing industry offers various roles into supply chain management and procurement, which is very well versed in MBA operations curriculum. If you're looking for automobiles industry into sales division then MBA marketing is best.

There are many colleges in Delhi like Manav Rachna, LBS, ILAM with lower fees. Check the below link-
https://www.shiksha.com/mba/colleges/mba-in-logistics-management-colleges-in-delhi-ncr

Yes, you can get admission. Admission to PUMBA is through CAP rounds conducted by DTE and round starts in June. For details please visit: www.dtemaharashtra.gov.in

Admission in PUMBA is based on CAP rounds and in cap rounds cut off are based on following parameters
1. Home university (Maharashtra based universities)
2. Different cut offs on the basis of caste reservations
3. Other than home university
4. All India candidates
Fees is quite very nominal as PUMBA is Government College and placements are good too.
All the very best

IIM – A, B, C and I are known. Other colleges are NITIE, SJSOM, IIT - Bombay, NMIMS, SIOM - Nashik, SP Jain – Mumbai and XLRI - Jamshedpur.
You can check the below mentioned link:
https://www.shiksha.com/mba/colleges/mba-in-operations-colleges-in-india

This will be dependent on the cutoffs set by IBS Hyderabad after declaration of results.

Some known colleges for MBA in operations other than IIMs-
XLRI, Jamshedpur
NITIE, Mumbai
SPJIMR, Mumbai
SJSOM IIT-Bombay
IIT, Delhi
IIT, Madras
FORE Business School
SIOM, Nashik
NMIMS, Mumbai
IIT, Kharagpur

You can pursue MBA in operation management or PG Diploma in operation management. Many top level institutes offer MBA in operations management including University of Mumbai, IIT, IIMs, etc.