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Hi Dilip,
EMBA are usually offered by various Universities and autonomous Institutes and the accreditation may vary depending on the institute.
To know about the institutes offering executive MBA, you may refer to the following link:
http://tinyurl.com/yjo65gt
In most of the well reputed institutes, one requires to write and qualify the entrance/ written test as required by the particular institutes followed by the Group Discussion and Personal Interview.
To know about institutes in Mumbai offering these courses, refer to the following link:
http://tinyurl.com/yhxr56k
Kindly revert for any further queries, also if you liked this answer then rate it 'Best answer' or give a 'Thumbs Up' rating.
All the Best!

While a Fresher MBA is an option. Remember MBA is not your only option for a management qualification. If you are not very keen on taking a intensive MSc program in your own field - Mechanical Engineering, then you also go for MSc program that give you good Engineering Management subjects.
These techno-management programs are ideally designed for Technology graduates to make a transition into management fields.
Another advantage of such program is that as a fresher, it gives you more focused management modules than the generic ones offered by the MBA program.
Example: An MSc program in Engineering Management or MBA / MSc in Logsistics and Supply Chain Management; MSc Advanced Engineering and Management.
As Mechanical Engineer, you can also opt for programs such as MSc in Energy Management, Petroleum Engineering, Oil and Gas Enterprise Management and so on which are relevant to your field of study and at the same time provide you with good management grounding.
Think, consult more - with professors or people you know in the industry, write back for more details and then take a decision.