Distance

No there is no problem while taking admission in PGDM . You just have to register yourself by filling a simple form and then appear for a group discussion and personal interview.

No, presently, School of Open Learning provides correspondence courses in commerce subject only.

Hi,
Kindly, look below for in-depth details:
https://www.shiksha.com/mba/colleges/distance-correspondence-mba-colleges-in-uttar-pradesh

You can pursue it from Institute of Mechanical Engineers.

Hi,
Some colleges for the same are:
Government Medical College, Nagpur
SRM University, Chennai
Jaipur Dental College, Jaipur
Government Medical College, Amritsar

MBA through correspondence generally requires 2 to 4 years of relevant work experience and to tell you the truth, correspondence course of MBA for a fresh graduate will also not carry any weight in the job market. So, if you bent on doing MBA through distance education mode then get some good work experience before it.

It is always advisable to pursue MBA full time to extract the right career benefits. However, if you are currently employed and would not like to take the risk in pursuing full time MBA then a distance / eMBA / Executive MBA program can also be explored. Try and pursue it from the top institutes for the right career benefits.

Hello,
Of course, you can get a government job after completing your engineering.
You should apply for competitive exams like Bank SO/IT Exam, Railway JE, SSE Exams, SSC Junior Engineer Exams, etc.
In most of competitive exams, the eligibility criteria required is graduation. So, you can also apply for UPSC Exams, IBPS PO, etc.
Also read -
https://ask.shiksha.com/my-question-is-that-the-b-sc-degree-from-subharti-is-valid-for-all-government-exams-or-not-like-cgl-ias-ips-exams-qna-3869662
I hope it will help you.
Best of luck.