PGDM i.e. post graduate diploma in management is provided by institutes that are approved by AICTE (Government of India, All India Council for Technical Education).You can definitely apply for a government job after persuing your PGDM.The credentials of the institute offering the program also matter a lot. An entrance exam is a prerequisite for most of the government jobs. Higher Qualification is never a waste. It all depends on your potential and calibre. If you crack IPS, Banking exam, more weight age will be given to you.