Yes you can go for NET exam after your MBA as eligibility criteria needed to apply for an UGC / NET Examination given below

Applicant must have completed their Masters' with 55% for (General) 50% for (SC/ST /) in their respective subjects from recognized University and MBA is PG degree itself .

Applying for a JRF your age must be within 28 years .

Applying for only lectureship there is no age limit .

as per my knowledge you should go for subject like

-Management
-English
-Personnel Management
-Mass Communication

There are two papers conducted in UGC NET exam which are following :

Paper I - This test would be for your general aptitude test in which you will get - Quantitive Aptitude, Reasoning Ability, General Awareness and Numerical Ability subjects and this would be an objective type.

Paper II - This test would be for your specialization subject which you have chosen in UGC-NET exam means if you have chosen Management then you will have to face management test