Hello,

First of all in majority of government exams such as UPSC, State PSCs, SSC CGL/CPO, CDS(OTA only for female), banking/insurance exams for the post of assistant or officer, these simply ask for a graduate degree in any discipline from a recognized university, yes there may be some variations like few exams specifically ask for 50% or above aggregate, or subject combinations such as  in case of SSC CGL there are three posts in exception which have different criteria of having studied maths or statistics as one of the subject in three years of graduation, but with BA degree you will be eligible for SBI PO/Clerk, IBPS PO/Clerk, IBPS RRB Office Assistant/PO or Assistant or AAO Officer in major insurance companies as these don't have specific aggregate factor requirements however for RBI Assistant/NABARD Grade B Officer  50% aggregate in graduation is mandatory and in case of RBI Grade B Officer 60% aggregate is mandatory, so basically if your target is a decent government jobs there are many options, of course the best being UPSC in terms of prestige, salary, work opportunities as these are considered as best options.

Now, coming to your second query regarding professional degree, you may opt for BBA if you're interested in management or want to have it as a back-up career, or go for integrated law course from top law university, and you can fetch a good placement in private sector as well, or you can practice on your own, set up your company to consult clients, there is also good scope in media industry if you're interested in journalism and mass communication, you can pursue DEd if you're interested in career in teaching or hotel management/hospitality and travel/fashion designing/animation to name a few, so there are numerous options available you should choose as per your areas of interest, skills, aptitude etc.