Hello,
When it comes to eligibility criteria for UPCS, candidates need to pass graduation in any discipline from a recognized university, those in the final year of graduation too are eligible to apply, there is no specific aggregate required here, candidates need to attain 21 years as on 1st August of the appearing year,
see when it comes to UPSC syllabus, then comparatively there is more areas of commonality foe BA than that of BBA which is more of business administration domain, and doesn't share any common features with UPSC, however BA is more of a general degree and BBA is a professional degree and if you're not fully confident about UPSC and want to have another back up plan then go for BBA,
see there is no restrictions in terms of belonging to specific stream for qualifying upsc, it's always more about your efforts, strategies that will help you sail through the exam not your discipline, the reason being if you have a look at the previous year toppers they come from as diverse backgrounds as that of science, engineering, commerce, medical etc, the only thing that helps BA or BA Hons people is there is considerable amount of overlap of syllabus, also humanities students are already well acquainted with the subject at 10+2 and graduation level.
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