Which are the colleges in India providing BBA in public policy with integrated coaching for UPSC and other government job oriented exams?

In my opinion, if you want to prepare for UPSC or any other competitive exams later, you can pursue a BA in Political Science, Economics, History, or Sociology. Since their syllabus is heavily equipped with GK, Indian and world history, public policy, public administration, Indian and world politics, it'll be easier for you to strengthen your base. 

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BA Course Admission

No, the Commission do not mention any Minimum Qualifying Marks for the General Studies Paper 1. But there is a criteria of Minimum 33 % for the General Studies Paper 2 (Aptitude) paper. 

The IAS Prelims exam is conducted offline in the pen and paper mode. There is no sectional cutoff in the IAS prelims exam because the number of questions from a section is not fixed and they vary year to year.

The Union Public Service Commission conduct the Civil Service (IAS) main (written) exam offline in pen and paper mode. This exam is a descriptive type exam where the candidates are required to breach this cutoff score to get a call for the interview phase.

No, the number of IAS vacancies is fixed to 180. Every year, the Commission recommend 180 candidates for the Indian Administrative Services (IAS). In case of any change, the Commission will notify.