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Indian Administrative Service IAS was formerly known as the Imperial Civil Service (ICS) is the Civil Services Examination and one of the toughest competitive exams in India. It is conducted by the Union Public Service Commission for the recruitment of officers for the All India Administrative Civil Service. The eligibility criteria of UPSC CSE is given below. Educational qualification : Candidate must hold a Bachelor's Degree from any of the recognised universities. Candidates who have appeared for the qualifying examination and are awaiting results or those who are yet to appear for the qualifying examination are also eligible for the Preliminary Examination. Such candidates have to produce proof of passing the said examination along with the application for the Main Examination
Age: A candidate should be a minimum of 21 years and maximum 32 years old as on August 01, 2021. But he/she must have been born not earlier than August 02, 1989 and not later than August 01, 2000. Necessary action will take to make corresponding changes in respective Rules/Regulations pertaining to various services. So you are eligible for UPSC CSE and can give the exam.

There is no restriction about the distance degree for appearing in IIT JAM exam for M.Sc. Mathematics. So you can be eligible if meeting the below criteria. Educational qualification for M.Sc. Mathematics :
1. All candidates admitted through JAM should have a Bachelors degree.
2. In the qualifying degree, the aggregate marks or CGPA/CPI without rounding-off (taking into account all subjects, including languages and subsidiaries, all years combined) should be at least 55% or 5.5 out of 10 for General/OBC (NCL)/EWS category candidates, and 50% or 5.0 out of 10 for SC/ST and PwD category candidates.
3. Studied Mathematics in graduation for at least two years/four semesters.