Colleges in Meghalaya

You need to have passed B.A(Hons.) in sociology to be eligible to apply for M.A. in Sociology.

Yes, you can apply for M.Sc after you have cleared all your backlogs and obtained your B.Sc. Degree.

Apply online through their official website and exam is held in July.

No good schools allow direct admission, so prepare well and study is our advice, check top colleges under MAT exam below:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306.

Candidates with a great CAT score (95+ percentile) and excellent performance in the interview rounds can get admission in an institute like IIM Trichy. The level of difficulty entirely lies in the number of efforts taken to prepare for the exam and interviews. Interested candidates can apply by visting the offcial website. Also, candidates need to fulfil the eligibility criteria for IIM Trichy admissions.

Some universities might allow you but it is hard to say. If there's an entrance then you could just prove your caliber in the same and easily secure admission.