Science

Most of the students graduating from this college opt for higher studies. Most of them prefer doing their ms from abroad universities, so you can say that MITWPU has a large alumni network who have done PG abroad. This university is recognized by UGC as well as AICTE so it is safe to say you will not have difficulties regarding college status when applying for universities for PG. Research scenario is quite moderate and you can check further details on their website.

Yes, you can do M.Sc in mathematics through distance education.

You have to go to the respective website where you can get all the information regarding environment management courses, entrance exam and syllabus.

Yes, you should be expecting a regular seat with this rank because you have secured a good rank.

No, it is not mandatory to do the integrated program but you have to apply for the M.Sc. You just apply for it and don't go for the integrated courses.

According to your score in BHU maths group and according to my knowledge, you will get a regular seat in any of the affiliated colleges.

If you want to become an IAS officer then I think that doing graduation in BA would be a better option and it would be truly appreciable if you could take political science or history.

Can you please elaborate your question because I am unable to understand what you have asked?

For a guaranteed job in India, most important is communication or you can say English and which can secure a successful career is, undoubtedly, maths.
Good wishes.

You can use the below tool to clear your doubts:
https://www.shiksha.com/college-predictor