Science

Council of Architecture had not included this clause, as when you should have cleared the exams, so yes you will be eligible.

I presume you have done B.Sc in agriculture. You can do a course in agribusiness management from IRMA Anand or pursue M.Sc, if interested in higher studies. Then, Ph.D research to be a researcher which has great scope (respect) in India as also abroad. But, perseverance is important. Or, start your

You get to work with the domain from where you have pursued your M.Sc, as a part of their research project, right at the IISc campus. Duration is of 2 years.

Yes, student from other state can apply also.
Eligibility is B.Sc with various subject in any discipline.

No, a student of Indian origin can only give NIMCET.

Yes, you can proceed, but for researcher a lot of basic subject skills and practical knowledge is important work continuously, you will definitely succeed. All the best.

There are exams conducted by ISRO, DRDO etc. For scientist post. These notifications are announced on the official websites of the departments. Keep checking these.

No Mathematics is not at all taught in B.A. It is completely different aspect.

MS in Canadian University is completely funded by the central government and the university fund, and thus talking about the cost, it is a steal deal, but the problem is with the recommendation for the project funding. While PGDM neither assure you for the low cost stay and job thereafter.