B.A

Dear Pradeep, yes Jawaharlal Nehru technological university Hyderabad offering that courses is excellent. Go for the same. No problem, you can opt for it. All the best.

Harshit, it basically is a test to check your proficiency in the English language. The questions are going to be basis in nature related to syllabus of 12th.
You can try for admission in other good private universities like Lovely, Manav rachna, etc too, their Arts and Humanities departments are very good. Lovely even offers scholarship on basis of previous qualification.
Good luck.

If u are serious to become an ias officer then you should take ba because it will help more in your upsc exam

It depends as to in which field you wish to make your career.?

BA eco requires maths as one of the subjects in 12th so you cant because economics has lot of maths in it. If you are very keen then either take maths additional in 12th or appear for mathematics paper from NIOS. I am not sure if all universities will accept two score cards but you can try.

Few DU colleges are: ATMA Ram Sanatan Dharma College, Deshbandhu College, Hans Raj College, Dyal Singh College, Ramjas College, Maharaja Agrasen College for B.A. (Hons) in Mathematics. Good Luck!

Under certain circumstances you can change your subject in second year. For this you must check your university's guideline regarding the subject change.

Some of the leading management institutes offering Distance MBA programs are SymbiosisCenter for Distance Learning, Narsee Monji Institute of Management Studies' School for Continuing Education, Sikkim Manipal University Directorate of Distance Education, ICFAIUniversity and IGNOU among others. You can plan your admission by checking out this list of Institutes offering Distance MBA programs across India. You can sort them course-wise and city-wise to suit your requirement.
You can also refer this link: https://www.shiksha.com/top-institutes-offering-distance-mba-in-human-resource-management-article-7880-1