Economics

Hello,
Yes, you are eligible to apply for UGC NET Exam. IGNOU is also a recognised university for UGC NET. As you said, your subject is Economics, therefore you are eligible to take your exam with Economics subject. Before applying, make sure that you have fulfilled the eligibility criteria or not. You can check the paper pattern from here: https://medium.com/@shonalig31/best-preparation-strategies-to-get-good-marks-in-ugc-net-exam-2019-63850dd300d5
You wanted to apply for Professor post, so there is no upper age limit for applying but you should have minimum 55% marks in your master's.

Yes dear, you can do BA in Economics. It has a far better scope in India because of hard grab in the Indian market that's why it will be better for you to take admission in BA in Economics.

Dear, BA in Economics or BA in Geography will be better for you instead of BA in History as they have a better scope and good package in an Indian University.

Yes. You are eligible.
Visit this link for more details: https://www.shiksha.com/humanities-social-sciences/economics/course/b-a-hons-in-economics-sri-guru-gobind-singh-college-of-commerce-pitampura-delhi-247997

Duration:
Two hours
BA honours exam pattern:
Topics
Section A - Grammar (15 marks)
Section B - Vocabulary (10 marks)
Section C- Reading (15 marks)
Section D- Writing (10 marks)
Section E- General Knowledge (10 marks)
Section F- Reasoning (20 marks)
Section G- Literature (20 marks).

You can get the previous year papers from https://www.shiksha.com/science/cucet-exam-question-papers.

For OBC-NC, overall CAT percentile is 80.

Adamas University
Aliah University
Budge College
and many more.

Yes, all the three courses are available in Presidency College. One can easily apply for the courses by giving the entrance test.