Hello,

Bachelor if Arts degree is provided by many colleges in India and many centralised universities within India . Some of the exams required to qualify to do BA in a college are : IPU CET, BHU, etc. Here is a link for further information regarding BA in regards to college, faculty, exposure and placements. 
https://media.careers360.com/colleges/list-of-ba-bachelor-of-arts-colleges-in-india

Dear student, you can definitely go for polytechnic and bachelor of arts altogether. But it must be that one of the coaches is from Distance Education College. Moreover you will have to see that the exam dates of both the courses do not clash, as there are frequent chances that the exams clash for some of the colleges.