Colleges in Uttar Pradesh

Yes, as both courses complements each other. Amity may not be a good institute for this instead you should prefer well reputed colleges like Deccan College. Following is the eligibility criteria
Eligibility for Admission
B.A. degree, with Ancient Indian History, Culture and / or Archaeology / History

Check the link below for knowing admission criteria:
http://www.jiit.ac.in/admission-procedures

JIIT University, Noida is a better option for doing B.Tech CSE in comparison to your other choice. Demand of CSE graduates is higher in comparison to IT grads. JIIT University has a better brand image and placement record.

Amity is among top 50 BSchools of India. It has a good brand image and placement records. If you are unable to crack CAT and XAT then MBA HR at Amity University is a good decision.

JAYPEE 2017 is an entrance examination which offers admission to the engineering aspirants in the institutes of Noida, Guha, and Wakanghat and is conducted by JIIT, Noida every year. JIIT was established in 2001 and today it is ranked amongst the top 10 engineering colleges in Delhi, NCR. The stream

Do BBA from Asian School of business.
You'll also get a college life and environment instead of sitting at home.