Here I am providing the list of few BBA entrance exams available in India which you are looking for .

Pune University BBA / BBM CET

GGSIPU CET is a common entrance test for BBA

GITAM University Admission Test (GAT) UGM BBA Entrance Exam GAT UGM

AIMA-UGAT:- All India Management Association BBA Entrance Examination
Symbiosis International University

Symbiosis Entrance Test:- Symbiosis Entrance Test (SET)

The core subjects of BBA in India are as follows:
Business Law and Ethics
Quantitative Techniques (financial mathematics, business statistics, operations research)
Organizational Behavior
Strategic Management
Accounting
Financial Management
Economics
Information Technology
Human Resource Management
Operations Management
Marketing

In addition, applicants can specialize in the following topics:
Entrepreneurship
Accounting
Design Management
Marketing
Management Information Systems (MIS)
Supply Chain Management
Operations Management
Tourism Management
Real Estate
Finance
International Business
Human Resource Management
Legal Management
Information Technology
Management