B.A Entrance Exam

The questions that can be asked in BA entrance exam can be multiple choice question, objective question or descriptive questions and mostly, questions will be asked related to your general knowledge, general awareness, and your class 10th, class 12th NCERT books.
I would suggest you to read newspapers, magazines. So that you can get more information about your surroundings. And also read your NCERT books as much as you can. As maximum entrance exam questions are put up from NCERT books

Yes, there is a criteria of entrance examination for taking admission there.

Yes, there's a criteria of entrance examination for taking admission there. You can visit their website to check out the date of entrance exam.

No, it has a merit based criteria of admission.

You first have to clear their entrance exam. You can study NCERT books, it is quite helpful.

Before preparing for any exam first you have to understand the test format after that you can check the study material. Mock test is very important because it shows were you stand, in mock test you can understand your weakness and strong points and also it's helpful for time management.

Here is the syllabus:
Ancient History
Classic Antiquity
Middle to Late Bronze Age
Before Christ
Greek and Roman Civilizations
Early ancient History
Timeline of Ancient History
Late Ancient History and Post-classical History
Early Iron Age
Prehistory
Chemical Preservation of Monuments and Antiquities
Museology
Epigraphy and Numismatics
Application of Science in Archaeology
Principles and Methods of Archaeology
Structural Conservation of Ancient Monuments.

B.A. Entrance exam syllabus is varies from college to college, however the following books and methods can be helpful in entrance preparation:
1. For general studies, you should study Lucents General Knowledge.
2. For mental ability, you can choose Arihants Reasoning Book.
3. You should read newspapers for Current Affairs.
4. You should have knowledge about all the books, e. g. , Science, history, geography, economics, civics, from 6th to 10th.
5. You should have sufficient knowledge of English Literature and English Grammar or Hindi Literature and Hindi Grammar of Intermediate level (11th & 12th).

You can take coaching, or you can purchase a book and read thoroughly.