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The syllabus for entrance is same as commerce of class 11 and 12 in addition to logical reasoning .
The entrance exam is CUET for some national colleges and others conduct their own entrance tests( can be registered from their sites )

Yes, you are eligible for B.Ed as minimum criteria for B.Ed is 50% either in graduation or post graduation.

Few good option could be -
- DU affiliated colleges
- IP university campus colleges
- Delhi Technical University
- Jamia Milia
- Jamia Humdard
- JIMS
- Netaji Subhas University
- Symbosis Noida
- Jindal global university
- JK Buisness Scholl
Also I suggest more to focus on college brand value rather than a specializations from BBA. It is better to choose a specializations at PG level.

If you are talking about Diploma and abroad, Diploma in Computer Science will be good, this course offer to learn coding.

Yes, it definitely is a good option to study liberal arts course for UG.

Here is the list of few colleges-
Presidency university
GITAM Hyderabad business school
GEMS Tirupati
PIMR Indore
Jindal Global Business School
Mount Carmel College.

Jaipuria Institute of management Ghaziabad provides two courses I. e MBA (Dual specialisation) and MBA (Business analytics). .

Jaipuria Institute of Management Ghaziabad has in campus hostels for Girls and for boys in separate tower as it is residential programme.

You are not eligible to apply for JEE as you are a commerce student. JEE Eligibility - You must have passed (10+2) in science stream with PCM as a main subject and with at least 5 subjects.

List of Best B.Com Colleges Without Maths
Sri Ram College of Commerce, Delhi. Hindu College, Delhi University. LSR, Delhi University. Hansraj college, Delhi University. Loyola College, Chennai. MCC, University of Madras. KMC, Delhi University. St. Xaviers College, Mumbai.

You can go for post graduate in economic or in accounting which ever is best as per your prefers both have great scope.