Some of the colleges for International Business studies in India are:

Pondicherry University

Pune University

Punjab University

JIMS

Loyola

LPU
Gitam Institute of Technology

Amity University

Some colleges take their own entrance exam and other can take through national level exams like CAT, CMAT etc.

You can even check the official site for details.

Good luck!

You can check the list of the colleges below 

1- UEI Global, Chandigarh

Affiliated to Bharathiar University, Fees-1.82 Lakh

2- Jagan Institute of Management Studies 

AICTE Approved, Total Fees (INR) 6.35 Lakh, Intake Exam- CAT, MAT, XAT,CMAT,ATMA and NMAT

3- Shri Ram Murti Smarak College of Engineering and Technology

AICTE Approved, Total Fees (INR) 2.23 Lakh, Intake Exam- CAT, MAT, CMAT, ATMA and UPSEE

4- Quantum School of Business 

AICTE Approved, Total Fees (INR) 2.66 Lakh

5- Amity University, Gwalior 

Total Fees (INR) 5.70 Lakh, Intake exam CAT- 75%ile, MAT-500 Marks, GMAT-500 marks and NMAT-75%ile

6- Sankara Institute of Management Science

AICTE Approved, Total Fees (INR) 1.80 Lakh, Intake exam- TANCET, MAT,CMAT and Sankara Institute CET

To check the top colleges for MBA you can refer below link

Top MBA Colleges 

Good Luck!!