Hi. IIM Indore, Ranchi, Rohtak, Jammu and Bodhgaya offer integrated BBA+MBA course. The program is called IPM ( Integrated Program Management) .  It is a 5 year program for which entrance exams are conducted. The details regarding the same could be found here :

IIM INDORE

https://www.careers360.com/university/indian-institute-of-management-indore/integrated-programme-in-management-course

IIM ROHTAK

https://www.careers360.com/university/indian-institute-of-management-rohtak/integrated-programme-in-management-course

IIM RANCHI

https://iimranchi.ac.in/p/ipm

IIM JAMMU

https://news.careers360.com/ipm-admission-2021-26-at-iim-bodh-gaya-and-iim-jammu-check-first-and-second-jipmat-cut-off-list

IIM BODHGAYA

https://www.careers360.com/university/indian-institute-of-management-bodh-gaya/integrated-programme-in-management-course