Hello Aspirant,

Most Indian business schools provide preference to applicants who have completed competitive tests such as CAT, MAT, XAT, and so forth. But the real question here is whether it's feasible to get an MBA in India without CAT.  A few renowned B-schools furthermore provide admission for Direct MBA programmes without the need for the CAT.
You can refer the below link for private institutions:

https://bschool.careers360.com/colleges/list-of-private-mba-colleges-in-indore

ALL THE BEST