Department of Management Sciences, Pune University (PUMBA)

Yes, you can apply through CMAT scores. PUMBA accepts CAT/CMAT/MAH-CET scores for admissions into the MBA program.

The admission process is online. You will have to apply through the CCEP portal of the University. And yes there is a defence quota

Maharashtra domicile is added advantage .PUMBA release seperate merit list for Maharashtra and all India candidates.
PUMBA give admission on basis of CAT, MH CET, CMAT score and subject to minimum 50% marks in graduation.
For CAT , the cut off was 85-90 for 2019.

Yes, you can get admission in DOMS PUMBA. The eligibility criteria is given below.
Eligibility: A student must have passed with a minimum of 50 percent marks or equivalent CGPA (45 percent in case of backward class and persons with disability)in any bachelor's degree awarded by any University.
Admission process : PUMBA strictly follows the DTE rules for its admission process of MBA+.
For Maharashtra candidates, students have to qualify MH-CET exam. For Outside Maharashtra Candidates (OMS), students can apply through CMAT/CAT/MH-CET.
So you have to appear an inappropriate entrance exam for getting admission here in the MBA program.