Colleges in Hyderabad

According to several sources, It can be said that in order to pursue an MBA, XIMB would be a better option in terms of placements and ROI.

Yes, you can get.

The eligibility criteria of M.A Psychology of Osmania University is given below.
Eligibility criteria : Must have obtained a Degree with 40% marks or equivalent CGPA with Psychology as an optional at B.A. / B.M.R.
or
Must have obtained a Degree with 40% marks or equivalent CGPA with Psychology in M.Ed. / M.A.(Education) / M.Sc. (Home Science) / Diploma in Child Psychology or Industrial Psychology.
Because you have not mentioned about the subjects studied at graduation level, So your eligibility can not be confirmed. However on the basis of yours PG degree you are not eligible for M.A Psychology of Osmania University.

Please write about the course name for better response. However as per the eligibility criteria of PGP in Management (12 months course) of ISB is given below.
1. Educational qualification : Bachelors or equivalent degree
2. Entrance tests acceptable : Valid GMAT / GRE score
3. Work experience : Minimum two years full time
So from above CAT is not applicable in ISB. For more clarity please visit https://www.isb.edu/.