XLRI Xavier School of Management

If you are asking for XLRI or XIMB, then sorry, they don't offer BBA programs.

XLRI does not accept CAT scores. It only accepts XAT and GMAT scores for admission.

It depends on how you perform in XAT and then in GD-PI. What matters is your knowledge of the respective field, not the college you studied in.

Your background never makes a difference in getting admission to any college. An important element is getting the right score and then having the confidence to crack an interview. Your percentage of boards and graduation help you. But that doesn't mean that you can't get an admission.
For preparing for XAT, one year of hard work is enough.

XLRI does not offer Masters in industrial psychology. However, it offers Post Graduate Diploma in Business Management and Human Resource Management courses.

For getting admission in XLRI, you need to take XAT exam and you need to clear their cut-off as well.

That is not true and I can vouch for that because I myself am currently interning with students from IIM A, C and L and we all have the same package. There is no disparity. So, rest assured, colleges like XLRI and FMS definitely stand in line with the top IIMs.

If you score high percentile (more than 95%) in CAT or similar entrance exam XAT MAT FCAT), you can get admission in Iims. For detailed information visit the websites of different management institutions.