The processing time varies for the different types of residence permit applications. Therefore, see the service goals (http://www.nyidanmark.dk/en-us/authorities/the_danish_immigration_service/service_goals/service_goals.htm) of the Danish Immigration Service as well as the Danish Agency for Labour Retention and International Recruitment for more information.
Kindly note that the Embassy primarily has a mailbox function in residence permit cases! All applications are processed by the Danish Agency for Labour Retention and International Recruitment or the Danish Immigration Service.
For certain undergraduate studies and courses as well as in cases of Family Reunification with a Danish family member (FA1), the Embassy will request applicants to come for an interview. The Embassy will contact the applicants in these cases.