@praby
There is a likely chance that your application might get rejected even though its not your fault
Unfortunately thats how all govt organisations including the DGCA work and they wont care if any delays take place at the courier level
I would still recommend that you keep studying for RT though because in case they do accept it then you might not have a lot of time to prepare
For the next attempt please send the application atleast 7 days ( the earlier the better ) before the last date and keep a lookout for any public holdidays as well