Thank you very much for your answers. I helps, but just a little bit. There is STILL trial & errors involved.
Please check.
Using your own example,
1. I selected the first option for 'from station' for Mumbai - got ADH
2....
more... I selected the first option for 'to station' for Chennai - got HOM
Result: Sorry. No trains found.
Later I checked the NEXT option for Chennai - MAS and THEN got results. So as I said there IS TRIAL / ERROR involved.
As far as my original query goes, I am sure there is SOME train option for going from Mumbai to Darjeeling. Not direct, but some train connecting the two cities. Evidently, I would NEVER get those results here. I will have to research elsewhere and come back here.
Thanks for pitching in to help me though.