The whole genus is a taxonomic mystery and a play of names by various authors. There is no one opinion. There are so many intermediate types and so, it is not right to separate these into different species.
So, in the broad sense, the names T.racemosus and T.biflorus is used for many of the described species. T.mongolorum was also placed as a synonym of T.berteronianus by Anton in "The genus Tragus (Gramineae)" (Kew Bulletin 36(1)).
So, basically, it is ok to place it under T.racemosus (L.) All. , which is the oldest one based on the basionym Cenchrus racemosus L. in species plantarum
No idea why POWO has not shown India in its distribution map.
Regards...
Manoj