Took 60 Sec for the correct option and its C.
[url](A) a greater number of residences per square kilometer than any other Indian city.[/url]
Residences are compared to city which is illogical here.
(B) greater numbers of residences per square kilometer than any other Indian city.
"Numbers of" is wrong here and unidiomatic. Also comparison is not correct with city.
(C) a greater number of residences per square kilometer than does any other Indian city.Is the correct option as Mumbai is compared to the other city and all idioms are correct here.
(D) greater numbers of residences per square kilometer than do other Indian cities.
"Numbers of" is wrong here and unidiomatic. Also comparison is not correct with city.
(E) a great per square kilometer number of residences, more than does any other Indian city.
Illogical starting of the sentence using "a great per square kilometer number of residences".
POE suits best strategy for this Question as Options A,B,D and E are easily eliminated.
Kudos if it helps anyone.