where is its name first believed to have originated?
One of them is derived from "Dhillu" or "Dilu", a king who built a city at this location in 50 BCE and named it after himself.
Delhi
There are a number of myths and legends associated with the origin of the name "Delhi". One of them is derived from "Dhillu" or "Dilu", a king who built a city at this location in 50 BCE and named it after himself. Another legend holds that the name of the city is based on the Hindi/Prakrit word ("loose") and that it was used by the Tomaras to refer to the city because the iron pillar of Delhi had a weak foundation and had to be moved. According to Panjab Notes and Queries, the name of the city at the time of King Prithviraj was , and that and are probably derived from the old Hindi word meaning "eminence". The former director of the Archaeological Survey of India, Alexander Cunningham, mentioned that later became . Some suggest the coins in circulation in the region under the Tomaras were called "dehliwal". 
when did new delhi became the capital of india 13 February 1931 where is this place located? Indo-Gangetic Plain what is the total population of this place? New Delhi city has a population of 257,803 while New Delhi district has a population of 142,004.
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Delhi [SEP] Toponym
There are a number of myths and legends associated with the origin of the name "Delhi". One of them is derived from "Dhillu" or "Dilu", a king who built a city at this location in 50 BCE and named it after himself. Another legend holds that the name of the city is based on the Hindi/Prakrit word ("loose") and that it was used by the Tomaras to refer to the city because the iron pillar of Delhi had a weak foundation and had to be moved. According to Panjab Notes and Queries, the name of the city at the time of King Prithviraj was , and that and are probably derived from the old Hindi word meaning "eminence".