I want to know whether delhi is a state or not.

Delhi is a Special State , which has a city called New Delhi , and New Delhi is capital of India.
But Delhi is not a full government , Govt of Delhi only handles civic facilities and Security of Delhi City and Delhi state are handled by the central govt.

Also please open the link below for more information, Thanks.

John

Delhi City Guide (http://www.mapsofworld.com/cities/india/delhi/)