Article 343 of the Constitution declares Hindi as the official language of the Union of India. English remains the additional official language. It is the authoritative legislative and judicial language. In fact, one could say that English is the official language of India for all practical purposes.
NOW::: what is the difference between national and official language?
The national language defines the people of the nation, culture and history. The official language is used for official communication. While the national language can become the official language by default, an official language has to be approved by law in order to become the national language.
India has no legally-defined national language; it has only 18 official languages according to the Constitution.
In other words all these are national languages!!
The fun fact is that even wikipedia has an entry about India when you type national language!! It says that we do not have single national language; but different official languages