Which of the following State has English as the only official language?

In Indian federal practice, each state is free to decide its own official language(s) for state government business; most states settle on the locally dominant language, but a linguistically diverse state with no single majority language may adopt English alone as its sole official language, with no additional state-recognised regional language sharing that status.

Nagaland's state Assembly proclaimed English the state's official language in 1967 -- four years after statehood (1963) -- and no additional regional language has ever been notified alongside it, a direct consequence of the state's highly diverse mix of Naga tribal languages, none of which commands a statewide majority.

Checking each offered state against the same 'only official language' test confirms the choice:

Only Nagaland satisfies the 'only official language is English' condition, so it is the correct state.