Explanation:

Citizenship and Domicile: India has only one citizenship, i.e., national citizenship. Unlike some countries like the U.S., where there is dual citizenship (national and state), in India, there is no state citizenship. However, the term 'domicile' can be different for different states, particularly for certain legal and administrative purposes.

Citizen by Birth for Head of State: The President of India (Head of State) needs to be an Indian citizen, but the constitution does not specify that they must be a citizen by birth.

Deprivation of Citizenship for a Foreigner: A foreigner, once granted Indian citizenship, can be deprived of it under specific circumstances mentioned in the Citizenship Act, 1955.

Given the above explanations, the correct statement is only the first one.