Option (b) is correct.

Explanation:

• Statement 1 is incorrect: The Constitution deals with citizenship from Articles 5 to 11 under Part II. The Constitution did not have permanent or detailed provisions on citizenship. It only listed who became Indian citizens on January 26, 1950. It does not deal with the problem of acquisition or loss of citizenship after its commencement. It empowers the Parliament to enact a law to provide for such matters and any other matter relating to citizenship.  
• Statement 2 is correct: According to the Constitution, the following categories of persons became the citizens of India at its commencement:  
  • Anyone with a domicile in India and meeting one of three conditions — born in India, either parent born in India, or five years’ ordinary residence in India before the Constitution’s commencement — became an Indian citizen. 
  • A person who migrated to India from Pakistan became an Indian citizen if he or either of his parents or any of his grandparents was born in undivided India.

Option (b) is correct.

Explanation:
The Citizenship Act, 1955, prescribes three ways of losing citizenship whether acquired under the Act or prior to it under the Constitution, viz, renunciation, termination and deprivation:

• By Renunciation:

Any citizen of India of full age and capacity can make a declaration renouncing his Indian citizenship. Upon the registration of that declaration, that person ceases to be a citizen of India. However, if such a declaration is made during a war in which India is engaged, its registration shall be withheld by the Central Government. Further, when a person renounces his Indian citizenship, every minor child of that person also loses Indian citizenship. However, when such a child attains the age of eighteen, he may resume Indian citizenship.

• By Termination:

Statement 1 is correct: When an Indian citizen voluntarily (consciously, knowingly and without duress, undue influence or compulsion) acquires the citizenship of another country, his Indian citizenship automatically terminates. This provision, however, does not apply during a war in which India is engaged.

• By Deprivation:

It is a compulsory termination of Indian citizenship by the Central government, if:

• The citizen has obtained citizenship by fraud.
• Statement 2 is incorrect: The citizen has been ordinarily resident out of India for seven years continuously.
• Statement 3 is correct: The citizen has shown disloyalty to the Constitution of India.
• The citizen has unlawfully traded or communicated with the enemy during a war.

• Statement 4 is incorrect: The citizen has, within five years after Registration or Naturalisation, been imprisoned in any country for two years. 

Option (d) is correct.

Explanation

Statement 1 is incorrect: The Indian Constitution provides for only a single citizenship, that is, the Indian citizenship. The citizens in India owe allegiance only to the Union. There is no separate state citizenship. Also, when an Indian citizen voluntarily acquires the citizenship of another country, his Indian citizenship automatically terminates. 

There is only one domicile allowed in India. Domicile Certificate can be made only in one State/UT. But one can have multiple residences as provided by Article 19 which gives the Right to every citizen to reside and settle in any part of the territory of the country.

Statement 2 is incorrect: A person who has been earlier granted Indian citizenship, can be deprived of his citizenship.  His Indian citizenship can be terminated by the Central government, if: 

• He has obtained citizenship by fraud.
• He has shown disloyalty to the Constitution of India.
• He has unlawfully traded or communicated with the enemy during a war.
• He has, within five years after registration or naturalisation, been imprisoned in any country for two years; and 
• He has been ordinarily resident out of India for seven years continuously.

Option (c) is correct.

Explanation

The Citizenship Act of 1955 prescribes five ways of acquiring citizenship, viz, birth, descent, registration, naturalisation and incorporation of territory. 

• By Incorporation of Territory: If any foreign territory becomes a part of India, the Government of India specifies the persons who among the people of the territory shall be the citizens of India. Such persons become citizens of India from the notified date. For example, when Pondicherry became a part of India, the Government of India issued the Citizenship (Pondicherry) Order, 1962, under the Citizenship Act, 1955.

Option (c) is correct.

Explanation:

Statement 1 is correct: A person registered as Overseas Citizen of India (OCI) Cardholder under the Citizenship Act, 1955 is an Overseas Citizen of India. They can have multiple entry lifelong visas for visiting India for any purpose (However, OCI Cardholders will require a special permission to undertake research work in India for which they may submit the application to the Indian Mission/ Post/ FRRO concerned).

Statement 2 is incorrect: Overseas Citizens of India have parity with Non-Resident Indians (NRIs) in respect of all facilities available to them in economic, financial, and educational fields except in matters relating to the acquisition of agricultural or plantation properties.

Statement 3 is correct: Registered Overseas Citizen of India Cardholders shall be treated at par with Resident Indian nationals in the matter of tariffs in air fares in domestic sectors in India.

Statement 4 is correct: Overseas Citizen of India have Parity with Non- Resident Indians (NRI) regarding appearance for the NEET-UG or such other tests to make them eligible for admission in pursuance of the provisions contained in the relevant Acts.