Background:
The Indian National Congress (INC) played a significant role in the struggle for India's independence from British colonial rule. Established in 1885, the INC initially focused on seeking political and social reforms within the framework of the British Empire. However, as the demand for complete independence grew stronger, the INC began advocating for a more radical approach.

Answer:
The Indian National Congress celebrated the Independence Day for the first time on 26th January, 1930 (option B). This date holds historical significance as it marked the declaration of Purna Swaraj, or complete independence, by the Indian National Congress.

The Significance of 26th January, 1930:
- Declaration of Purna Swaraj: On 26th January, 1930, the Indian National Congress passed a resolution declaring Purna Swaraj as their goal. Purna Swaraj meant complete independence from British rule, including the establishment of a sovereign and democratic nation.
- Lahore Session of the INC: The resolution for Purna Swaraj was passed during the Lahore Session of the Indian National Congress held from 26th to 31st January, 1930. This session was attended by numerous Indian leaders, including Jawaharlal Nehru, who later became the first Prime Minister of India.
- Civil Disobedience Movement: The declaration of Purna Swaraj and the celebration of Independence Day on 26th January, 1930, was a significant step in the larger context of the Civil Disobedience Movement. This movement, led by Mahatma Gandhi, aimed to challenge British authority through nonviolent resistance and mass civil disobedience.
- Hoisting of the Flag: As a part of the Independence Day celebrations, the Indian National Congress hoisted the Indian flag for the first time on 26th January, 1930. This act symbolized the assertion of Indian self-rule and independence.
- Transition to Republic Day: After India gained independence on 15th August, 1947, the significance of 26th January continued. It was chosen as the date to enact the Constitution of India, and since 1950, it has been celebrated as Republic Day, marking the establishment of India as a republic.

Conclusion:
The Indian National Congress celebrated the Independence Day for the first time on 26th January, 1930, during the Lahore Session. This date represents the declaration of Purna Swaraj and the beginning of a new phase in the struggle for India's independence. It eventually became the chosen day for the enactment of the Indian Constitution and is now celebrated as Republic Day in India.