The correct answer is (d) Lucknow.
The North-Central Zonal Cultural Centre is located in Lucknow, Uttar Pradesh. It is one of the six zonal cultural centres of India, established by the Ministry of Culture, Government of India. The centre is responsible for promoting and preserving the cultural heritage of the North Central Zone, which includes the states of Uttar Pradesh, Uttarakhand, Madhya Pradesh, Chhattisgarh, and Bihar.
The centre organizes a variety of cultural activities, including music, dance, theatre, and art exhibitions. It also offers training in traditional arts and crafts. The centre is open to the public and admission is free.
The other options are incorrect because they are not the locations of the North-Central Zonal Cultural Centre.
(a) Allahabad is a city in Uttar Pradesh. It is the headquarters of Allahabad district and the Allahabad division. Allahabad is one of the oldest cities in India and is considered to be one of the seven sacred cities of Hinduism.
(b) Varanasi is a city in Uttar Pradesh. It is the headquarters of Varanasi district and the Varanasi division. Varanasi is one of the oldest cities in India and is considered to be one of the seven sacred cities of Hinduism.
(c) Agra is a city in Uttar Pradesh. It is the headquarters of Agra district and the Agra division. Agra is famous for the Taj Mahal, a white marble mausoleum built by Mughal emperor Shah Jahan in memory of his wife Mumtaz Mahal.
I hope this helps!