The tagline "Invaluable Treasures of Incredible India" is associated with the logo for option 4, which is the "Geographical Indications (GI) of India."

1) The Archaeological Survey of India (option 1) is responsible for the preservation, conservation, and maintenance of historical sites and monuments in India. It does not use the tagline mentioned in the question.

2) India Tourism Development Corporation (option 2) is a government-owned corporation that focuses on the development and promotion of tourism in India. While it may use various taglines for its campaigns, the given tagline is not specifically associated with its logo.

3) The Geological Survey of India (option 3) is responsible for surveying, exploration, and research of the country`s geological resources. It does not utilize the mentioned tagline.

Therefore, the correct answer is option 4, Geographical Indications (GI) of India, which refers to specific products that are associated with a particular region in India and have unique qualities or reputation. The tagline "Invaluable Treasures of Incredible India" reflects the cultural and natural heritage represented by these geographical indications.