The correct answer to the question is option 3: the Ministry of Education.

The Government of India has introduced a new initiative called `Stay in India and Study in India`, which aims to encourage and attract international students to pursue their education in India. The focus of this initiative is to promote India as an educational hub and provide quality education to students from around the world.

Option 1: The Ministry of Youth Affairs and Sports is not responsible for initiating this program. This ministry focuses on youth development, sports, and physical education-related matters.

Option 2: The Ministry of Culture is also not the correct answer. This ministry is responsible for the preservation, promotion, and development of India`s cultural heritage.

Option 4: The Ministry of Tourism is not the correct answer either. This ministry focuses on the development and promotion of tourism in India.

Therefore, the correct answer is option 3: the Ministry of Education. This ministry is responsible for the development and implementation of educational policies and programs in India.