Step 1: Understanding the Concept: The Ministry of Youth Affairs and Sports runs various schemes for the development of youth, categorized by the type of activities they fund.
Step 2: Detailed Explanation: The activities mentioned in the question (mountaineering, trekking, canoeing, coastal sailing) are strictly adventure sports.
The 'Promotion of Adventure' scheme provides financial assistance to institutions, youth clubs, and NGOs to organize such adventurous activities.
The goal is to instill traits like courage, teamwork, and risk-taking capacity in the youth.
Other schemes like NSS focus on social service, and National Integration focuses on cultural exchange.
Step 3: Final Answer: These activities fall under the Promotion of adventure programme.