Step 1: The question asks which country was the first to set up a dedicated, full-fledged central government ministry devoted only to new and renewable energy sources.
Step 2: India created the Department of Non-Conventional Energy Sources in 1982, which was later upgraded to a full ministry, the Ministry of Non-Conventional Energy Sources, and is known today as the Ministry of New and Renewable Energy (MNRE). India remains widely cited as the first country in the world to set up such a full-fledged ministry for this purpose.
Step 3: Bangladesh, Japan and China all run renewable energy programs, but these are handled through their general energy or power ministries and departments rather than a separate, full-fledged renewable energy ministry, so options 2, 3 and 4 are incorrect.
Step 4: Therefore the correct answer is India.