Answer : 1. "1976"
Explanation :

1. The Fundamental Duties of the citizens were added to the Constitution of India by the 42nd Constitutional Amendment Act, 1976.

2. By this amendment a new Part IV-A was added to the Constitution

3. In which 10 fundamental duties were included under Article 51A.

4. The idea of Fundamental Duties is inspired by the Constitution of Russia (erstwhile Soviet Union).

5. The 11th Fundamental Duties were added to the Constitution of India in the year 2002 through the '86th Constitutional Amendment'