Step 1: Recall the source.
Fundamental Duties are in Part IVA, Article 51A of the Constitution. They were not in the original 1950 text.
Step 2: Recall the year.
They were added in 1976, based on the Swaran Singh Committee. The same amendment is often called the Mini Constitution because it changed so much.
Step 3: Match the year with the amendment number.
The amendment passed in 1976 with this content is the 42nd. The 44th, in 1978, worked in the opposite direction by undoing some changes.
Step 4: Select.
So the correct choice is option 2.
Final Answer:
Part IVA with Article 51A was inserted by the 42nd Amendment of 1976, so the answer is option 2.
\[ \boxed{\text{Option 2}} \]