Which Fundamental Duty was added by the 86^th Constitutional Amendment in 2002?

The correct option is "To provide opportunities for education to children aged 6–14 years".

Step-by-Step Explanation:

1. Background of Fundamental Duties:
Fundamental Duties were not part of the original Constitution of India. They were incorporated into Part IV-A (Article 51A) of the Constitution by the 42^nd Constitutional Amendment Act in 1976, following the recommendations of the Swaran Singh Committee. Originally, ten Fundamental Duties were added.

2. The 86^th Amendment Act, 2002:
In 2002, the 86^th Constitutional Amendment Act was enacted to make education a fundamental right for children. This amendment made major changes across different parts of the Constitution:
- It inserted Article 21A (Right to Education as a Fundamental Right).
- It modified the directive principle in Article 45.
- It added an eleventh duty to the list of Fundamental Duties under Article 51A(k).

3. The Eleventh Duty:
The newly added eleventh duty states that it is the duty of every citizen of India who is a parent or guardian to provide opportunities for education to his child or ward between the age of six and fourteen years.

Therefore, the duty "To provide opportunities for education to children aged 6–14 years" is the correct answer.