According to the provisions of the Constitution of India, the fundamental duties are a set of moral obligations that citizens are expected to follow. They were added to the Constitution in 1976 through the 42nd Amendment. These duties are not legally enforceable like fundamental rights, but they serve as a moral guide for citizens.

Option 1: To respect the National Flag – This is a fundamental duty as it emphasizes the importance of showing respect to the National Flag, which is a symbol of our nation and its values.

Option 2: To defend the country – This is a fundamental duty as it emphasizes the importance of protecting and defending our country from external threats and upholding its sovereignty.

Option 3: To provide education to one’s child – This is a fundamental duty as it emphasizes the importance of education and the responsibility of parents to provide education to their children.

Option 4: To promote village and cottage industries – This is not a fundamental duty. While promoting village and cottage industries may be important for rural development and the economy, it is not explicitly mentioned as a fundamental duty in the Constitution of India.

Therefore, the correct answer is option 4.