The correct answer is option 4: Neither 1 nor 2.
Let`s dissect each option to better understand why the answer is option 4.
Option 1 states that the Fundamental Duties were added to the Constitution of India during the tenure of Lal Bahadur Shastri as the Prime Minister of India. However, this statement is incorrect. The Fundamental Duties were actually added to the Constitution of India through the 42nd Amendment Act of 1976, which took place during the tenure of Prime Minister Indira Gandhi.
Option 2 states that there are ten Fundamental Duties for every citizen of India according to the Constitution. This statement is also incorrect. The Constitution of India originally listed eight Fundamental Duties. However, the 86th Amendment Act of 2002 added one more Fundamental Duty, making it a total of nine.
Since both statements in the options are incorrect, the correct answer is option 4: Neither 1 nor 2.
Note: It is important to keep in mind that the Fundamental Duties are a set of moral, ethical, and civic obligations for citizens and were added to the Constitution to promote and uphold the values of the Indian society.