The correct answer is: A. The 35th constitutional Amendment Act (1975).
Sikkim was a monarchy until 1975, when it became the 22nd state of India. The 35th constitutional Amendment Act, passed in 1975, made Sikkim a full-fledged state of India. The Act also provided for the appointment of a Governor for Sikkim and the creation of a Legislative Assembly for the state.
The other options are incorrect. The 37th constitutional Amendment Act (1975) amended the Constitution of India to provide for the creation of a new state of Meghalaya. The 38th constitutional Amendment Act (1975) amended the Constitution of India to provide for the creation of a new state of Manipur. The 36th constitutional Amendment Act (1975) amended the Constitution of India to provide for the creation of a new state of Andhra Pradesh.