Option 1: 35th Amendment Act: This option cannot be the correct answer because it does not pertain to the admission of Sikkim into the Union of India.

Option 2: 36th Amendment Act: This is the correct answer. The 36th Amendment Act, passed in 1975, was responsible for Sikkim`s admission into the Union of India. Prior to this amendment, Sikkim was a protectorate under the Indian government but not a full-fledged state.

Option 3: 37th Amendment Act: This option cannot be the correct answer as it is not the correct Amendment Act related to Sikkim`s admission into the Union of India.

Option 4: 38th Amendment Act: This option cannot be the correct answer as it is not the correct Amendment Act related to Sikkim`s admission into the Union of India.

In conclusion, the correct answer is option 2, the 36th Amendment Act. This Act facilitated the admission of Sikkim into the Union of India in 1975.