The correct answer is option 1, which states that only statement 1 is correct. Let`s dissect each option to understand why.

Option 1: "I only" - This option is correct because it states that only statement 1 is correct. Statement 1 says that the five permanent members of the Security Council are the only countries recognized as nuclear-weapon States under the Nuclear Non-Proliferation Treaty. This is true, as the five permanent members (United States, Russia, China, France, and the United Kingdom) are the only countries recognized as nuclear-weapon states.

Option 2: "2 only" - This option is incorrect. Statement 2 says that the term of non-permanent members of the Council is five years. However, this is not true. The term of non-permanent members of the Security Council is actually two years.

Option 3: "Both 1 and 2" - This option is incorrect. As mentioned earlier, statement 2 is incorrect, so both statements cannot be correct.

Option 4: "Neither 1 nor 2" - This option is also incorrect. Statement 1 is correct, so this option cannot be correct.

In conclusion, the correct answer is option 1, as statement