Step 1: Understanding the Concept:
This question tests the knowledge of chemical nomenclature for common oxides of nitrogen. Both systematic names and common names are used.
Step 2: Detailed Explanation:
Let's identify the correct name for each chemical formula:
(A) N\(_2\)O: The systematic name is dinitrogen monoxide. Its widely used common name is Nitrous oxide. So, (A) matches with (II).
(B) NO: The systematic name is nitrogen monoxide. Its common name is Nitric oxide. So, (B) matches with (III).
(C) N\(_2\)O\(_3\): The systematic name is Dinitrogen trioxide. So, (C) matches with (I).
(D) N\(_2\)O\(_4\): The systematic name is Dinitrogen tetroxide. This molecule exists in equilibrium with nitrogen dioxide (NO\(_2\)). So, (D) matches with (IV).
Step 3: Final Answer:
The correct matching is: (A)-(II), (B)-(III), (C)-(I), (D)-(IV). This corresponds to option 3.