Step 1: Understanding the brown ring test.
In the brown ring test, nitrate ions (NO\(_3^-\)) react with iron(II) sulfate to form a brown-colored iron nitrosyl complex, which is paramagnetic. The test is used to confirm the presence of nitrate ions.
Step 2: Conclusion.
The correct statements are that the brown ring is due to the formation of the iron nitrosyl complex, and the brown complex is paramagnetic. Thus, the correct options are (A) and (D).