Step 1: Understanding the Concept:
Henry law says the solubility of a gas in a liquid is proportional to its partial pressure. It holds only when the gas does not react with the solvent.
Step 2: Detailed Explanation:
Ammonia reacts with water to give \(\text{NH}_4^+\) and \(\text{OH}^-\). Carbon dioxide reacts with water to give carbonic acid. Their solubility is far more than the law predicts.
Oxygen, nitrogen and methane dissolve physically in water without reacting, so they follow Henry law.
Step 3: Check the options.
(A) NH\(_3\) and CO\(_2\): both react, so the pair does not obey. (B) CO\(_2\) with O\(_2\): O\(_2\) obeys, so not both disobey. (C) NH\(_3\) with N\(_2\) and (D) N\(_2\) with CH\(_4\) each contain a gas that obeys.
Final Answer:
Both gases in option (A) react with water, so they deviate from Henry law.
\[ \boxed{\text{(A)}} \]