Statement (I) is correct because the term 'Union Cabinet' is indeed mentioned only once in the Constitution of India, specifically in Article 352(3) which deals with the National Emergency. Statement (II) is incorrect. The term 'Union Cabinet' was not inserted by the 42nd Amendment. It was already present in Article 352(3) prior to the 42nd Amendment. However, the 42nd Amendment did make significant changes regarding the President's power to declare an emergency, including specifying that the President can only issue a proclamation of national emergency after receiving a written recommendation from the Cabinet. The term 'Cabinet' was explicitly added to Article 352(3) by the 44th Amendment Act, 1978, not the 42nd Amendment.