Statement I: Correct. Raga Bhairav is traditionally sung in the early morning hours, specifically during sandhiprakash kaal — the transitional twilight period at sunrise. Its mood and structure suit the peaceful, calm morning atmosphere.
Statement II: Incorrect. Raga Malkauns is a late night raga, usually performed between midnight and 3 AM. It is known for its serious, deep, meditative feel, which does not align with morning time.
So, only Statement I is true.