Option 1: K. M. Cariappa - K. M. Cariappa was the first Indian Commander-in-Chief of the Indian Army but not the first Defence Minister of India.
Option 2: Gopalaswami Aiyangar - Gopalaswami Aiyangar was a prominent Indian politician and served as the Minister of Finance in the Interim Government of India in 1946. He did not hold the post of Defence Minister.
Option 3: Baldev Singh - Baldev Singh was the first Defence Minister of India. He served as the Defence Minister from 1950 to 1952. He played a crucial role in the integration of princely states into the Indian Union.
Option 4: Sardar Patel - Although Sardar Patel was a key figure in the Indian independence movement and played a significant role in the integration of princely states, he did not serve as the Defence Minister of India.
Therefore, the correct answer is option 3, Baldev Singh.