The correct answer to the question is option 4, Dadabhai Naoroji. Dadabhai Naoroji was the first Indian to be elected to the Parliament of Great Britain. He was elected as a Liberal Party member from Finsbury Central in London in the year 1892. Naoroji was a prominent Indian political leader, scholar, and social reformer. He is often referred to as the "Grand Old Man of India" and played a significant role in the Indian National Congress and the Indian independence movement.

Option 1, Pheroz Shah Mehta, was an influential Indian political leader and social activist, but he was not the first Indian elected to the Parliament of Great Britain.

Option 2, Lai Mohan Ghosh, is not a historically known figure in the context of Indian politicians being elected to the Parliament of Great Britain.

Option 3, Romesh Chandra Dutt, was an Indian civil servant and writer, but he was not elected to the Parliament of Great Britain.

In conclusion, Dadabhai Naoroji holds the distinction of being the first Indian elected to the Parliament of Great Britain.