The correct answer is option 3, M. Veerappa Moily. The second Administrative Reforms Commission (ARC) was established in 2005 with the aim of studying and recommending measures to improve the efficiency, effectiveness, and accountability of the Indian administrative system. M. Veerappa Moily, a senior Indian National Congress politician, served as the chairman of the commission.
Option 1, Bimal Jalan, is not the correct answer. Bimal Jalan is an Indian economist and former Governor of the Reserve Bank of India, but he did not serve as the chairman of the second Administrative Reforms Commission.
Option 2, Dr. Karan Singh, is also not the correct answer. Although Dr. Karan Singh is a prominent Indian politician and served in various government positions, he was not the chairman of the second Administrative Reforms Commission.
Option 4, Ahmed Patel, is also not the correct answer. Ahmed Patel was a senior Indian National Congress politician, but he did not serve as the chairman of the second Administrative Reforms Commission.
Therefore, the correct answer is option 3, M. Veerappa Moily.