The correct answer is option 1: Ministry of Finance. The Department of Public Enterprises is a part of the Ministry of Finance in the Indian government. The Department of Public Enterprises is responsible for the policy, coordination, and evaluation of the performance of central public sector enterprises (CPSEs). CPSEs are government-owned corporations or companies in which the government has a majority stake.

Option 2: Ministry of Heavy Industries is incorrect because the Department of Public Enterprises is not a part of this ministry. The Ministry of Heavy Industries is responsible for the development and growth of the heavy engineering and machine tools industries in India.

Option 3: PMO (Prime Minister`s Office) is incorrect because the Department of Public Enterprises is not a part of the PMO. The PMO is the central advisory and coordinating body for the Prime Minister of India.

Option 4: Ministry of Commerce and Industry is incorrect because the Department of Public Enterprises is not a part of this ministry. The Ministry of Commerce and Industry is responsible for the promotion of trade, commerce, and industrial development in India.

In conclusion, the Department of Public Enterprises is a part of the Ministry of Finance and plays a crucial role in the management and regulation of central public sector enterprises in India.