The correct answer is option 'A' - Home Minister.

The political executive is a branch of the government responsible for making and implementing policies and laws. It consists of individuals who hold political offices and are elected or appointed to represent the interests of the people. In the context of the given question, let's discuss each option and identify which one is a part of the political executive.

a) Home Minister:
The Home Minister is a political executive who is responsible for the maintenance of law and order, internal security, and overall administration of the country. They head the Ministry of Home Affairs and are appointed by the President or Prime Minister. The Home Minister formulates policies, oversees the functioning of various departments under the ministry, and plays a crucial role in decision-making related to national security and public safety. Therefore, the Home Minister is a part of the political executive.

b) District Collector:
A District Collector is a bureaucrat who belongs to the administrative executive rather than the political executive. They are appointed by the state government and are responsible for the overall administration of the district. The District Collector's role includes implementing government policies, maintaining law and order, collecting revenue, and coordinating with various government departments. They work under the guidance and supervision of the political executive but are not a part of it.

c) Secretary of the Ministry of Home Affairs:
The Secretary of the Ministry of Home Affairs is a bureaucratic position and a part of the administrative executive. They are appointed based on their administrative expertise and are responsible for assisting the Home Minister in policy formulation, implementation, and coordination of various departments under the ministry. The Secretary is not a political executive as their appointment is not based on a political mandate.

d) Director General of Police:
The Director General of Police (DGP) is a high-ranking police officer responsible for the overall functioning of the police force in a state or a particular region. They are appointed by the state government or the Union Home Ministry. While the DGP plays a crucial role in maintaining law and order and implementing government policies related to policing, they are part of the administrative executive and not the political executive.

In conclusion, among the given options, only the Home Minister (option 'A') is a part of the political executive as they hold a political office and are responsible for policy-making and implementation in the Ministry of Home Affairs.