The political executive consists of individuals who hold positions of power and authority within the government and are responsible for making and implementing policies and decisions. These individuals are typically elected or appointed to their positions. From the given options, the following individuals are a part of the political executive:

a. District Collector:
- The District Collector is an administrative officer who is responsible for the overall administration of a district.
- They are appointed by the state government and are responsible for implementing government policies and programs at the district level.
- While the District Collector plays an important role in the administrative functioning of the district, they are not a part of the political executive. They act as a representative of the state government and work under the guidance and supervision of the political executive.

b. Secretary of the Ministry of Home Affairs:
- The Secretary of the Ministry of Home Affairs is a senior bureaucrat who is responsible for overseeing the functioning of the ministry.
- They provide administrative support and advice to the Home Minister and other political executives in the ministry.
- While the Secretary plays a crucial role in the decision-making process and policy implementation, they are not a part of the political executive. They are appointed based on their administrative expertise and serve as civil servants.

c. Home Minister:
- The Home Minister is a high-ranking political executive who is responsible for the overall administration of the country's internal affairs.
- They are typically appointed by the head of state or government and are accountable for maintaining law and order, national security, and disaster management.
- The Home Minister plays a pivotal role in the political executive as they are responsible for formulating and implementing policies related to internal security.

d. Director General of Police:
- The Director General of Police is a high-ranking police officer who is responsible for the overall management and functioning of the police force in a state or at the national level.
- They are appointed by the state government or the central government and work in close coordination with the Home Minister.
- While the Director General of Police holds a position of authority and plays a crucial role in maintaining law and order, they are not a part of the political executive. They are part of the administrative machinery and their role is to implement the policies formulated by the political executive.

In conclusion, among the options given, the individuals who are a part of the political executive are the Home Minister and the Director General of Police. The District Collector and the Secretary of the Ministry of Home Affairs are not a part of the political executive, but they play important roles in the administrative functioning of the government.

According to me the answer is Home minister