The real executive of the Indian Union is the Prime Minister. This is because the Prime Minister is the head of the Council of Ministers, which is responsible for the administration and governance of the country. The Prime Minister is appointed by the President and is the leader of the political party or coalition that has the majority in the Lok Sabha, the lower house of the Parliament of India.

The Prime Minister holds the most powerful position in the executive branch of the government. They have the authority to make key decisions and implement policies that affect the functioning of the country. The Prime Minister represents the country both domestically and internationally and is responsible for maintaining the unity, integrity, and security of the nation.

The Prime Minister's role and powers can be further understood by considering the following points:

1. Head of Government: The Prime Minister is the head of the government and exercises executive powers. They are responsible for the day-to-day administration of the country.

2. Forming the Council of Ministers: The Prime Minister selects and appoints ministers to the Council of Ministers. They allocate portfolios to the ministers and can reshuffle the cabinet as and when required.

3. Policy Formulation: The Prime Minister plays a crucial role in formulating policies and making important decisions. They provide leadership and direction to the government in matters of national importance.

4. Legislative Functions: The Prime Minister plays a significant role in the legislative process. They are responsible for guiding government bills through the Parliament and ensuring their passage.

5. International Relations: The Prime Minister represents the country in international forums and plays a key role in foreign policy formulation. They engage in diplomatic negotiations and maintain relationships with other countries.

6. Crisis Management: The Prime Minister is responsible for managing crises and emergencies that may arise in the country. They provide leadership and take necessary actions to address the situation.

In conclusion, the Prime Minister is the real executive of the Indian Union as they hold the highest executive authority and are responsible for the governance and administration of the country. Their role encompasses policy formulation, decision-making, legislative functions, international relations, and crisis management.