Why in India and great Britain king and rastrapati never do mistake, but in both countries prime minister is head of state executive body, cabinet is under prime minister's control?

The roles and responsibilities of the head of state and head of government differ in India and Great Britain, which is why the king/queen and the president (rastrapati) are less likely to make mistakes compared to the prime minister.

In India, the president is the head of state and is considered the ceremonial figurehead. The president's role is largely symbolic, and they do not have much executive power. The president's duties include the appointment of the prime minister, the opening and closing of parliamentary sessions, and the assent to bills passed by the parliament. However, the president's actions are largely guided by the advice of the council of ministers, headed by the prime minister.

On the other hand, in Great Britain, the monarch (king/queen) is the head of state, but their role is also largely ceremonial. The monarch's powers are limited, and they do not have much involvement in the day-to-day governance of the country. The prime minister, who is the head of government, holds the executive power and is responsible for the administration of the country. The prime minister is the leader of the political party that holds the majority in the parliament and is accountable for the government's actions.

The reason why the king/queen and the president are less likely to make mistakes is that their roles are more symbolic and they do not have direct control over the executive body. They act as a unifying figure and represent the nation, while the prime minister and the cabinet are responsible for the actual governance and decision-making.