The correct statement that brings out the principle underlying the Cabinet form of Government is Option 3: A mechanism of parliamentary democracy for ensuring collective responsibility of the Government to the people.

The Cabinet form of government is a system of parliamentary democracy in which the real executive power is vested in a group of officials, known as the Cabinet or Council of Ministers, who are appointed by the Head of the State or Government. The Cabinet members are responsible to the Legislature, which can scrutinize and hold them accountable for their actions.

The principle underlying the Cabinet form of Government is collective responsibility. This means that the Cabinet, as a body, is collectively responsible to the Parliament for all its decisions and actions. If any member of the Cabinet fails to carry out the policies of the Government or makes a decision that is not in the best interest of the people, the entire Cabinet is responsible and can be held accountable by the Parliament.

This principle of collective responsibility ensures that the Government is accountable to the people and is working in their best interest. It also ensures that there is cohesion and coordination among the various departments and ministries of the Government, which is essential for effective governance.

Option 1, which suggests that the Cabinet is formed to minimize criticism against the Government, is not a fundamental principle of the Cabinet form of Government. While it is true that the Cabinet may work to minimize criticism, it is not the primary reason for its formation.

Option 2, which suggests that the Cabinet is formed to speed up the activities of the Government, is not a fundamental principle of the Cabinet form of Government. While the Cabinet may work to expedite the decision-making process, its primary function is to ensure that the decisions made are in the best interest of the people.

Option 4, which suggests that the Cabinet is formed to strengthen the hands of the Head of the Government, is also not a fundamental principle of the Cabinet form of Government. The Cabinet is formed to ensure collective responsibility, and its members work together to make decisions that are in the best interest of the people, not to bolster the power of the Head of the Government.

In conclusion, the Cabinet form of Government is based on the principle of collective responsibility, which ensures that the Government is accountable to the people and working in their best interest. While the Cabinet may work to minimize criticism and expedite decision-making, these are not the fundamental principles underlying its formation.