In political science, a republic is a form of government where a state or country is primarily governed in which of the following ways?

Introduction / Context:
The word republic is frequently used in civics and political science, but learners often confuse it with terms like democracy or monarchy. Understanding the meaning of a republic is essential for exams on Indian polity and general knowledge, because the Preamble of the Constitution of India clearly describes the country as a sovereign, socialist, secular, democratic republic. This question tests whether you understand that a republic is defined by the way the head of state and the government are chosen and how they derive their authority from the people through representation.

Given Data / Assumptions:

• The term to be defined is republic in the context of political science and constitutional law.
• We are comparing different possible forms of rule such as rule by nobody, rule directly by the public, rule by elected representatives and rule by a royal family.
• The focus is on how power is held and exercised in a republic, not on economic or social systems.
• We assume the standard textbook definition where a republic has an elected head of state and government that is responsible to the people.

Concept / Approach:
A republic is usually defined as a form of government in which the head of state is not a hereditary monarch and where public offices are held by individuals chosen, directly or indirectly, by the people. In a republic, the authority of the government comes from the consent of the governed, expressed through elections and representation. Therefore, the key phrase you should look for is peoples elected representatives. The question asks which description best fits this idea, so we evaluate each option in light of this central concept, rejecting those that point to anarchy, pure direct democracy or monarchy.

Step-by-Step Solution:
Step 1: Recall that in a republic there is no hereditary monarch as head of state. Step 2: Remember that in a republic authority is exercised by representatives who are elected by the people. Step 3: Examine option C, which says the state is ruled by peoples elected representatives on behalf of the citizens. This exactly matches the core idea of a republic. Step 4: Check option A, which describes rule by no one at all, a situation closer to anarchy rather than a republic. Step 5: Check option B, which speaks of direct rule by the public without representatives, a model closer to pure direct democracy than to a representative republic. Step 6: Check option D, which speaks of rule by a king's family, clearly indicating monarchy, the opposite of a republic. Step 7: Conclude that option C is the only description that correctly captures the idea of a republic.

Verification / Alternative check:
To verify, think about modern countries that officially call themselves republics, such as India or France. In both nations, there is an elected President and elected legislatures. The people vote in elections to choose Members of Parliament or Members of the National Assembly, and these representatives, in turn, make laws and hold the executive accountable. There is no hereditary monarch. When you compare this real world pattern with the options, the description that best matches is rule by peoples elected representatives. This cross check confirms that our choice of the correct option is consistent with both theory and practice.

Why Other Options Are Wrong:
Option A: Rule by no one at all would describe a complete absence of government, similar to anarchy, not the structured representative rule of a republic.
Option B: Direct rule by the public without representatives describes pure direct democracy, where citizens vote on every single law, which is not generally how large modern republics operate.
Option D: Rule by a king's family is the definition of a hereditary monarchy, the opposite of what a republic is meant to be, because in a republic leadership is not inherited.

Common Pitfalls:
A recurring confusion is to think that democracy and republic are exactly the same thing. In reality, democracy refers to the broader principle of rule by the people, while republic focuses on the absence of hereditary monarchy and the presence of elected representatives. Another mistake is to think that if people vote in any form, that system must automatically be a republic; however, there are constitutional monarchies where people vote for the legislature but still retain a monarch. Learners should connect the word republic with ideas such as elected head of state, representation, and non hereditary rule, which will help in answering many polity questions more accurately.

Final Answer:
Ruled by peoples elected representatives on behalf of the citizens.