The characteristic of a nation-state includes:

Common political institutions and geographical boundary

The correct answer is Option (1) → Common political institutions and geographical boundary.

1. Common political institutions: A nation-state usually has a unified government system that exercises authority over the entire territory. This may include institutions such as a central government, legislative bodies, judiciary, and administrative agencies. These institutions work together to govern the population within the defined territory.

2. Geographical boundary: A nation-state has clearly defined borders or boundaries that demarcate its territory from neighboring states or territories. These boundaries are recognized internationally and serve to establish the extent of the nation-state's sovereignty and jurisdiction.

These two characteristics are fundamental to the concept of a nation-state, as they signify a political entity with a distinct territory and a unified system of governance over the population residing within that territory.