Munich is Bavaria’s state capital.

Capital describes a particular political role.

For the exam question, you need a clear connection: Bavaria → Munich. It asks neither for your home town nor for the city most familiar from a trip or history book. State capital is a specific, established designation.

Munich is also a city with its own municipal administration. Munich’s city administration and the Bavarian State Government are therefore not the same institution, even though both work in Munich. An administrative region within Bavaria is likewise a different level from the entire Free State.

The other three answers

The other city names do not change which city is Bavaria’s capital.

Not every state authority must be based exclusively in Munich.

The official ministries directory lists additional offices in places such as Nürnberg and Augsburg alongside Munich addresses. That is compatible with Munich’s status as state capital. The answer depends on that status, not a complete list of administrative locations.

The English explanation uses Munich while preserving the existing answer München. The two names do not identify different cities. The full stop at the end of the catalogue answer is simply part of its sentence formatting.