The constitution states the answer directly.
You do not need to choose the best-known city or compare population figures. “State capital” is a political and legal designation. For the Free State of Sachsen, that role belongs to Dresden.
A concrete reference is the state parliament: Sachsen’s Landtag has its address at Bernhard-von-Lindenau-Platz in Dresden. The Sachsen–Dresden connection therefore becomes more than a memorised city name.

The other three answers
Familiarity does not determine capital status.
Leipzig
Leipzig is not the state capital named in Article 2. Even if that name is especially familiar to you, the required capital is Dresden.
Chemnitz
Chemnitz is not the Free State’s capital. The question requires the fixed pairing of Sachsen and Dresden.
Zwickau
Zwickau is also not the required state capital. Distinguish recognising a city name from identifying the explicitly designated capital.
The city and federal state are different levels.
The Landtag in Dresden is the parliament of all Sachsen. It is not Dresden’s city council. A state institution and a municipal institution can work in the same city while having different responsibilities.
The capital question requires neither a current officeholder’s name nor a ranking by city size. The constitutional rule is the appropriate reference for the answer.
Article 2(1) · Constitution of Sachsen ↗Sachsen → Dresden.
Link the pair to Sachsen’s Landtag in Dresden.
Three words for this question
- die Landeshauptstadtstate capital
- The capital of a federal state; for Sachsen, this is Dresden.
- der FreistaatFree State
- Part of Sachsen’s official name as a German federal state.
- der Landtagstate parliament
- The elected representative assembly of the whole federal state.
