Always connect the particular state with its capital.
Read the state’s full name in the question. Baden-Württemberg connects to Stuttgart. The four options are city names; the question asks about their political function, not how familiar a city is to you.
Stuttgart is home to both state institutions and the city’s own administration. Being in the same city does not make them one authority. A municipal question and a question for a state ministry may therefore have different points of contact.
The other three answers
None of the other three city names is the capital sought here.
Heidelberg.
Heidelberg is not the state capital in this question. A familiar city name is not enough; the pair to learn is Baden-Württemberg and Stuttgart.
Karlsruhe.
Karlsruhe is not the state capital of Baden-Württemberg sought here. Do not confuse a city’s importance or institutions located there with the role of state capital.
Mannheim.
Mannheim is also incorrect. The question does not ask you to choose by size, familiarity or economic importance; it asks for the state capital’s name.
State, city and individual authority remain distinct.
Being the capital does not mean that the city administration governs the entire federal state. The state government and municipal administration have different functions and responsibilities.
Population figures and rankings can change and are unnecessary for this answer. What matters is the capital relationship explicitly identified by the state and city portals.
Geography · State capital · State of Baden-Württemberg ↗Baden-Württemberg → Stuttgart.
Say the two names together. Learn “state capital” as a function, not merely praise for an important city.
Three words for this question
- die Landeshauptstadtstate capital
- The capital of a federal state.
- die Stadtverwaltungcity administration
- The administration responsible for a city’s municipal affairs.
- der Dienstsitzofficial office location
- The place where an authority or office is based.