The correct answer is:
the Federal President.
der Bundespräsident / die Bundespräsidentin.
Independent study resource, not a BAMF website. Translations are study aids; the exam is in German.
Quick explanation
Federal ministers are appointed by the Federal President.
Why is this correct?
The President acts on the proposal of the Federal Chancellor (Article 64 of the Basic Law).
Background
The federal government consists of the Federal Chancellor and the federal ministers. The Chancellor decides who becomes a minister, usually in agreement with the coalition partners. The ministers are then formally appointed by the Federal President, who hands them their certificate of appointment. They then take their oath of office in the Bundestag.
Why are the other answers wrong?
The President of the Federal Constitutional Court heads the court and has nothing to do with forming the government. The President of the Bundesrat chairs the Bundesrat, the President of the Bundestag chairs the sessions of the Bundestag – neither appoints ministers.
Memory tip
The Chancellor proposes – the President appoints.
Legal basis: Art. 64 Basic Law (GG) ↗
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