vernehmen
to question
(Technical language, especially legal) To officially question or interrogate a person, especially a witness or suspect.
Die Polizei wird den Zeugen morgen vernehmen.
The police will question the witness tomorrow.

to question / to perceive
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to question
(Technical language, especially legal) To officially question or interrogate a person, especially a witness or suspect.
Die Polizei wird den Zeugen morgen vernehmen.
The police will question the witness tomorrow.

'Vernehmen' (to question / to perceive) is an inseparable verb. The prefix 'ver-' remains firmly attached to the verb stem 'nehmen' in all tenses and sentence constructions.
Der Richter vernahm den Angeklagten den ganzen Vormittag.
The judge questioned the defendant all morning.
The verb is derived from 'nehmen' (to take). The prefix 'ver-' gives the word the meaning of taking in or learning something through questioning or through hearing.
Man konnte aus der Ferne laute Rufe vernehmen.
Loud calls could be perceived from a distance.
This meaning of 'vernehmen' (to question) belongs to the technical language of the justice system and police. In everyday language, words like 'befragen' (to question) or 'verhören' (to interrogate) are used instead.
Der Beschuldigte wurde von der Staatsanwaltschaft vernommen.
The suspect was questioned by the public prosecutor's office.
In this meaning, 'vernehmen' (to question) always takes an accusative object that refers to the person being questioned. The person's role is often added with 'als' (as), for example 'jemanden als Zeugen vernehmen' (to question someone as a witness).
Die Kriminalpolizei wird sie als Zeugin vernehmen.
The criminal police will question her as a witness.
In the meaning of 'hören' (to hear), 'vernehmen' (to perceive) is elevated and somewhat old-fashioned. It is found mainly in literature or very formal language to describe the conscious perception of a sound.
In der Stille der Nacht vernahm sie plötzlich Schritte im Flur.
In the silence of the night, she suddenly perceived footsteps in the hallway.
to learn
'lernen' and 'vernehmen' can both have to do with perceiving or becoming aware of something in an elevated or formal style. In this meaning, 'lernen' means to find out a piece of information; however, that already sounds formal. 'vernehmen' here means more that you hear a sound, noise, or voice. It is elevated and not very common in everyday speech today. The difference is important: 'lernen' refers to information, while 'vernehmen' refers to hearing or perceiving something. In everyday language, people usually say the simpler 'erfahren' (to find out) or 'hören' (to hear).

In der stillen Bibliothek konnte man plötzlich eine leise Stimme vernehmen.
In the quiet library, one could suddenly hear a soft voice.
Aus dem Bericht lernte er, dass die Sitzung verschoben worden war.
From the report, he learned that the meeting had been postponed.