Jeg spørger ved receptionen, om der er en udgang tæt på metroens indgang.

Spørge is the infinitive, meaning to ask.
Spørger is the present tense, meaning ask / am asking.

A very common pattern in Danish is:

• spørge = to ask
• spørger = ask / is asking

So after jeg, you need the finite verb spørger.

Danish present tense often covers several things that English separates:

• I ask
• I am asking
• sometimes even I will ask

The exact meaning depends on context. So Jeg spørger ved receptionen can mean I ask at the reception desk, I’m asking at the reception desk, or in the right context I’ll ask at the reception desk.

In a normal Danish main clause, the finite verb usually comes in second position. This is the famous V2 rule.

So in:

• Jeg spørger ved receptionen ...

Jeg is the first element, and spørger is the second.

If you moved another part to the front, the verb would still stay second:

• Ved receptionen spørger jeg ...

That word order is very typical in Danish.

Here ved means something like at, by, or near.

So ved receptionen means at the reception, by the reception, or more naturally at the reception desk / front desk.

Why not i receptionen? Because:

• ved receptionen suggests being at the desk or dealing with the staff there
• i receptionen would more literally mean in the reception area

So ved is a very natural choice here.

Because the sentence refers to a specific reception/front desk, not just any reception.

Danish usually marks definiteness by adding an ending to the noun:

• en reception = a reception
• receptionen = the reception

Also, in this sentence receptionen means the reception desk/front desk, not a social event.

Here om means whether or if. It introduces an indirect yes/no question.

So:

• Jeg spørger ..., om der er en udgang ...

means:

• I ask ..., whether there is an exit ...
• or more naturally, I ask if there is an exit ...

This is different from other uses of om, such as about in some contexts.

Because after om, you have a subordinate clause, and subordinate clauses in Danish do not use main-clause V2 word order.

Compare:

• direct question: Er der en udgang?
• indirect question: ... om der er en udgang

So once the question becomes embedded after om, the order changes to der er, not er der.

This der is a dummy subject, just like English there in:

• there is an exit

So:

• der er en udgang = there is an exit

It does not mean a physical location here. It is just part of the standard existential structure used to say that something exists.

Udgang is a common-gender noun, so the singular indefinite article is en:

• en udgang = an exit

It is indefinite because the speaker is asking about any exit, not a specific exit already known to both speaker and listener.

If it were definite, it would be:

• udgangen = the exit

They are a very neat pair:

• indgang = entrance
• udgang = exit

The prefixes help:

• ind- = in
• ud- = out

So the sentence is contrasting an exit with the metro’s entrance.

Tæt på is a fixed expression meaning close to or near.

So:

• tæt på metroens indgang = close to the metro’s entrance

You can use tæt på with many kinds of nouns:

• tæt på stationen = close to the station
• tæt på hotellet = close to the hotel
• tæt på mig = close to me

It works very much like English close to.

Yes, you could also say indgangen til metroen.

In the sentence you were given, metroens is the genitive form of metroen:

• metroen = the metro
• metroens = the metro’s

So:

• metroens indgang = the metro’s entrance

This is a perfectly normal Danish possessive structure.
But indgangen til metroen is also very natural and often feels a bit more like standard everyday phrasing in this kind of context.

The comma marks the beginning of the subordinate clause:

• om der er en udgang tæt på metroens indgang

In Danish, many writers place a comma before subordinate clauses like this.

You may also see sentences without that comma, depending on the comma style being used. So the comma here is normal, but its omission can also be acceptable.