Moet ik mijn jas uitdoen?

Because this is a yes/no question in Dutch. In main-clause questions, Dutch usually puts the verb first and the subject second:

• Statement: Ik moet mijn jas uitdoen.
• Question: Moet ik mijn jas uitdoen?

This is similar to English Must I...?/Do I have to...?

Moet is the singular present tense of moeten, which usually means:

• must
• have to
• need to

In this sentence, it can sound like:

• Do I have to take off my coat?
• Should I take off my coat?

The exact English translation depends on context. Dutch moeten often covers both obligation and practical necessity.

Mijn jas means my coat/jacket.

• mijn = my
• jas = coat / jacket

Jas is the normal dictionary form.
Jasje would be a diminutive, meaning something like little jacket or sometimes just a lighter, smaller jacket, depending on context.

So mijn jas is the neutral, standard form.

Because mijn is the possessive adjective meaning my.

Compare:

• mijn jas = my coat
• mij = me

So:

• Moet ik mijn jas uitdoen? = correct
• Moet ik mij jas uitdoen? = incorrect

Uitdoen is a separable verb.

It is made of:

• uit = out/off
• doen = do

Together, uitdoen means things like:

• take off (clothes)
• switch off / turn off (a light, device)

In Dutch, separable verbs often split in main clauses:

• Ik doe mijn jas uit. = I take off my coat.

But when the verb is in the infinitive, as here after moet, it stays together:

• Moet ik mijn jas uitdoen?

Because after a modal verb like moeten, the second verb usually appears as an infinitive at the end of the clause.

So:

• moet = conjugated modal verb
• uitdoen = infinitive

That is why you get:

• Moet ik mijn jas uitdoen?

Compare:

• Ik doe mijn jas uit. → split, because doe is the conjugated main verb
• Ik moet mijn jas uitdoen. → together, because uitdoen is an infinitive

No, that is not natural Dutch for this meaning.

The normal expression is:

• je jas uitdoen = to take off your coat

So the correct sentence is:

• Moet ik mijn jas uitdoen?

Dutch treats uitdoen as one separable verb, not as a separate uit placed before mijn jas in this structure.

Jas is a de-word noun: de jas.

For this sentence, that does not really affect the form, because:

• mijn is used with both de and het nouns in the singular
• there is no adjective here that changes form

So you simply say:

• mijn jas

It is neutral and works in both formal and informal situations.

Nothing in the sentence itself is especially formal or casual. It could be used:

• at someone’s house
• at a doctor’s office
• in a classroom
• in a cloakroom or waiting room

If needed, politeness usually comes from tone or extra words, for example:

• Moet ik mijn jas uitdoen, of niet?
• Moet ik mijn jas uitdoen, mevrouw?

They ask different things:

• Moet ik mijn jas uitdoen? = Do I have to / Should I take off my coat?
• Mag ik mijn jas uitdoen? = May I take off my coat? / Am I allowed to take off my coat?

So:

• moeten = obligation / necessity
• mogen = permission

That is a very important distinction in Dutch.

Yes. Uitdoen is commonly used for more than one thing:

• je jas uitdoen = take off your coat
• het licht uitdoen = turn off the light
• de tv uitdoen = switch off the TV

So the meaning depends on the object. With jas, it clearly means take off.

The normal statement is:

• Ik moet mijn jas uitdoen. = I have to take off my coat.

This helps show the word order:

• Statement: Ik moet mijn jas uitdoen.
• Question: Moet ik mijn jas uitdoen?

The only change is that the finite verb moet moves to the front for the yes/no question.