"How is your mother?"

Translation: तुम्हारी माँ कैसी हैं?

[Mark314319]

Why is it plural at the end?

[vinay92]

In Hindi, words referring to people elder than you or in positions of authority are treated as if they were plural as a way of showing respect. This is not a grammatical requirement but is usually done in practice.

So, माँ is conjugated with the plural form हैं.

[pauline286306]

Why it is not "ho" at the end ?

[vinay92]

The verb is conjugating with माँ ('mother') not तुम ('you').

[MartinBetz2]

Is तुम्हारी rude / too personal? Or would that be तेरी?

[vinay92]

तुम्हारी is less personal/more formal than तेरी but more personal/less formal than आपकी.

In general, you can use the तुम forms (like तुम्हारी) with most people who are around the same age as you or younger (except in a formal/professional context where आप forms would be more appropriate). It might also be a good idea to start off with आप forms for strangers and then move on to तुम once you get to know the person a little.