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is Mum a proper noun/title so it takes a capital?
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I would think that it could be either, depending on whether you are talking about mums in general (common noun) or a particular mum (proper noun) as it is then her 'name'.

So,

Teacher: 'Would all mums and dads please make sure their children bring a packed lunch to school tomorrow'.

Kid: 'Mum, can I have cheese and pickle sandwiches?'.

I don't think anyone would object if you always treated it as a proper noun though.
Comments  
The word mum used as an adjective means silent.

The word mum used as an noun means silent

The word mum is British which is means Mom.

Hope this helps Emotion: smile
 nona the brit's reply was promoted to an answer.