What does 'fetch' mean and is 'object to' followed by a gerund?

[dorados]

Dear Alan I did tests and there were such questions:
Somebody must ........up her daughter at the airport.
a)catch
b)fetch
c)take
d)pick
I answered take. Is it correct or not?

And second question:
Teacher objected to students.........gum.
a)to chew
b)chew
c)chewing
I answered chewing.

[Alan]

You need pick up, which means in fact fetch and object to someone would be followed by the gerund/ing form chewing.
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