Sentences with "a pair of"

[jack]

I have a pair of socks. <--correct?
I have a pair of sock. <--incorrect?

"I like your new pair of shoes." <--correct?
"I like your new pair of shoe." <--incorrect?

"A pair of" makes the object plural right? Does this apply to all cases?

[Tdol]

Pair = 2, so use the plural.

[jack]

What do these mean?

1. Your trousers are coated in mud!
2. Your pair of trousers is coated in mud!
3. Your trousers is coated in mud! (This is wrong right?)

[Casiopea]

Trousers have two legs, and so they are called a pair. Note, 'a pair' is treated as a singular noun; it's a unit, and it's countable: one pair, two pairs, three pairs, and so on.

1. is correct; 2. is correct; 3. is incorrect. In addition, 4. is correct:

4. Your trouser is in the mud. (It means, Your trouser (leg) is in the mud; 'leg' has been omitted.)

[jack]

1. Your trousers are coated in mud! (Since 'are' is here, does it mean many pairs of trousers? Or is it a shorthand for 'Your pair of trousers is coated in mud!' ? )

[blacknomi]

Logically, yes. Unless you can wear as many pairs as possible to join the Guiness World Records.

http://www.guinnessworldrecords.com/

[jack]

Thanks.

[blacknomi]

No problem. Jack-O' Lantern.