"There are 2 words one of which I don't know the meaning."
"There are 2 words one of which I don't know the meaning of."
Which one is correct and why? If one of them is at all correct.
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Only the first sentence is correct.
The relative pronoun together with "of" heads the subordinate clause and sets the possessive relationship with antecedent, 'Words'. "Of which" serves the function of " whose". However, 'whose' cannot be used here because of the 'two' we like to highlight 'one' unknown.
If we are asked to split the sentence the last "of " is simply redundant.
Had we been a bit more idiotic we have a chance to relegate "of" to the end point.
There are instances where in informal speech (even in literal use) we use relative pronoun and preposition separately and sometimes ellide the relative pronoun all together, but that's not the case here.
two words... the meaning of one of which ... I do not know
two words ... one of which... I do not know the meaning of.
There are two words. I do not know the meaning of one of them.
We can concatenate these attributive of-phrases.
the market price of the catch of the day.
I do not know the market price of the catch of the day.
...the retail and wholesale prices of the catch of the day. Two prices, one of which I do not know. I know only the retail price.