Whose = Whose is the possessive form of both who and which. We use whose to refer to “animate antecedent.” “Animate” conveys living people and animals (but not plants):
Hot Dog whose dislike of Reggie Mantle is no secret to anyone is now coming to terms with him. √
Here “Hot Dog” is the antecedent of whose.
The plant whose roots had been submerged in water for a long time seems to be dying. ✗
So, when there’s a reference to an animal, the construction of of which seems to be weird. Then, we use ‘whose’:
Researchers claim that the female cheetah named Sarah, the speed of which has been timed at 100 meter dash in 5.95 seconds, is the world’s fastest land animal. (awkward)
Researchers claim that the female cheetah named Sarah, whose speed has been timed at 100 meter dash in 5.95 seconds, is the world’s fastest land animal. √
Some sticklers for perfection say that we use whose to refer to animate antecedents only, but Henry Watson Fowler — perhaps the most strict, and old-fashioned counsellor on English usage termed it as a “folk-belief”.
Nevertheless, if you really want to avoid using whose, you may rephrase the sentence as follows:
The car whose one of the headlights was burned out met with an accident on the National highway.
Since the car’s one of the headlights was burned out, it met with an accident on the National highway.
Of which = When a possessive form is necessitated by a statement, of which is the part of a relative clause. Which is the relative pronoun and of is a preposition that is positioned at the beginning of the relative clause, instead of at the end:
The car, the wheel of which got flat, crashed into a pole.
The room, the roof of which is leaking, needs elaborate repairs.
President said that Democrats are just focusing on impeachment, the purpose of which is to win an election.
I saw a scary movie about ghosts of which I’ve forgotten the name.
Be careful! If your report is full of of whiches, then it is going to do no good. Although, on some particular instances, you might be able to use of which, most of the time, your sentence will look clumsy and unnatural. Most grammar books agree that of which is not a perfect substitute for whose. So, in the end, you will settle with replacing of which with whose when you needed to show possession. It is therefore grammatically correct to write:
President said that Democrats are just focusing on impeachment, whose purpose is to win an election.
Again, this statement looks weird:
President may try to come up with a proposal for the second term the time of which has come. (extremely uncommon)
President may try to come up with a proposal for the second term whose time has come. √
In any case, it may be suggested that unless you’re sure that your sentence doesn’t sound too awkward, just keep away from using of which.