word order - How can I say it? "the questions whose answers I don't know" or "the questions that I don't know their answers"?

This may be silly question, looks like the first option is obvious but when I was writing some time ago I couldn't figure out until I wrote it here. Still, I wanted to ask you to learn shortest and best way of articulation.

the questions whose answers I don't know

the questions that I don't know their answers

Answer

The question posits only two possible formations of this phrase:

• The questions whose answers I don't know



• The questions that I don't know their answers

Of these, the second is ungrammatical. The first is acceptable, although many English speakers intuitively feel that "something is wrong" about using whose to refer to things instead of beings (in spite of the fact that Shakespeare himself did so in ~1600CE!)

This usage can be avoided by (as noted in another answer) using the pronoun which instead...

• The questions to which I do not know the answers

This may be preferable in formal writing. However, in idiomatic English, the most common form is...

• The questions [that] I don't know the answers to