how you arrived at (d) for the second blank?

A full account of the complexities of sleep, sought after by scientists, philosophers, and mystics for millennia, continues to elude us. That we are still so ignorant about a topic so (i) _________ to our daily lives is at once fascinating and (ii) _________.

Blank (i)	Blank (ii)
(A) mysterious	(D) deeply humbling
(B) obscure	(E) fully impenetrable
(C) pertinent	(F) totally blatant

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Explanation

Sleep is important, or relevant, to your daily life, making pertinent the best word for the first blank. Don’t be misled by the fact that you don’t fully understand sleep into choosing mysterious or obscure; both are trap answers (being ignorant about a mysterious or obscure topic is hardly “fascinating”).

It is also grammatically incorrect to call a topic mysterious or obscure to your daily life. Regarding the second blank, the expression “at once X and Y” indicates at least a loose contrast, so you need something that could contrast with fascinating. The clue “so ignorant” is a good indication that what you want is deeply humbling. Don’t fall for the trap answer fully impenetrable. While the topic of sleep is presented as somewhat impenetrable (that is, hard to understand), the blank is not describing sleep, but rather your ignorance about it.

Pertinent, deeply humbling.
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"Philosophers, scientists and Mystics"-none of them have been able to make a full account of the complexities of sleep hence it is fascinating that people of such caliber have not been able to find all the information yet it also puts a question mark on their capabilities, or pride that comes with their status and hence makes deeply humbling a proper contrast to fascinating.
We can also get rid of "fully impenetrable" because yes none of the above mentioned type of people have been able to find all about sleep but this does not mean that the task is fully impenetrable. Totally blatant is not coherent with the sentence, it does not establish any contrast.
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A full account of the complexities of sleep, sought after by scientists, philosophers, and mystics for millennia,continues to elude us. That we are still so ignorant about a topic so (i) _________ to our daily lives is at once fascinating and (ii) _________.


That we are still so ignorant about a topic so (i) relevant to our daily lives is at once fascinating and (ii) ___________.

The word from the choice list is pertinent.

The phrase "at once" suggests opposites. We need a sentiment that is opposite to that conveyed by fascinating.

While we are fascinated by our ignorance,we are also conscious of our ignorance, which can upset us or make us be aware of our limitations when it comes to knowing things.

The word from the choice list is deeply humbling.

There is nothing fully impenetrable about our ignorance of complexities of sleep. It is the complexity itself that ma be impenetrable.

The phrase totally blatant does not convey the opposite sentiment of fascinating.
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obscure and deeply humbling

Kindly explain blank 2. Please.

what is the doubt you have in mind ??