While the disease is in (i) critical state it is almost impossible to determine its existence by (ii)observation .

Let me add to that. Latent means that a condition has yet to manifest, so there are no signs to be seen. So it cannot be seen by observation. The other choices are not as good as there are no good answers for them in the second blank.

Critical doesn't fit well here. Can you think of a disease that does not show signs and/or symptoms in its critical stage? You would expect a disease in its critical stage to cause symptoms and signs that we can easily observe.

You would however expect a disease in its latent stage to be to not cause any signs or symptoms making it nearly impossible to observe. It is estimated that one third of the human population is infected with the bacterium that causes tuberculosis. However, in most people, the disease is latent and will not manifest the usual symptoms and signs associated with TB. The only way you can know for sure someone is infected with latent TB is by doing an X-ray of their lungs. I hope the example helps.

Why is "while" used here? There is no contradiction here. If it is latent, it cannot be observed.

Because in this particular context, the word "while" means "during". The word "while" has multiple meanings.

You are thinking of the deffinition of "while" like in this sentence here:

While I like all types of fish, my girlfriend always chooses meat dishes when we go out to eat.

In this example "while" means "although" or "whereas". I can actually see how this definition of while might work in the desease phrase but notice that in the example I provided there is comma between fish and my. There is no comma in the desease phrase. The absense of the comma is a hint that while means during and not although.

Thanks for the explanation!

Here while is used not as a contradiction, while reviewing the question, I understood that.

There is no contrast in this sentence.
By choosing an answer without looking at the answer choices I come up with "its beginning," or "dormant," for the 1st blank and "examination," or "looking for it," in the 2nd blank.
Choice B,F work.

Why not option D

If is the disease is in a latent state, I:E: it exists, it is there, but is not clear where. It is NOT manifest to the external observation. It is hidden, eventually.

Then we cannot observe it

I hope now is clear why it is F

The latent is an appropriate word for the first blank because it is clear from the sentence that it is impossible to determine its existence by observation. the disease is not apparent in any shape therefor it can not be determined by any methodology or other types of tests. regards