It is the powerful compound capsaicin that makes a chili pepper hot;
a single drop that has no taste and odor is capable of detection by humans at one part per million.
Notice how we have a semicolon after the first sentence. This means that the second sentence should be an independent sentence.
(A) a single drop that has no taste and odor is capable of detection
- The drop does not have any capability of its own - incorrect
(B) a single drop is detectable, though without taste and odor,
- seems like a run on sentence and even the meaning is not very clear from the sentence.
also taste and odour should modify a drop but here its modifying detectable so another reason to discard this answer choice.
(C) a single tasteless and odorless drop can be detected
- Correct answer choice - the meaning is clear.
(D) single tasteless and odorless drops are capable of detection
- a run on sentence - does not look like an independent sentence.
Also same error as mentioned in A.
(E) single drops that have no taste or odor can be detectable
- usage of detectable is incorrect.