The answer for the blank(i) should carry a positive meaning as the drug do not have any side effects. And also the blank(ii) should contrast with benign. So it must be a negative word. Hence, promulgate and nugatory are the answers.

How can the first blank be positive when the drug is actually futile? I think wane should be the answer for blank 1.

Yes true. Promulgate does not make any sense.

the stocks will plunge because the related product on the market share was not so good as promising

The answer must be C.

Options are sequenced incorrectly in the original post. Please update accordingly. Below is the actual ques:

Analysts project that the pharmaceutical company’s stock price will (i)__________as the “promising” new drug’s effects have turned out to be largely (ii)__________but benign.

Blank (i)	Blank (ii)
dally	antiseptic
wane	noisome
promulgate	nugatory

Official explanation - ManhattanPrep
The quotation marks around “promising” indicate that the new drug did not perform up to expectations; this would have a negative effect on the stock price. Thus, a good filler for blank (i) is “decrease” or “go down.”

(A) Dally means either “to play, trifle, or toy with” or “to dawdle, waste time, or loiter.” Neither definition matches the filler. Even if it could be said that a stock price will dawdle or loiter, that would probably mean “do nothing, remain the same” not “go down.”
(B) CORRECT. Wane means “to decrease in intensity, quantity, or strength,” so this is a good match.
(C) Promulgate means “to make widely known by public declaration or official announcement.” This is not a good match.

We already know that the new drug did not perform up to expectations. The drug’s effects are contrasted with the fact that they are also “benign,” which means “neutral or harmless in its effects and influence” Thus, blank (ii) cannot be either “gentle” (i.e. good) or “harmful.”

(D) Noisome means “noxious, harmful, or dangerous.” If the effects were noisome, they could not also be “benign.”
(E) Antiseptic means “protecting against infection” or “clean, sanitized.” This choice does not match well with “but benign”: if the drug protected against infection that would be a good thing. This choice relates to medicine but is a theme trap; it does not fit within the specific context of the sentence.
(F) CORRECT. Nugatory means “of little value; inconsequential” or “without effectiveness.” This is a good match.