The word "archaic" describes something that is very ancient. Often, this also implies that the given thing is out of date. The word "obsolete" best describes something of this sort. Do not be tricked by "historical". Things that are not very ancient can still be historical. Likewise, something archaic might be tedious to deal with, but this is not necessarily the case. 

"Intermittent" means sporadic, occurring randomly and infrequently. To provide further help, "fastidious" means obsessive and hard to please; "exhaustive" means comprehensive; "frequent" means occurring regularly; "torpid" means lethargic, lacking energy. 

"Expedient" when used as an adjective means convenient, advantageous. When used as a noun it means a means of achieving something, a scheme. To provide further help, "reticent" means reluctant to share, withdrawn; "truculent" means aggressive; "ebullient" means enthusiastic; "incumbent," when used as an adjective, means required, obligatory. "Incumbent" can also be used as a noun in which case it means person who already holds the office or title. 

Privy means to be in on or sharing some secret knowledge, or informed.

The word “spurious” most generally means false or fake, often implying that the fake thing does not at first appear to be fake, though it really is. Often, one will find the word used to describe a “spurious argument” or a “spurious claim,” meaning arguments and claims that are ultimately false.

"Demonstrative" is an adjective that can mean openly demonstrating feelings or providing conclusive proof. We need to pick out an adjective that means something like showing feelings or providing proof. "Inconclusive" cannot be the correct answer because it is an antonym of the second meaning of "demonstrative," providing conclusive proof. "Indisputable," however, is an adjective that means unable to be disputed and because it is the answer choice closest in meaning to "demonstrative," "indisputable" is the correct answer.

Affected means artificial or pretentious.

When used as an adjective, the word “dubious” means “doubting” or “hesitating.” It is clearly related to “dubious” as well as the word “indubitable,” which means “unable to be doubted.” It would be used in a sentence like, “Since the argument presented to him was rather weak, John remained rather dubious regarding the truth of its conclusions.” Among the options provided, “uncertain” is the closest to this sense.

"Candid" means impartial, open, or honest. "Caustic" means burning or sarcastic. "Corporal" means bodily or physical. "Prevalent" means accepted or widespread. "Ubiquitous" means ever-present or pervasive. 

"Cognitive" and "logical" both mean reasonable or rational. "Irrational" means illogical or senseless. "Eclectic" means comprehensive or diverse. "Irascible" means crabby or cantankerous. "Voluble" means talkative or chatty.