I am looking for a particular word that describes:
a question that is asked in order to expose ignorance/lack of knowledge.
As with a rhetorical question, the questioner knows the answer, but suspects the person being addressed doesn't.
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Teachers sometimes refer to this kind of question as a trap:
From The Pragmatics of Mathematics Education by Tim Rowland:
One common perception is that the questions teachers ask their pupils are not searchlights focused to reveal truth, but traps set to expose ignorance.
Rowland was quoted in Teacher-student Interaction by Alandeom Wanderlei de Oliveira.
Seymour B. Sarason expresses the same notion in a different way in Letters to a Serious Education President:
They are both surprised and puzzled by my question, as if I am setting a trap to expose their ignorance.
Teachers and politicians sometimes call these "gotcha questions."
Here's an excerpt from a discussion of gotcha questions in a Daily Caller article:
The infamous “gotcha” question is something politicians always rail >against. But what exactly defines a “gotcha”?
“I suppose a gotcha question is one that’s fundamentally unfair because it has a hidden or misleading premise,” former Clinton White House adviser and CNN contributor Paul Begala told The Daily Caller. He provided this example: “Q: Which Yankee before Jeter had 3,000 hits? A: No one!”
“A gotcha question is a knowledge question in which the moderator attempts to make the person … look stupid,” offered infamous Republican political consultant Roger Stone. “I think it is more like saying to Donald Trump, you know: ‘How many members of the U.S. House of Representatives [are there]?’”
A pointed question; one that cannot be answered with a vague generalization, but only precisely.
BTW "asking a rhetorical question" doesn't mean that you suspect the hearer(s) don't already know the answer. It means you are making a statement (perhaps of something that is obvious) more emphatic by expressing it as a question, for example "Do you want to be free men or slaves?"
While I am unable to offer a noun, there are a couple of adjectival descriptions which typify questions designed to achieve certain ends, which could prove useful, i.e., “tactical”, “calculated”.
tactical adjective: of, relating to, or constituting actions carefully planned to gain a specific military end.
• (of a person or their actions) showing adroit planning; aiming at an end beyond the immediate action.
synonyms: calculated, planned; see Google tactical
calculate verb: 3rd person present: calculates; past tense: calculated; past participle: calculated; gerund or present participle: calculating
2. intend (an action) to have a particular effect. "his last words were calculated to wound her"
Or, “the question was calculated to expose his ignorance.”
synonyms: intend, mean, aim, design; Google calculate
test \ˈtest\ noun -MW
2,a : (2) something (as a series of questions or exercises) for measuring the skill, knowledge, intelligence, capacities, or aptitudes of an individual or group
If (underlined) If you happen to be a troll, this question was a test of our gullibility; seeking the knowledge of if we're unbeknownst to your trollishness and how far you'd get away with it.
I think the closest term to what you're looking for is a trick question, defined by Wiktionary as:
A complex question, whose wording hinders the ability to answer it correctly.
Basically, these are questions designed to make the person answering fail. For example:
- When did Elvis Presley die?
- Is that a trick question? The King's not dead!
I saw it wasn't listed so it took me an hour of googling to find this specific word for you. Depending on your intention of use this is a word that captures a different but similar meaning to what you said you are trying to find.
A shibboleth (/ˈʃɪbəlɛθ/ or /ˈʃɪbələθ/) is a word or custom whose variations in pronunciation or style can be used to differentiate members of ingroups from those of outgroups. Within the mindset of the ingroup, a connotation or value judgment of correct/incorrect or superior/inferior can be ascribed to the two variants.
'In A cleft stick' - "In a difficult situation, unable to choose between unfavourable options; in a dilemma. "
Source; Wiktionary http://en.wiktionary.org/wiki/in_a_cleft_stick
'Caught between a rock and a hard place' - "Having the choice between two unpleasant or distasteful options; in a predicament or quandary."
Source; Wiktionary http://en.wiktionary.org/wiki/between_a_rock_and_a_hard_place
I think a "trick question" usually means what you are asking about. While it is a colloquial phrase, it usually means a question which offers a choice of answers none of which is the correct one. It forces the person answering the question to pick one of the answers thereby exposing the fact that he does not know the true answer.
probing or fathoming one's depth
1 : that investigates something in a tentative way : that tests or tries out something experimentally
a probing procedure
2 : that penetrates deeply in an exploratory way to the essence of something : keen and to the point : sharply analytical : searching
a probing question
a probing study
Merriam-Webster Unabridged Dictionary