In each of the following questions, an Idiom or Phrase is given. Choose the alternative which best expresses its meaning: Draw a blank.

Introduction / Context:
The idiom draw a blank is often used in everyday conversation, in examinations, and in crime or investigation stories. It is one of those expressions whose meaning cannot be guessed directly from the individual words, so candidates must know it as a fixed phrase. The exam asks you to pick the alternative that best matches this idiomatic meaning in standard English usage.

Given Data / Assumptions:
The expression provided is Draw a blank. The options are Paint something, Find no favour, Oblige someone, and Teach someone. We assume that the question refers to the common modern meaning of the idiom, which is connected with failure to obtain a result or to remember or discover something, rather than any older specialised meaning.

Concept / Approach:
In present day English, draw a blank usually means to fail to get an answer, to fail to find the information sought, or to receive no response. For example, when someone tries to recall a name during a test and cannot remember it, they might say I drew a blank. In situations where a search for information, clues, or support produces nothing useful, the same phrase applies. Among the given options, find no favour comes closest to this sense of failing to get the desired response or support.

Step-by-Step Solution:
Step 1: Recall typical contexts: attempts to remember something or to get a useful result that fail completely. Step 2: Understand that draw a blank refers to ending up with nothing to show for the effort. Step 3: Check each option and see whether it matches the idea of receiving no result or no positive response. Step 4: Note that find no favour captures the idea of not receiving approval or positive outcome and is the nearest choice available. Step 5: Select find no favour as the best explanation among the four options given.

Verification / Alternative check:
Consider a sample sentence: The police searched the area for hours but drew a blank. This clearly means that they found nothing useful. If we paraphrase, The police searched the area for hours but found no favour is not perfect but still reflects the idea that their efforts did not receive the desired successful result. The other options do not fit even loosely in this type of context, which confirms that find no favour is the intended choice here, even though in natural English one might prefer a more precise paraphrase like found nothing or got no result.

Why Other Options Are Wrong:
Paint something has a literal meaning related to art and does not share any connection with failing to find an answer.
Oblige someone means to do a favour for someone, which is unrelated to failure or lack of result.
Teach someone refers to the act of instructing or educating another person and again has no link to the sense of drawing a blank in memory or investigation.

Common Pitfalls:
A frequent problem is that candidates try to interpret idioms literally, leading to confusion. They may connect draw with painting and therefore mistakenly choose paint something. To avoid this, it is important to build a mental list of idioms along with example sentences. For draw a blank, remembering situations like forgetting an answer in a test or a search yielding nothing can make the meaning stick and help you identify the nearest paraphrase offered in exam options.

Final Answer:
The idiom Draw a blank most nearly means Find no favour, that is, to fail to get an answer or useful result.