Choose the word that best defines the given phrase or idiomatic expression. The phrase is "to talk through one’s hat", which is used informally in English.

Introduction / Context:
This question tests your understanding of an informal English idiom. The expression "to talk through one’s hat" is a colourful way of criticising someone's speech. It suggests that the person is speaking without real knowledge, saying things that are foolish or unrelated to facts. Recognising such idioms is important for comprehension of colloquial English, novels, and dialogues.

Given Data / Assumptions:

The phrase is "to talk through one's hat".
We assume common informal usage in British or Indian English, where the idiom is understood to mean speaking nonsense or without knowledge.

The correct meaning should express that the speaker's words are unreliable, foolish, or baseless.

Options include speaking fluently, talking nonsense, talking wisdom, speaking at random with authority, and remaining silent.

Concept / Approach:
When someone "talks through their hat", they are speaking as if they know something but in reality are talking nonsense. The idiom mocks the idea that their words might as well be coming from their hat, not from clear thinking. It does not praise fluency or wisdom. Instead, it focuses on content that is rubbish, uninformed, or ridiculous. Therefore, "to talk nonsense" is the closest simple explanation. Speaking at random with authority is close, but the key idea is nonsense, not just randomness.

Step-by-Step Solution:
Step 1: Understand that the idiom is critical: it is used to accuse someone of speaking foolishly or without knowledge. Step 2: Look for an option that directly states this idea in simple terms. Step 3: Option B To talk nonsense expresses exactly that: talking in a way that has no real sense or basis. Step 4: Option A To speak fluently refers to smooth speech, which may be used for good or bad ideas and does not capture the criticism. Step 5: Option C To talk wisdom is the opposite of the idiom's intention and therefore cannot be correct. Step 6: Option D To speak at random with authority is close but focuses more on randomness; not all through-the-hat talk is random, but it is all nonsense. Step 7: Option E To remain completely silent contradicts the literal action of talking and is therefore not relevant.

Verification / Alternative check:
Consider a typical use: "He claims to be an expert on finance, but most of the time he is just talking through his hat." Here, the sentence clearly means he is talking nonsense or talking without real knowledge. Replacing the idiom with "talking nonsense" preserves the meaning perfectly. Substituting "speaking fluently" or "talking wisdom" would reverse or soften the criticism. "Speaking at random with authority" might partially fit, but the focus in exam definitions is more straightforward: nonsense. This supports option B as the best choice.

Why Other Options Are Wrong:
Option A To speak fluently is neutral or even positive; it describes how someone speaks, not whether what they say is true or foolish.
Option C To talk wisdom is the opposite of what the idiom implies; the idiom criticises, it does not praise wise speech.
Option D To speak at random with authority adds an extra nuance of randomness and authority that is not always implied; the core idea of nonsense is better captured by option B.
Option E To remain completely silent contradicts the verb talk and does not match the image of someone speaking foolishly.

Common Pitfalls:
Because the idiom is informal, some learners may guess based on the literal image of a hat and think it has to do with hiding or secrecy. In reality, many idioms cannot be understood literally; they must be learned as fixed expressions with figurative meanings. A useful strategy is to remember that idioms involving body parts or clothing often comment on behaviour—here, on foolish talk—rather than describing the objects themselves.

Final Answer:
The phrase "to talk through one's hat" means to talk nonsense.