Which of the following words implies annoyance?

The word "beleaguer" is correct because it means to besiege or surround, often causing someone to feel troubled or annoyed. When someone is beleaguered, they are typically overwhelmed by a persistent problem or a series of troubles, which can easily lead to feelings of annoyance or frustration. This term evokes the sense of being plagued or harassed by difficulties, making it inherently tied to feelings of irritation.

The other words have different meanings that do not convey annoyance. "Astute" refers to being clever or having a sharp insight, which is neither negative nor related to feelings of frustration. "Coalesce" describes the process of coming together to form one whole, which is a neutral or even positive term. "Covet" means to yearn to possess something, often with an implication of envy, but it does not specifically denote annoyance. Thus, "beleaguer" stands out as the term that aptly captures the essence of annoyance.