In each of the following questions, a word has been

Solution

I. Despite facing numerous challenges, her piqued efforts to master the new programming language eventually paid off, leading to successful project completion. - This sentence uses "piqued" incorrectly. "Piqued" usually refers to a sudden or slight interest or curiosity, not sustained effort. In this case, "increased" or "persistent" would be more accurate words to describe her dedication. II. Her curiosity was piqued when she overheard the intriguing conversation at the neighboring table, prompting her to learn more about the mysterious topic. - This sentence uses "piqued" correctly. It describes a sudden spark of curiosity aroused by the overheard conversation, which led her to further exploration. III. The pique rain over several days led to flooding in low-lying areas, highlighting the need for improved drainage systems in the region. - This sentence uses "pique" incorrectly. While "pique" can refer to a light rainfall, the flooding suggests a heavier and more sustained downpour. Words like "heavy" or "persistent" would be more appropriate to describe the rainfall in this context.