Any good dictionary gives example sentences. The Collins dictionary also gives frequency information. The most common 10,000 words are known to almost all teenagers and adults, but the word inaugurate is not in this group [the frequency dots show that inaugurate is in the 30,000 most common words]. https://www.collinsdictionary.com/dictionary/english/inaugurate

Thanks Orange

As a non-eglishmen, my take on this question: Yes 1 testament Yes 2 fiercely Yes 3 inaugurate No 4 tersely No 5 furtively Yes 6 zeal