課題【かだい】
subject, theme, issue, matter, homework, assignment, task, challenge, problem, question
問題【もんだい】
question (e.g. on a test), problem, problem (e.g. societal, political), question, issue, subject (e.g. of research), case, matter, question (i.e. doubt), public discussion, controversy, trouble, problem, inconvenience, difficulty
話題【わだい】
topic, subject, much talked about, topical, in the news, hot
議題【ぎだい】
topic of discussion, agenda
題材【だいざい】
subject, theme
主題【しゅだい】
subject, theme, motif
宿題【しゅくだい】
homework, assignment, pending issue, unresolved problem, open question
題名【だいめい】
title, caption, heading
難題【なんだい】
difficult problem, challenge
放題【ほうだい】
(doing) as one pleases, to one's heart's content, letting (something) go unchecked, leaving uncontrolled, leaving (something) to take its own course
表題【ひょうだい】
title, index, heading, headline, caption
副題【ふくだい】
subtitle, subheading
出題【しゅつだい】
setting a question (for an exam, quiz, etc.), setting a theme (for composition of poetry)
別問題【べつもんだい】
different thing, another question, different case