This is the 9736th most frequent Japanese word.
落第
"落第" means "failure" or "failing an exam/course."
The word 落第 (rakudai) is used here as a verb to indicate failing an academic test or examination.
彼は試験で落第しました。
He failed the exam.
The word 落第 (rakudai) is used here as a noun to refer to the act or condition of failing, affecting grade progression.
落第すると、次の学年に進めません。
If you fail, you won't be able to advance to the next grade level.
The word 落第 (rakudai) in this sentence is used in a negative conditional context, implying the need to study to prevent failure.