Some examples, from the last such traditional exam:

首题为：“大学之道，在明明德，在亲民，在止于至善义”；

Explain: The great learning is about enlightenment moralities, at being close to the people, at promoting good actions.

“裴度奏宰相宜招延四方贤才与参谋请于私第见客论”。

Discuss: Pei Du presented (the idea) that the prime minister should be able to discuss plans with sages and advisers in his own house. (At Pei’s time every discussion needed to be done at court before the emperor)

“日本变法之初，聘用西人而国以日强，埃及用外国人至千余员，遂至失财政裁判之权而国以不振。试详言其得失利弊策”。

When Japan began its reforms, they employed westerners thus they became strong. Now Egypt also employed more than 1000 foreigners but end up losing money and power and become a client state. Discuss the reason behind this.

The last of these is a very modern question, concerning recent international event, but the first two are classic questions that could have been asked a millennium earlier.

Some relevant past discussion on the topic:

• u/Tiako on the general structure in https://www.reddit.com/r/AskHistorians/comments/ydtya/what_were_the_questions_on_ancient_chinese_civil/

• u/Vox_Imperatoris with more details on the types of questions and required answers in https://www.reddit.com/r/AskHistorians/comments/2nrv12/what_was_the_actual_content_of_chinese_civil/ and u/xingfenzhen providing the questions on the last exam administered (from which I quoted the above questions).

• [deleted] providing a useful reference in https://www.reddit.com/r/AskHistorians/comments/1br6t2/chinese_imperial_civil_service_exam_ming_dynasty/ - Benjamin A. Elman, A Cultural History of Civil Examinations in Late Imperial China, University of California Press, 2000.

Elman's book is a great resource for learning more about the Ming-Qing examination system. Comprehensive, and lots of stuff that is difficult to find elsewhere, e.g., pp 388-399: A close look at the eight-legged essay, with two examples by Wang Ao (1450-1524), a first-ranked examinee twice (running into a jealous examiner for the 3rd (palace) examination, who was the only Ming three-times first-ranker and wanted to preserve that status). Despite his difficulty with his third exam, Wang Ao's 3rd essay was regarded as great, and his writing influence future essays greatly.

If the first two past answers don't satisfy, try Elman's book for 800 pages of juicy examination goodness.

[This is a recycled answer, assembled and lightly edited from two of my past answers. Contains 100% recycled electrons.]

Here's a few Korean ones form the Joseon era. Thankfully these were often compiled into chaekmun (책문), which were essentially test prep material passed around among students. In brackets is the king when that question was asked. As a nation obsessed with writing things down, there are many, many, many more that we know of not mentioned here. I have made a conscious choice to exclude ones that ask about specific ideas in Confucianism or international relations, like Dokdo, pirates or Manchuria.

• What is the most urgent matter in the current state of affairs? (Gwanghaegun)
• Speak of the harms of alcohol. (Jungjong)
• How must a king act to keep his country alive? (Myeongjong)
• Why do we feel sad, on the last night of the year? (Gwanghaegun)
• What would Confucius have done today? (Jungjong)
• What must I (the king) do to save the country in this crisis? (Gwanghaegun)
• War or peace? (Seonjo)
• How should the six ministries (government) be reformed? (Myeongjong)
• What qualities should a diplomat have? (Jungjong)
• What is education? (Myeongjong)
• How do we evaluate people by merit? (Sejong)
• What does politics that is good from start to finish look like? (Jungjong)
• How do we fix the side effects of law? (Sejong)
• What value is there in building two capital cities? (Sejong)
• How should taxes be calculated? (Taejong)
• Is transportation better by sea or land? (Taejong)
• How can we prepare for floods and snowfall? (Taejong)
• Should administrative borders be redefined? (Sejong)
• A conscription system leaves the army weak and inexperienced, but a permanent army leaves families without able workers for their farms. Where is the balance between the two? (Sejong)
• If there is an urgent matter or mistake I (the king) am not aware of, tell me. (Munjong)
• Speak of the latest trends in music. (Sejo)
• Population in the North keeps shrinking, while the South keeps growing. How do we maintain geographical equity? (Sejo)

​

Sources: (apologies for all Korean)

김태완, <<시대의 물음에 대한 답변, 책문>>. 2009-11-10. 소나무.

박재경, <<조선시대 책문 연구>>, 2020-11-15. 이담북스.