The public school set the question as part of an exam to win one of 14 King's Scholarships, which is worth one tenth of Eton's £10,689 termly fees.
"You are the Prime Minister. Write the script for a speech to be broadcast to the nation in which you explain why employing the Army against violent protesters was the only option available to you and one which was both necessary and moral."
Tony Little, headmaster of Eton College, emailed HuffPost UK and said the school does not favour "any particular political viewpoint".
"The question starts with that well-known section from Machiavelli’s The Prince about whether it is better to be feared than loved as a ruler, and then asks candidates to imagine a situation where law and order is breaking down, oil crisis, troops on the streets have killed protestors."
"We are looking for candidates who can see both sides of an idea an express them clearly – both directly and through more imaginative writing," he added. "High ability candidates at this level are often asked to put themselves in other people’s shoes. In that regard this is no different from a GCSE English question which might ask “Imagine you are Lady Macbeth, write a diary entry to express your feelings on receiving your husband’s letter.
"A similar question on the previous year’s paper is about a community without any government."