Problem: Later the emphasis was on classical studies, dominated by Latin and Ancient History, and, for boys with sufficient ability, Classical Greek. From the latter part of the 19th century this curriculum has changed and broadened: for example, there are now more than 100 students of Chinese, which is a non-curriculum course. In the 1970s, there was just one school computer, in a small room attached to the science buildings. It used paper tape to store programs. Today, all boys must have laptop computers, and the school fibre-optic network connects all classrooms and all boys' bedrooms to the internet.
Is Chinese a required or non-curriculum course?
The answer is the following: non-curriculum

Problem: The Mīmāṃsā school has several subschools defined by epistemology. The Prābhākara subschool of Mīmāṃsā considered five epistemically reliable means to gaining knowledge: pratyakṣa (perception), anumāṇa (inference), upamāṇa (comparison and analogy), arthāpatti (postulation, derivation from circumstances), and śabda (word, testimony of past or present reliable experts). The Kumārila Bhaṭṭa sub-school of Mīmāṃsā added sixth to its canon of reliable epistemology - anupalabdi (non-perception, negative/cognitive proof).
What is comparison and analogy in the Prabhakara school?
The answer is the following: upamāṇa

Problem: In 941, Igor led another major Rus' attack on Constantinople, probably over trading rights again. A navy of 10,000 vessels, including Pecheneg allies, landed on the Bithynian coast and devastated the Asiatic shore of the Bosphorus. The attack was well-timed, perhaps due to intelligence, as the Byzantine fleet was occupied with the Arabs in the Mediterranean, and the bulk of its army was stationed in the east. The Rus’ burned towns, churches, and monasteries, butchering the people and amassing booty. The emperor arranged for a small group of retired ships to be outfitted with Greek fire throwers and sent them out to meet the Rus’, luring them into surrounding the contingent before unleashing the Greek fire. Liutprand of Cremona wrote that "the Rus', seeing the flames, jumped overboard, preferring water to fire. Some sank, weighed down by the weight of their breastplates and helmets; others caught fire." Those captured were beheaded. The ploy dispelled the Rus’ fleet, but their attacks continued into the hinterland as far as Nicomedia, with many atrocities reported as victims were crucified and set up for use as targets. At last a Byzantine army arrived from the Balkans to drive the Rus' back, and a naval contingent reportedly destroyed much of the Rus' fleet on its return voyage (possibly an exaggeration since the Rus' soon mounted another attack). The outcome indicates increased military might by Byzantium since 911, suggesting a shift in the balance of power.
Why did the attack by the Rus go so well on the coast at the start?
The answer is the following: Byzantine fleet was occupied with the Arabs

Problem: The ultimate substantive legacy of Principia Mathematica is mixed. It is generally accepted that Kurt Gödel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims. However, Gödel could not have come to this conclusion without Whitehead and Russell's book. In this way, Principia Mathematica's legacy might be described as its key role in disproving the possibility of achieving its own stated goals. But beyond this somewhat ironic legacy, the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics.
Despite its imperfection, what are now considered valuable achievements of Principia Mathematica?
The answer is the following:
the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics