QUES: With Constantinople as its capital and control of lands around the Mediterranean basin, the Ottoman Empire was at the centre of interactions between the Eastern and Western worlds for six centuries. Following a long period of military setbacks against European powers, the Ottoman Empire gradually declined into the late nineteenth century. The empire allied with Germany in the early 20th century, with the imperial ambition of recovering its lost territories, joining in World War I to achieve this ambition on the side of Germany and the Central Powers. While the Empire was able to largely hold its own during the conflict, it was struggling with internal dissent, especially with the Arab Revolt in its Arabian holdings. Starting before the war, but growing increasingly common and violent during it, major atrocities were committed by the Ottoman government against the Armenians, Assyrians and Pontic Greeks. The Empire's defeat and the occupation of part of its territory by the Allied Powers in the aftermath of World War I resulted in the emergence of a new state, Turkey, in the Ottoman Anatolian heartland following the Turkish War of Independence, as well as the founding of modern Balkan and Middle Eastern states and the partitioning of the Ottoman Empire.

When did the Ottoman empire decline?
What is the answer?
ANS: into the late nineteenth century
QUES: By the turn of the 20th century, fears had begun to grow in Britain that it would no longer be able to defend the metropole and the entirety of the empire while at the same time maintaining the policy of "splendid isolation". Germany was rapidly rising as a military and industrial power and was now seen as the most likely opponent in any future war. Recognising that it was overstretched in the Pacific and threatened at home by the Imperial German Navy, Britain formed an alliance with Japan in 1902 and with its old enemies France and Russia in 1904 and 1907, respectively.

Which country seemed like Britain's most likely threat in the early 20th century?
What is the answer?
ANS: Germany
QUES: Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.

What are used to express the solutions of polynomials?
What is the answer?
ANS:
radicals