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The correct pairs are AE, BD, and CF. AE - The noun phrase A FRAGMENT OF ROCK given in E can function as the object of the preposition ON. The sentence conveys that if a picture could convey something, in that case, the design on a fragment of an ancient rock could convey a lot of things. "If a picture tells a thousand words, a cross-hatched design drawn on a fragment of rock some 73,000 years ago could speak volumes." BD - The verb IMPROVED in D can be modified by the adverb RADICALLY given in B. The sentence here seeks to convey that human progress, driven by various factors, has improved multiple aspects of human life. "Human progress, driven by advances in science, medicine and technology, has radically improved average living standards, health and life expectancy." CF - The noun PHOTO given in F can function as the object of the preposition AT. The sentence seeks to convey that it requires one to be good at noticing details when looking at a photo of the Earth hanging in the sky over the surface of the moon. "It takes an eye for a certain type of detail to look at a photo of the bejewelled Earth hanging in the sky over the sterile terrain of the Moon." Thus, C is the right answer.
What is the maximal number of spherical balls of radius 1 cm each that can be placed inside a cubical box of height 10 cm?
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2.189...
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(b) Magnetic field lines can be...
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