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CAT Questions

• 1.

  ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is

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• 2.

  The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question.
  In the summer of 2022, subscribers to the US streaming service HBO MAX were alarmed to discover that dozens of the platform’s offerings – from the Covid-themed heist thriller Locked Down to the recent remake of The Witches – had been quietly removed from the service . . . The news seemed like vindication to those who had long warned that streaming was more about controlling access to the cultural commons than expanding it, as did reports (since denied by the show’s creators) that Netflix had begun editing old episodes of Stranger Things to retroactively improve their visual effects.
  What’s less clear is whether the commonly prescribed cure for these cultural ills – a return to the material pleasures of physical media – is the right one. While the makers of Blu-ray discs claim they have a shelf life of 100 years, such statistics remain largely theoretical until they come to pass, and are dependent on storage conditions, not to mention the continued availability of playback equipment. The humble DVD has already proved far less resilient, with many early releases already beginning to deteriorate in quality Digital movie purchases provide even less security. Any film “bought” on iTunes could disappear if you move to another territory with a different rights agreement and try to redownload it. It’s a bold new frontier in the commodification of art: the birth of the product recall. After a man took to Twitter to bemoan losing access to Cars 2 after moving from Canada to Australia, Apple clarified that users who downloaded films to their devices would retain permanent access to those downloads, even if they relocated to a hemisphere where the [content was] subject to a different set of rights agreements. Thanks to the company’s ironclad digital rights management technology, however, such files cannot be moved or backed up, locking you into watching with your Apple account.
  Anyone who does manage to acquire Digital Rights Management free (DRM-free) copies of their favourite films must nonetheless grapple with ever-changing file format standards, not to mention data decay – the gradual process by which electronic information slowly but surely corrupts. Only the regular migration of files from hard drive to hard drive can delay the inevitable, in a sisyphean battle against the ravages of digital time.
  In a sense, none of this is new. Charlie Chaplin burned the negative of his 1926 film A Woman of the Sea as a tax write-off. Many more films have been lost through accident, negligence or plain indifference. During a heatwave in July 1937, a Fox film vault in New Jersey burned down, destroying a majority of the silent films produced by the studio.
  Back then, at least, cinema was defined by its ephemerality: the sense that a film was as good as gone once it left your local cinema. Today, with film studios keen to stress the breadth of their back catalogues (or to put in Hollywood terms, the value of their IPs), audiences may start to wonder why those same studios seem happy to set the vault alight themselves if it’ll help next quarter’s numbers.

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• 3.

  When 3³³³ is divided by 11, the remainder is

  • 1
  • 6
  • 5
  • 10
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• 4.

  When $10^{100}$ is divided by 7, the remainder is ?

  • 6
  • 3
  • 1
  • 4
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• 5.

  A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

  • 42
  • 18
  • 36
  • 50
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• 6.

  \( 10^{68} \) is divided by 13, the remainder is  is

  • 9
  • 4
  • 5
  • 8
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