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91. There is a circular path around a sports Held. Priya takes 18 minutes to drive one round of the Held, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point ?

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92. The sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of Physics books is 12, the number of Chemistry books 20 and the number of Mathematics books is 30. Assuming that the books are of the same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.

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93. In a morning walk Nimit, Tanvika and Mehul step off together, their steps measure 84 cm, 90 cm and 120 cm respectively. What is the minimum distance each should walk so that one can cover the distance in complete steps.

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94.
Prove that $square root of 2$ is irrational.

Let us assume that

square root of 2

is is rational. We know that, rational number can be written as

space space straight a over straight b comma

where ‘a’ and ‘b’ are integers and b ≠ 0. i.e.. Assume that

square root of 2 equals straight a over straight b

Squaring both sides

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⇒ a² is divisible by 2

⇒ a is divisible by 2

Let a = 2c for some integer c.

Putting a = 2c in (i), we get

2 b² = (2c)²

⇒ 2b² = 4c²

⇒ b² — 2c²

⇒ b² is divisible by 2

⇒ b is divisible by 2.

Thus, 2 is a common factor of a and b. But, this contradicts the fact that ‘a’ and ‘b’ have no common factor other than 1.

The contradiction arises by assuming that $square root of 2 space$ is rational.
Hence, $square root of 2$ is irrational.

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95.

Prove that $square root of 3$ is irrational.

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96.

Show that $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ is an irrational number.

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97. 135 cartons of English NCERI books 225 cartons of Maths books are to be stocked in a book store. If each stock is of the same height and is to contain cartons at the same type of books, what would be the greatest number of cartons each stock would have ?

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98. Two tankers contain 135 and 225 litres of water respectively. Find the maximum capacity of a container which can measure the water of either tanker in exact number of times.

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99. Mr. Pankaj Mishra, a merchant in a colony has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such tin ?

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100.

Find the largest number that will divide 398,436 and 542 leaving remainders 7, 11 and 15 respectively. Problems Based on Fundamental Theorem of Arithmetic

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