116. The least number, that must be added to 1720 so as to obtain a perfect cube, is

1. 1. 7

   
   
   

   2. 8

   
   
   

   3. 11

   
   
   

   4. 13

   
   
   

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1. View Hint View Answer Discuss in Forum

   12 × 12 × 12 = 1728
   ∴  Required number
   = 1728 – 1720 = 8

   Correct Option: B

   12 × 12 × 12 = 1728
   ∴  Required number
   = 1728 – 1720 = 8

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117. By what least number should 675 be multiplied so as to obtain a perfect cube number ?

1. 1. 3

   
   
   

   2. 5

   
   
   

   3. 24

   
   
   

   4. 40

   
   
   

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1. View Hint View Answer Discuss in Forum

   675 = 5 × 5 × 3 × 3 × 3
   ∴  Required number = 5

   Correct Option: B

   675 = 5 × 5 × 3 × 3 × 3
   ∴  Required number = 5

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118. The smallest positive integer n, for which 864n is a perfect cube, is :

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   ∴  864 = 2³ × 3³ × 2²
   For 864n to be a perfect cube,
   n = 2

   Correct Option: B

   
   ∴  864 = 2³ × 3³ × 2²
   For 864n to be a perfect cube,
   n = 2

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119. The smallest natural number, by which 3000 must be divided to make the quotient a perfect cube, is :

1. 1. 3

   
   
   

   2. 4

   
   
   

   3. 5

   
   
   

   4. 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   3000 = 3 × 1000 = 3 × 10³
   Clearly, when we divide 3000 by natural number 3, the quotient is 1000 which is a perfect cube.

   Correct Option: A

   3000 = 3 × 1000 = 3 × 10³
   Clearly, when we divide 3000 by natural number 3, the quotient is 1000 which is a perfect cube.

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120. Which smallest number must be added to 710 so that the sum is a perfect cube ?

1. 1. 29

   
   
   

   2. 19

   
   
   

   3. 11

   
   
   

   4. 21

   
   
   

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1. View Hint View Answer Discuss in Forum

   Clearly,  ³√729 = 9
   ∴  19 should be added to 710 to get a perfect cube.

   Correct Option: B

   Clearly,  ³√729 = 9
   ∴  19 should be added to 710 to get a perfect cube.

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