206. The least integer which should be added to 1000 so as to make it a perfect square is

1. 1. 10

   
   
   

   2. 18

   
   
   

   3. 24

   
   
   

   4. 89

   
   
   

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1. View Hint View Answer Discuss in Forum

   (31)² < 1000 < 32²
   32 × 32 = 1024
   ∴  Required number
   = 1024 – 1000 = 24

   Correct Option: C

   (31)² < 1000 < 32²
   32 × 32 = 1024
   ∴  Required number
   = 1024 – 1000 = 24

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207. The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is

1. 1. 37

   
   
   

   2. 38

   
   
   

   3. 39

   
   
   

   4. 40

   
   
   

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1. View Hint View Answer Discuss in Forum

   31² = 961
   32² = 1024
   ∴  Required number
   = 1000 – 961 = 39

   Correct Option: C

   31² = 961
   32² = 1024
   ∴  Required number
   = 1000 – 961 = 39

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208. How many perfect squares lie between 120 and 300 ?

1. 1. 5

   
   
   

   2. 6

   
   
   

   3. 7

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   11² = 121, 12² = 144,
   13² = 169, 14² = 196
   15² = 225, 16² = 256,
   17² = 289
   So, total perfect squares = 7

   Correct Option: C

   11² = 121, 12² = 144,
   13² = 169, 14² = 196
   15² = 225, 16² = 256,
   17² = 289
   So, total perfect squares = 7

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209. The largest number of five digits, which is a perfect square is

1. 1. 99999

   
   
   

   2. 99976

   
   
   

   3. 99856

   
   
   

   4. 99764

   
   
   

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1. View Hint View Answer Discuss in Forum

   Largest 5-digit number = 99999
   Now,
   
   ∴  Required number
   = 99999 – 43 = 99856

   Correct Option: C

   Largest 5-digit number = 99999
   Now,
   
   ∴  Required number
   = 99999 – 43 = 99856

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210. The smallest number which should be added to the number 8958 so that the result is a perfect square is

1. 1. 69

   
   
   

   2. 67

   
   
   

   3. 77

   
   
   

   4. 79

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Now, 95 × 95 = 9025
   ∴  Required number
   = 9025 – 8958 = 67

   Correct Option: B

   
   Now, 95 × 95 = 9025
   ∴  Required number
   = 9025 – 8958 = 67

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