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If the mean and the variance of the numbers a ,   b ,   8,   5 and 10 are 6 and 6 . 8 respectively, then the value of a 3 + b 3 is equal to

Options

  1. A58
  2. B61
  3. C91
  4. D89

Correct answer

C. 91

Step-by-step solution

Mean = 6 = a + b + 8 + 5 + 10 5 ⇒ a + b = 7 Variance = 6 . 8 = a 2 + b 2 + 64 + 25 + 100 5 - 36 ⇒ a 2 + b 2 = 2 5 2 a b = a + b 2 - a 2 + b 2 ⇒ a b = 1 2 Now, a 3 + b 3 = a + b 3 - 3 a b a + b = 343 - 3 × 12 × 7 = 9 1

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