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If two distinct numbers a and b are selected from the set 5 1 ,   5 2 ,   5 3 . . . . . . . 5 9 , then the probability that log a b is an integer is

Options

  1. A7 18
  2. B5 9
  3. C7 36
  4. D3 16

Correct answer

A. 7 18

Step-by-step solution

Total cases = C 2 9 For favorable cases, let a = 5 i ,   b = 5 j log a b = j i (must be an integer) if i = 1 ⇒ j = 2,3 , 4,5 , 6,7 , 8,9 if i = 2 ⇒ j = 4,6 , 8 if i = 3 ⇒ j = 6,9 if i = 4 ⇒ j = 8 for i = 5,6 , 7,8 , 9 ⇒ no such value of j is possible Hence, the required probability = 14 9 C 2 = 14 36 = 7 18

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