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JEE Main202227 Jul 2022Morning ShiftMathematicsProbabilityActual

Let S be the sample space of all five digit numbers. If p is the probability that a randomly selected number from S , is a multiple of 7 but not divisible by 5 , then 9 p is equal to

Options

  1. A1 . 0146
  2. B1 . 2085
  3. C1 . 0285
  4. D1 . 1521

Correct answer

C. 1 . 0285

Step-by-step solution

Given, five-digit number, So n S = total 5 digit number will be = 9 × 10 4 Now let A : number is multiple of 7 but not divisible by 5 Smallest 5 digit divisible by 7 is 10003 Largest 5 digit divisible by 7 is 99995 Now by using n t h term of A.P formula we have, ∴     99995 = 10003 + n - 1 7 ⇒ n = 12857 Now finding number which is divisible by 35 Again using A.P formula we have, 99995 = 10010 + P - 1 35 ⇒ P = 2572 Now number divisible by 7 but not by 35 are 12857 - 2572 = 10285 So,

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