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JEE Main20248 Apr 2024Morning ShiftMathematicsProbabilityActual

Let the sum of two positive integers be 24 . If the probability, that their product is not less than 3 4 times their greatest possible product, is m n , where gcd (m, n)=1 , then n-m equals

Options

  1. A10
  2. B9
  3. C11
  4. D8

Correct answer

A. 10

Step-by-step solution

aligned & x+y=24, x, y N & A M>G M x y 144 & x y 108 aligned Favorable pairs of (x, y) are aligned & (13,11),(12,12),(14,10),(15,9),(16,8), & (17,7),(18,6),(6,18),(7,17),(8,16),(9,15), & (10,14),(11,13) aligned i.e. 13 cases Total choices for x + y =24 is 23 aligned & Probability = 13 23 = m n & n-m=10 aligned

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