JEE Mains · Maths · STD 12 - 13. probability
Let the sum of two positive integers be \(24\) . If the probability, that their product is not less than \(\frac{3}{4}\) times their greatest positive product, is \(\frac{\mathrm{m}}{\mathrm{n}}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then \(\mathrm{n}-\mathrm{m}\) equals :
- A \(9\)
- B \(11\)
- C \(8\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
\( x+y=24, x, y \in N \) \( A M>G M \Rightarrow x y \leq 144 \) \( x y \geq 108\) Favorable pairs of \((\mathrm{x}, \mathrm{y})\) are \( (13,11),(12,12),(14,10),(15,9),(16,8), \) \( (17,7),(18,6),(6,18),(7,17),(8,16),(9,15), \) \( (10,14),(11,13)\) i.e. \(13\) cases Total…
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