JEE Mains · Maths · STD 11 - 14. probability
Three distinct numbers are selected randomly from the set \(\{1,2,3, \ldots \ldots, 40\}\). If the probability, that the selected numbers are in an increasing G.P. is \(\frac{m}{n}\), \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to _____.
- A 1245
- B 5577
- C 2444
- D 2477
Answer & Solution
Correct Answer
(D) 2477
Step-by-step Solution
Detailed explanation
\(1 \leq \mathrm{a} \lt \mathrm{ar} \lt \mathrm{ar}^2 \leq 40\) (If \(r \in N\) ) If \(r=2\) \(1 \leq a \lt 2 a \lt 4 a \leq 40\) \(a \in\{1, \ldots \ldots ., 10\}\) ________ (10 GP) If \(r=3\) \(1 \leq a \lt 3 a \lt 9 a \leq 40\) \(\mathrm{a} \in\{1,2,3,4\}\) ________ ________…
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