Mathematics · Probability

JEE Main 2025 — 2 April, Morning Shift — Question 45

Three distinct numbers are selected randomly from the set $\{1,2,3, \ldots, 40\}$ . If the probability, that the selected members are in an increasing G.P., is $\frac{m}{n}, \operatorname{gcd}(m, n)=1$ , then $m+n$ is equal to $\_\_\_\_$

Answer: 4949

Numerical answer — enter this value.

Step-by-step solution

Common ratio	Last triplet	Total
r=2	10, 20, 40	10
r=3	4, 12, 36	4
r=4	2, 8, 32	2
r=5	1, 5, 25	1
r=6	1, 6, 36	1
	Total=18

Total choices $={ }^{40} C_{3}=9880$

Required probability $=\frac{18}{9880}=\frac{9}{4940}=\frac{m}{n}$

$m+n=4949$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 2 April, Morning Shift
Subject: Mathematics
Chapter: Probability
Topic: Problems based on P & C