Let be the sum of the numbers appeared when two fair dice are rolled and let the probability that are in geometric progression be . Then the value of is

4 Explanation: Solving 1. Condition for Geometric Progression (G.P.) If three numbers are in G.P., then . Here, , , and . Substituting these values: 2. Finding the value of Solve the quadratic equation: So, or . Since represents the sum of numbers on two dice, must be positive , so . 3. Probability of When two fair dice are rolled, the total number of outcomes is . The possible outcomes to get a sum of are: Total favorable outcomes = . 4. Finding the value of According to the problem, the probability is . Multiply both sides by : Correct Option: (4)

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2, \sqrt{3N}, N + 2$ are in geometric progression be $\frac{k}{48}$ . Then the value of $k$ is

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