GATE CS 2026 Set 1 Q10 — General Aptitude

Let the outcome of the first roll be $x$ and the second roll be $y$, where $x, y \in \{1, 2, 3, 4, 5, 6\}$.

Since the dice is rolled twice, the total number of possible outcomes in the sample space is:

We need to find the probability that $y$ is an integer multiple of $x$ (i.e., $y = k \cdot x$ for some positive integer $k$). Let's list the favorable outcomes $(x, y)$ systematically for each possible value of $x$:

• If $x = 1$: $y$ can be any multiple of $1$, which are $\{1, 2, 3, 4, 5, 6\}$ $\rightarrow$ $6$ outcomes
• If $x = 2$: $y$ can be $\{2, 4, 6\}$ $\rightarrow$ $3$ outcomes
• If $x = 3$: $y$ can be $\{3, 6\}$ $\rightarrow$ $2$ outcomes
• If $x = 4$: $y$ can be $\{4\}$ $\rightarrow$ $1$ outcome
• If $x = 5$: $y$ can be $\{5\}$ $\rightarrow$ $1$ outcome
• If $x = 6$: $y$ can be $\{6\}$ $\rightarrow$ $1$ outcome

Summing these up, the total number of favorable outcomes is:

Therefore, the required probability is:

Thus, the correct option is C.