JEE MAIN - Mathematics (2025 - 24th January Morning Shift - No. 23)
Let $S=\left\{p_1, p_2 \ldots, p_{10}\right\}$ be the set of first ten prime numbers. Let $A=S \cup P$, where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y), x \in S$, $y \in A$, such that $x$ divides $y$, is ________ .
Answer
5120
Explanation
$$\begin{aligned}
& \text { Let } \frac{\mathrm{y}}{\mathrm{x}}=\lambda \\
& \mathrm{y}=\lambda \mathrm{x} \\
& =10 \times\left({ }^9 \mathrm{C}_0+{ }^9 \mathrm{C}_1+{ }^9 \mathrm{C}_2+{ }^9 \mathrm{C}_3+\ldots .+{ }^9 \mathrm{C}_9\right) \\
& =10 \times\left(2^9\right) \\
& 10 \times 512 \\
& 5120
\end{aligned}$$
Comments (0)
