Medium INTEGER +4 / -1 PYQ · JEE Mains 2025

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 (integer) 5120

Solution

<p>$$\begin{aligned} & \text { Let } \frac{\mathrm{y}}{\mathrm{x}}=\lambda \\ & \mathrm{y}=\lambda \mathrm{x} \\ & =10 \times\left({ }^9 \mathrm{C}_0+{ }^9 \mathrm{C}_1+{ }^9 \mathrm{C}_2+{ }^9 \mathrm{C}_3+\ldots .+{ }^9 \mathrm{C}_9\right) \\ & =10 \times\left(2^9\right) \\ & 10 \times 512 \\ & 5120 \end{aligned}$$</p>

About this question

Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations

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