Verified Solution • 2025–26 Session moderate

QJEEM25Ma71f1: JEE Main 2025 Mathematics - Class 11 JEEM25Ma71f1 Solution: Let be the set of first ten prime numbers. Let , where is the…

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 ________ .

Step-by-Step Verified Solution

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

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