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JEE Main 202524 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 24 January · Morning Shift · Mathematics · Sets and Relations

Let S=\ p_1, p_2 ., p_ 10 \ be the set of first ten prime numbers....

Let S={p1,p2….,p10}S=\left\{p_1, p_2 \ldots ., p_{10}\right\} be the set of first ten prime numbers. Let A=S∪PA=S \cup P, where PP is the set of all possible products of distinct elements of SS. Then the number of all ordered pairs ( x,yx, y ), x∈Sx \in S, y∈Ay \in A, such that xx divides yy, is ______.

Correct answer

0

Step-by-step solution

 Let yx=λy=λx=10×(9C0+9C1+9C2+9C3+…+9C9)=10×2=10×512=5120\begin{aligned} & \text{ Let } \frac{y}{x}=\lambda \\ & y=\lambda x \\ & =10 \times\left({ }^9 C_0+{ }^9 C_1+{ }^9 C_2+{ }^9 C_3+\ldots+{ }^9 C_9\right) \\ & =10 \times 2 \\ & =10 \times 512=5120\end{aligned}
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