JEE Mains · Maths · STD 11 - 6. permutation and combination
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 ______.
- A 5120
- B 5130
- C 5140
- D 5150
Answer & Solution
Correct Answer
(A) 5120
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } \frac{y}{x}=\lambda \\ & y=\lambda x \\ & =10 \times\left({ }^9 C_0+{ }^9 C_1+{ }^9 C_2+{ }^9 C_3+\ldots+{ }^9 C_9\right) \\ & =10 \times 2 \\ & =10 \times 512=5120\end{aligned}\)
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