JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(\mathrm{n}>2\) be an integer. Suppose that there are \(n\) Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is \(99\) times the number of blue lines, then the value of \(n\) is
- A \(199\)
- B \(101\)
- C \(201\)
- D \(200\)
Answer & Solution
Correct Answer
(C) \(201\)
Step-by-step Solution
Detailed explanation
Number of blue lines \(=\) Number of sides \(=\mathrm{n}\) Number of red lines \(=\) number of diagonals \(={ }^{n} C_{2}-n\) \({ }^{\mathrm{n}} \mathrm{C}_{2}-\mathrm{n}=99 \mathrm{n} \Rightarrow \frac{\mathrm{n}(\mathrm{n}-1)}{2}-\mathrm{n}=99 \mathrm{n}\)…
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