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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let 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 :
Solution
There are \(n\) stations on a circle. Each pair is connected by a straight track.
Blue lines connect nearest neighbours, so the number of blue lines is
Blue lines connect nearest neighbours, so the number of blue lines is
Blue $ = n. $
Total lines is $
\binom{n}{2} = \frac{n(n-1)}{2}. $
Hence red lines are
$ \text{Red} = \binom{n}{2} - n. $
Given Red =$ 99 \times \text{Blue} $
$ \binom{n}{2} - n = 99n $
$ \;\;\Longrightarrow\;\;
\frac{n(n-1)}{2} - n = 99n$
$ \;\;\Longrightarrow\;\;
\frac{n(n-1)}{2} = 100n$
$ \;\;\Longrightarrow\;\;
n-1 = 200$
$ \;\;\Longrightarrow\;\;
n = 201.$
Final Answer: \(\boxed{201}\)
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