JEE MAIN - Mathematics (2020 - 2nd September Evening Slot - No. 5)
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 :
201
199
101
200
Explanation
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Number of blue lines = Number of sides = n
Number of red lines = number of diagonals = nC2 – n
According to question,
$${}^n{C_2} - n = 99n$$
$$ \Rightarrow {{n\left( {n - 1} \right)} \over 2} - n = 99n$$
$$ \Rightarrow {{n - 1} \over 2} = 99$$
$$ \Rightarrow n = 201$$
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