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QJEEM20Ma1a5e: JEE Main 2020 Mathematics - Class 11 JEEM20Ma1a5e Solution: Let n > 2 be an integer. Suppose that there are n Metro…

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 :

Multiple Choice Options

  • A 201
  • B 199
  • C 101
  • D 200

Step-by-Step Verified Solution

JEE Main 2020 (Online) 2nd September Evening Slot Mathematics - Permutations and Combinations Question 136 English Explanation
Number of blue lines = Number of sides = n

Number of red lines = number of diagonals = nC2 – n

According to question,

nC2−n=99n{}^n{C_2} - n = 99n

⇒n(n−1)2−n=99n\Rightarrow {{n\left( {n - 1} \right)} \over 2} - n = 99n

⇒n−12=99\Rightarrow {{n - 1} \over 2} = 99

⇒n=201\Rightarrow n = 201

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