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JEE Main 20202 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2020 · 2 September · Evening Shift · Mathematics · Permutation and Combination

Let n > 2 be an integer. Suppose that there are n Metro stations in...

Letn>2n > 2 be an integer. Suppose that there are nn Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is 9999 times the number of blue lines, then the value of nn is

Options

  1. A201201
  2. B200200
  3. C101101
  4. D199199

Correct answer

A. 201201

Step-by-step solution

Two consecutive stations =n= n

Two non-consecutive stations=C2n−n= C2 n - n

C2n−n=99nC2 n - n = 99n

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

⇒n2−n2=100n⇒ \dfrac{{n}^{2} - n}{2} = 100n

⇒n2=201n⇒ {n}^{2} = 201n

⇒n=0,201⇒ n = 0, 201

n=0n = 0 is not possible.

⇒n=201⇒ n = 201

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