Let n 2 be an integer. Suppose that there a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The number of blue lines corresponds to the number of sides of the polygon formed by the $n$ stations,which is $n$.The total number of ways to con

Vedclass · Accepted Answer

$201$

Vedclass · Answer

(C) The number of blue lines corresponds to the number of sides of the polygon formed by the $n$ stations,which is $n$.The total number of ways to connect any two stations is given by the combination formula ${}^{n}C_{2}$.The number of red lines is the total number of connections minus the number of blue lines (sides),which is the number of diagonals: ${}^{n}C_{2} - n$.According to the problem,the number of red lines is $99$ times the number of blue lines:${}^{n}C_{2} - n = 99n$Substituting the formula for ${}^{n}C_{2}$:$\frac{n(n-1)}{2} - n = 99n$Dividing both sides by $n$ (since $n > 2$):$\frac{n-1}{2} - 1 = 99$$\frac{n-1}{2} = 100$$n - 1 = 200$$n = 201$

Similar Questions

There are $8$ points in a plane,out of which $4$ are collinear. How many triangles can be formed by joining these points?

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. The probability that no two of them are consecutive is -

On an $n \times n$ chessboard,the total number of rectangles which are not squares is $350$. Then,the number of white squares on the chessboard is .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module