The number of points present on a straight line is-

Options

A. 10
B. 5
C. 3
D. 4

Answer

B

Explanation

Let the number of points marked on the plane = n
Then, according to the question
Total number of line segments = 10
`""^nC_2 = 10 `or,` (n(n − 1))/2 = 10 `
`[because ""^nC_2 = (n!)/(2!(n - 2)!) = (n(n - 1)n - 2!)/(2!n - 2!) = (n(n -1))/(2)]`
or `n^2 - n - 20 = 0`
or `(n - 5)(n + 4)`
or `n = 5 and n =4`
But, `n = -4` is rejected.
[`because` no. of points can.t be negative]
So, n=5.
Therefore, the number of points marked on the plane =n=5.