15 lines are concurrent at a point P. A line | vedclass

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

Question

(D) triangle is formed by selecting any $2$ lines out of the $15$ concurrent lines and the line $L$ acting as the third side.Since the $15$ lines are

Vedclass · Accepted Answer

$105$

Vedclass · Answer

(D) triangle is formed by selecting any $2$ lines out of the $15$ concurrent lines and the line $L$ acting as the third side.Since the $15$ lines are concurrent at point $P$,any pair of these lines will intersect at $P$.When these $2$ lines intersect the line $L$ at two distinct points,a triangle is formed with $L$ as one of its sides.The number of ways to choose $2$ lines out of $15$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Thus,the number of triangles is ${}^{15}C_{2} = \frac{15 	imes 14}{2 	imes 1} = 105$.

$15$ lines are concurrent at a point $P$. $A$ line $L$ not passing through $P$ intersects all the $15$ lines and forms triangles with them. Then the number of triangles having $L$ as one of its sides is

Similar Questions

There are $6$ points on a circle. Two triangles are drawn such that they have no common vertices. What is the probability that none of the sides of the triangles intersect?

How many chords can be drawn through $21$ points on a circle?

There is a rectangular sheet of dimension $(2m - 1) \times (2n - 1)$,(where $m > 0, n > 0$). It has been divided into squares of unit area by drawing lines perpendicular to the sides. Find the number of rectangles having sides of odd unit length.

The number of diagonals in a polygon is $20$. The number of sides of the polygon is:

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?

Vedclass Test Series

Exam Paper Generator

Online Exam Module