There are 20 straight lines in a plane such t | vedclass

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

Question

(B) Given $n = 20$ straight lines in a plane,where no two are parallel and no three are concurrent. The number of intersection points is given by $\bi

Vedclass · Accepted Answer

$14535$

Vedclass · Answer

(B) Given $n = 20$ straight lines in a plane,where no two are parallel and no three are concurrent. The number of intersection points is given by $\binom{n}{2} = \binom{20}{2} = \frac{20 	imes 19}{2} = 190$. Let $I = 190$ be the number of intersection points. Each pair of these intersection points forms a line segment. The total number of line segments formed by joining these $I$ points is $\binom{I}{2}$. However,we must exclude the segments that lie on the original $20$ lines. For each line,there are $n-1 = 19$ intersection points. The number of segments on one line is $\binom{19}{2}$. Since there are $20$ lines,the number of segments to exclude is $20 	imes \binom{19}{2} = 20 	imes \frac{19 	imes 18}{2} = 20 	imes 171 = 3420$. The number of new line segments is $\binom{190}{2} - 3420 = \frac{190 	imes 189}{2} - 3420 = 17955 - 3420 = 14535$.

There are $20$ straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined,then the number of new line segments formed is

Similar Questions

If the number of diagonals of a regular polygon of $n$ sides is $104$,then $n=$

If $5$ parallel lines are intersected by $4$ parallel lines,then what is the number of parallelograms formed?

The number of diagonals of a polygon is $35$. If $A$ and $B$ are two distinct vertices of this polygon,then the number of all those triangles formed by joining three vertices of the polygon having $AB$ as one of its sides is:

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these points coincides with $P$,then the number of triangles formed by these eight points is:

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module