In a plane,there are 37 straight lines,of whi | vedclass

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

Question

(C) The total number of ways to select $2$ lines out of $37$ is $^{37}C_2$. Since $13$ lines are concurrent at point $A$,they do not produce $^{13}C_2

Vedclass · Accepted Answer

$^{37}C_2 - ^{13}C_2 - ^{11}C_2 + 2$

Vedclass · Answer

(C) The total number of ways to select $2$ lines out of $37$ is $^{37}C_2$. Since $13$ lines are concurrent at point $A$,they do not produce $^{13}C_2$ distinct intersection points; instead,they all intersect at $1$ point. Thus,we subtract $^{13}C_2$ and add $1$. Similarly,since $11$ lines are concurrent at point $B$,they do not produce $^{11}C_2$ distinct intersection points; they all intersect at $1$ point. Thus,we subtract $^{11}C_2$ and add $1$. Therefore,the total number of points of intersection is $^{37}C_2 - ^{13}C_2 + 1 - ^{11}C_2 + 1 = ^{37}C_2 - ^{13}C_2 - ^{11}C_2 + 2$.

Similar Questions

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines and $(ii)$ triangles which can be formed by joining them is:

The greatest possible number of points of intersection of $8$ straight lines and $4$ circles is

$A$ simple graph contains $24$ edges. The degree of each vertex is $3$. The number of vertices is:

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module