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

In a regular $15$-sided polygon with all its diagonals drawn,a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

Out of $n$ points in a plane,$p$ points are collinear. (No three of the remaining points are collinear). The number of lines that can be drawn passing through these points is:

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 number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module