The greatest possible number of points of int | vedclass

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

Question

(D) To find the maximum number of intersection points,we consider the following interactions:$1$. Intersection between $8$ straight lines: The maximum

Vedclass · Accepted Answer

$104$

Vedclass · Answer

(D) To find the maximum number of intersection points,we consider the following interactions:$1$. Intersection between $8$ straight lines: The maximum number of points is given by $^8C_2 = \frac{8 	imes 7}{2} = 28$.$2$. Intersection between $4$ circles: Each pair of circles can intersect at $2$ points. The maximum number of points is $^4C_2 	imes 2 = 6 	imes 2 = 12$.$3$. Intersection between $8$ straight lines and $4$ circles: Each line can intersect each circle at $2$ points. The maximum number of points is $^8C_1 	imes ^4C_1 	imes 2 = 8 	imes 4 	imes 2 = 64$.Total points $= 28 + 12 + 64 = 104$.

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

Similar Questions

From $8$ men and $6$ women,a group of seven persons is to be formed. In how many ways can the group be formed such that the group includes at least two ladies?

How many $3$-digit numbers can be formed using $0, 1, 3, 5, 7$ when repetition is allowed?

The number of arrangements of the letters of the word $CALCUTTA$ is:

How many $4$-digit numbers are there with distinct digits?

$4$ books,$1$ each in Chemistry,Physics,Biology,and Mathematics,are to be arranged on a shelf. In how many ways can this be done?

Vedclass Test Series

Exam Paper Generator

Online Exam Module