Question:
The maximum number of points of intersection of 8 circles of unequal radii is 56.
The maximum number of points into which 4 circles of unequal radii and 4 non coincident straight lines intersect, is 50.
The maximum number of points of intersection of 8 circles of unequal radii is 56.
The maximum number of points into which 4 circles of unequal radii and 4 non coincident straight lines intersect, is 50.
Updated On: Sep 30, 2023
- Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement -1
- Statement -1 is true, Statement -2 is true ; Statement-2 is NOT a correct explanation for Statement - 1
- Statement -1 is false, Statement -2 is true
- Statement - 1 is true, Statement- 2 is false
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The Correct Option is B
Solution and Explanation
Two circles intersect in 2 points.
$\therefore$ Maximum number of points of intersection
$= 2 ?$ number of selections of two circles from 8 circles
$= 2 ? ^8C_2 = 2 ? 28 = 56$
Statement $2 : 4$ lines intersect each other in $^4C_2 = 6$ points
4 circles intersect each other in $2 ? ^4C_2 = 12$ points.
Further, one lines and one circle intersect in two points. So 4 lines will intersect four circles in 32 points.
Maximum number of points $= 6 + 12 + 32 = 50$
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Concepts Used:
Combinations
The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.
- It means the combination of about ‘n’ things taken ‘k’ at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.
- For example, Imagine you go to a restaurant and order some soup.
- Five toppings can complement the soup, namely:
- croutons,
- orange zest,
- grated cheese,
- chopped herbs,
- fried noodles.
But you are only allowed to pick three.
- There can be several ways in which you can enhance your soup with savory.
- The selection of three toppings (subset) from the five toppings (larger set) is called a combination.
Use of Combinations:
It is used for a group of data (where the order of data doesn’t matter).