Home
Class 12
MATHS
Let f(n) be the number of regions in...

Let `f(n)` be the number of regions in which `n` coplanar circles can divide the plane. If it is known that each pair of circles intersect in two different points and no three of them have common points of intersection, then `(i)` `f(20) = 382` `(ii)` `f(n)` is always an even number `(iii)` `f^(-1)(92) = 10` `(iv)` `f(n)` can be odd

Promotional Banner

Similar Questions

Explore conceptually related problems

Total numbers of regions in which |'n:)' coplanar lines can divide the plane,if it is known that no two lines are parallel and no three of them are concurrent,is equal to

Let N denotes,the greatest number of points in which m straight lines and n circles intersect. Then,

Let N denotes,the greatest number of points in which m straight lines and n circles intersect. Then,

If n straight lines in a plane are such that no two of them are parallel and no three of them are concurrent, prove that they intersect each other in (n(n-1))/2 points.

Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 if n is even. Show that f is invertible. Find the inverse of f. Here W is the set of all whole numbers.

Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.