QJEEAdv08Madb94: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Madb94 Solution: The number of elements in the set is

In the Cartesian coordinates sets A, B and C defined the regions given by

$A:y\ge1,B:(x-2)+(y-1)^2=9$

B and C being a circle and a straight line intersect in two points, out of which only one satisfies y > -1 .

Thus, the no. of elements in the set A $\cap$ B $\cap$ C is 1.