There are n lines in a plane ( may or may not be concurrent ) . Find out the maximum and the least number of regions that can be formed ?

How many squares can be formed in the following image by connecting four points of 8x8 grid?

If the centroid of a triangle is formed by the points (a,b), (b,c) and (c,a) is at the origin i.e. (0,0) then a^3 + b^3 + c^3 = ??

If repetition of numbers is not allowed then how many numbers of five digits can be formed by using 1,2,3,4,5. If 4 is necessarily taken at hundred's place and 2 is not allowed at unit's place