Progression

There are n stones in a line , the distance betwen the consecutive stones being 1m ,3m,5m etc. There is a basket fixed at the first stone.A man starting from the baskets collects all the stones in the basket one by one . Find the total distance described by him in colecting all the stones .

He starts from the first stone.

The distance to be travelled for the 1st stone is 0

for the 2nd it is 2.2
3rd it is 2.4

nth stone it is 2(2n-2)

Thus the sum is 2.2(1+2+3+... n-1)

= 2(n-1)n

Can the sides of a quadilateral be in AP ( not neccessarily taken in order) in which a circle can be inscribed ?

This is to be done by taking tangents...

the distance of tangent from a fixed point is constant.

Then try to do this. It is not a very tough question.. just try..

see what you can say about the sum of the opposite sides!