Simplify : $$\sqrt{[(12.1)^2-(8.1)^2]÷[(0.25)^2+(0.25)(19.95)]} $$

The upper part of a tree is broken over by the wind makes an angle of 60 ° with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree? 

From a right cone of height h and with base radius r a cone has been cut of from the centre of the height. The volume of remaining frustum of the cone is.

The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:

A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is 

Sanjay and Jacob start running in opposite directions from the same point at speeds of 7m/s and 5m/s. After 42 minutes, how far would they be from each other?

A woman invests Rs. 2000 at the start of each year at 5% compound interest per annum. How much will her investment be at the end of the 2^nd year?

If the speed of the boat in still water is 20 km / h and the speed of the stream is 5 km / h, then how long will it take for the ferry to travel 100 km with the speed of the stream?