A vertical stick which is ^@ 27 \space cm^@ long casts a ^@18 \space cm^@ long shadow on the ground. At the same time, a vertical tower casts a ^@70 \space m^@ long shadow on the ground. Find the height of the tower.
A straight highway leads to the foot of the tower. A man standing at the top of the tower observes a car at an angle of depression of ^@ 30^\circ ^@, which is approaching the foot of the tower with a uniform speed. ^@ 9 \space minutes ^@ later, the angle of depression of the car is found to be ^@ 60^\circ ^@. What is the time taken by the car after ^@ 9 \space minutes ^@ to reach the foot of the tower?
Two concentric circles are of radii ^@ 5 \space cm ^@ and ^@ r \space cm ^@ ^@ ( r > 5 ) ^@.A chord of the larger circle of length ^@ 43 \space cm ^@, touches the smaller circle. What is the value of ^@ r ^@ ?
Andre made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. If the height of the cylinder is 126 cm and its radius is 63 cm. Choose the correct total surface area of the bird-bath. (Take π = 22/7)
Ali and Rafa sit on the 8-member board of directors for company P. If the board is to be split up into two 4-person subcommittees, what is the percentage that Rafa and Ali are included in the same sub-committee?