In the given figure, ^@ XP ^@ and ^@ XQ ^@ are the two tangents to a circle with center ^@ O ^@ drawn from an external point ^@ X ^@. ^@ AB ^@ is another tangent touching the circle at ^@ R ^@, then ^@ XA + AR ^@ is equal to:
A camp is made in the form of a conic frustum, surmounted by a cone. The diameters of the base and top of the frustum are ^@ 6 \space m^@ and ^@ 3 \space m ^@ and its height ^@ 7.5 \space m ^@. The height of the camp is ^@ 12 \space m ^@. Find the quantity of canvas required to make the camp.
Rawan and Akku each have a bag that contains one ball each of the colors blue, orange, grey, yellow and green. Rawan randomly selects a ball from her bag and puts it in Akku's bag. Then Akku randomly selects a ball from his bag and puts it in Rawan's bag. What is the probability that after this the contents of the bag are the same as before?