The diagonals of a parallelogram ABCD intersect at O. A line through O intersect AB at X and DC at Y. if AB = 13 cm, AD = 5 cm, and OX = 3 cm, find the length of OY.

The area of a trapezium is 418 cm^{2} and the distance between its parallel sides is 22 cm. If one of the parallel sides is of length 16 cm, find the length of the other side.

Draw a circle of with its two chords ^@PQ^@ and ^@RS^@ such that ^@PQ^@ is not parallel to ^@RS^@. Draw the perpendicular bisector of ^@PQ^@ and ^@RS^@. At what point do they intersect each other.

The mean of the height of ^@ 4 ^@ pillars is ^@ 243 \space cm^@. If the individual height of ^@ 3 ^@ of them ^@ 179, 175, \text{ and } 186 \space cm^@, find the height of the ^@4^{ th }^@ pillar.

There are a total of 16 chocolates - 4 each in the flavors of grape, orange, cherry and strawberry. There are also 5 children. If each child is allowed to choose their own favorite flavor, what is the probability that all of them will get flavors of their choice?

If Joel drives at four fifth of his usual speed, he covers a certain distance in 3 hours more than the time he takes while driving at his usual speed. Find the time taken by him to cover this distance with his usual speed.