The area of a trapezium is 418.5 cm^{2} and the distance between its parallel sides is 27 cm. If one of the parallel sides is of length 23 cm, find the length of the other side.

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 5 cm, 7 cm and 3 cm. Find the area of the triangle.

The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere ^@S^@ from the cylinder, the remaining material is recast to form a solid sphere ^@S_1^@. What is the ratio of the radius of the sphere ^@S^@ to that of sphere ^@S_1 ?^@

Nuwan draws ^@4^@ cards out of a deck of ^@52^@ cards. What is the probability that he draws ^@a \space 7, \space a \space 9, \space a \space King, \space and \space a \space Jack^@?

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