A boat goes ^@25 \space km^@ upstream and ^@46 \space km^@ downstream in ^@10^@ hours. If one of the distance time relationships is represented by the following equation ^@\dfrac{ 25 }{ P } + \dfrac{ 46 }{ Q } = 10^@ then, which of the following correctly represents ^@P^@ and ^@Q^@?
Gabriel Felix
A.
^@P = \dfrac{1}{ x - y }^@ and ^@Q = \dfrac{1}{ x + y }^@
Two poles of equal heights are standing opposite to each other on either side of the road which is ^@ 20 \space meters ^@ wide. From a point between them on the road, the angles of elevation of the top of the poles are ^@ 30^\circ ^@ and ^@ 60^\circ ^@ respectively. Find the height of the poles.
Tangents ^@ PA ^@ and ^@ PB ^@ are drawn from an external point ^@ P ^@ to two concentric circles with center ^@ O ^@ and radii ^@ 8 \space cm ^@ and ^@ 5 \space cm ^@ respectively. If ^@ AP = 14 \space cm ^@, what the length of ^@ BP ^@ ?
An equilateral triangle has side length 11 cm. What is the area of a region of all the points outside the equilateral triangle that are within 5 cm of the triangle?
There is a cylindrical compass holder of height ^@ 10 \space cm^@ and diameter ^@ 11 \space cm^@. Now the compass holder is cut into two pieces such that the height of the new compass holder is reduced to ^@ \left(\dfrac{ 3 }{ 5 } \right)^{th} ^@ of the height. The diameter of the new compass holder remains the same. If the new compass holder is filled with water up to the brim, then find the amount of water held in liters. (Where ^@ \pi = 3.14 ^@)
The letters of the word STATISTICAL are rearranged in a random order. What is the probability that the letters C and L have exactly 5 letters between them?
UK
