In a seminar, the number of participants in German, English and French are 240, 180 and 204 respectively. Find the numbers of rooms required to house them if in each room, the same number of participants are to be accommodated and all of them must belong to the same language.
From a point ^@ P ^@ outside a circle with centre ^@ O ^@, tangents ^@ PA ^@ and ^@ PB ^@ are drawn to the circle. The line segment formed by joining the points ^@ A ^@ and ^@ B ^@ intersect the line segment ^@ OP ^@ at ^@ M ^@. What is the measure of ^@ \angle BMP ^@ ?
A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in the figure. If the height of the cylinder 43 cm and its base is of radius 13 cm, then the total surface area of the article when it is ready is: