Calendar: 1856-1857 Page 370

GENERAL LITERATURE AND SCIENCE 371 Given the perimeter and area of triangle and the angle find the side In bag there are placed 19 white balls and one red hall 20 per30ns successively draw hall and retain it compare the chances the first and the last have of drawing the red ball 10 Explain the following extract from the Times -" The quotation of gold at Paris is mille discount which the par of exchange being 25 17 gives an exchange of 25 095 and the exchange at Paris on London at short being 25 it follows that gold is about 38 per cent dearer in Paris than in London 11 Find the least common multiple of 8'1 and 8-076923 sin Θ cos β al 12 If sin -β ani cos β β at then cos -7- -7 13 Find the middle term of χ as 12 14 If a3 &c- 21- where 3" s" -a-3" &c then shall aK and prove that to η factors χ χ η 15 If be the radius of circle described about triangle and η the radius of the escribed circle touching the side the distance between the centre of the two circles γ Λ2 2Rr 16 If sum of the squares of the distances of the inscribed and escribed circles from the centre of the inscribed circle and Μ St area of the triangle and Ρ semi-perimeter then S- 4i22 P3 45Ji Tn any right-angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle Prove that the lines AL Β Κ pass through the same point