Calendar: 1881-1882 Page 637

638 GENERAL LITERATURE AND SCIENCE and Β can together do piece of work in 12 days and in 15 days Β and in 20 days In how many days can they do it working all together If and β are the roots of the equation ax2 hx form the equation whose roots are β and β Sum 21 terms of an Arithmetical Progression of which 10 is the middle term and find the sum of 30 terms of an Arithmetical Progression when the third term is and the tenth term is Sum to η terms 2a2 303 404 and show that if 20 geometrical means are found between and 10 their product will be 20 10 Transform 444-44 from scale of ten to that of five from scale of five to that ο iten Find the greatest and least numbers with given number of digits in any proposed scale Find the number of permutations of η things taken all together which are not all different In how many ways can sixes fives and twos be thrown with ten dice 10 Three flags are required to make signal How many signals can be given by twenty flags of five different colours there being four of each colour 11 Expand by the Binomial Theorem and find the value of the sum of the coefficients 12 Prove that the logarithm of product is equal to the sum of the logarithms of the factors Given log 30103 and log 47712 find log 0020736 13 With two units of angular measurement differing by 10 the measures of an angle are as to determine the units 14 Find the trigonometrical ratios for an angle of 60 From the top of hill are observed two consecutive mile- stones on horizontal road running from the base The