Calendar: 1860-1861 Page 485

486 GENERAL LITERATURE AND SCIENCE 21 There are letters of which some are a's and 840 permu- tations can be made with them How many a's are there 22 If the four court cards together with any other four are drawn from pack in how many ways may this be done 23 Extract the 4th root of 51 36 24 Expand χ as far as the term involving 25 Find the middle term of 0י 26 Find an expression for numbers which when diminished by are divisible by when diminished by are divisible by and when diminished by are divisible by 27 Express 80198 in the duodenary scale 28 Solve the equation ax -j- 29 Find the number of divisors of 31416 30 If be odd and prime to either n3 or n3 is divisible by 14 31 If η arithmetical and η harmonical means be inserted between quantities and and series of η terms be formed by dividing each arithmetic by the corresponding harmonical mean the sum of the series η -4- -ל-ך-- -Γτ1 η -f II -ffiuclft anU Plant Crigonomctrg If two straight lines be at right angles to the same plane they shall be parallel to one another If two straight lines be parallel the common section of any two planes passing through them will be parallel to either Investigate the connection between the measures of the same angles in degrees and in circular measure Ex What is the circular measure corresponding to 22 30 Prove the following formulae sin sin cos Β cos sin tan-1 cot tan-1 cot cos 36 cos 36 cos 54 cos 54 -Λ 003 2Λ