Calendar: 1861-1862 Page 499

500 GENERAL LITERATURE AND SCIENCE Extract the square root of- χ 2y 2y x2 yz Prove the rule for finding the Greatest Common Measure of two algebraic quantities and apply it to- x3 x1 a2 a2 and 4a 2b χ 2ab and Β have between them 168 and bet each staking sum of money proportional to that which he has If win he will have double what Β will have if he lose Β will have three times what will have What had each 10 Solve the equations- x'1 χ 2x 6x IT χ V9 τ 9x 2y2 4xy 3x2 17 y2 x1 10 31 r2 81 11 railway train travels from to passing through where it stops minutes two minutes after leaving it meets an express train which started from when the former was 28 miles on the other side of The express travels at double the rate of the other and performs the journey from to Β in 1J hours and if on reaching it returned at once to it would arrive minutes after the first train Find the distances between and and the speed of each train 12 Find when xyz ζ c2 13 How many distinct terms are there in the expansion of 14 Show how the number of divisors of given number may be found In bow many different ways can right angles be divided into equal parts When the unit is degree 2כ grade 15 What value of χ will make 3x" χ 01 square 16 If -1 be three consecutive fractions converging 13 to show that ρζ -ρΎ 3ן p2