Calendar: 1852-1853 Page 380

376 THE SCHOOL SECOND CLASS MATHEMATICAL SCHOLARSHIP -algebra If be in harmonic progression and η be positive integer a" c2 b'1 If 2x2 ab b2 2y ab 6ף a2 b2 x2- y2 -iab then χ χ If and be less than unity show that is χ ax Solve the equations l-2a -2 "16- ϊ 4λ2 2-2cx ax2-ac χ axy χ -f bx ζ czy There are η arithmetic series whose first term is unity and common differences η find the sum of all the series to η terms number consisting of digits is unaltered in value when its digits are read in reverse order also the square of the middle digit equals twice the sum of the first and third find the number Extract the square root of- 4c 4a6c3 abd2 ship sails with biscuit for 60 days at an allowance of lb per head daily After being at sea 20 days she loses men in storm and sustains damage that will cause delay of 24 days so that each man's allowance is reduced to fib find the original number of the crew If be prove that x- -a χ or if χ or