Calendar: 1873-1874 Page 537

GENERAL LITERATURE AND SCIENCE 537 Extract the square root of 61 28 and find the value of χ V3 when χ έ If and β are the roots of ax2 bx prove that β and αβ Form the equation of which the roots are and Ρ Express the number 579 35 in the scale whose radix is Prove that the difference of two numbers consisting of the same figures is divisible by If and be any multipliers prove that each fraction will be equal to pa qc re pb qd rf Solve ax by ez ax by 4- cz χ λζ ax 10 Find the sums of η terms of the series 27 ---- l2 22 32 ---- 99 999 λ 11 If be three quantities such that is the arithme- tical mean between and and the harmonical mean between and show that is the geometrical mean between and and compare 12 Find the number of combinations of η things taken at time Tbe captain of cricket club has 16 men from whom to choose an eleven How many diflerent elevens can be selected In how many of these will any two men appear