Calendar: 1876-1877 Page 583

GENERAL LITERATURE AND SCIENCE 583 If χ in tlie duplicate ratio of and in the sub-duplicate ratio of then 2x χ -y Form the equation whose roots are Shew what relation holds between and when the equation ax -f- bx has equal roots Transfer 42 36 from the denary to the quinary scale and find the radix of the scale in which the double of 145 is expressed by the same digits Prove that AH G2 when Ή are respectively the arithmetic geometric and harmonic means between two quantities Sum the following series each to η terms &c 2s 32 -I- ike &c 10 If ί ד Sic to infinity and -f f- infinity then 27 st 11 Find the number of combinations of η things taken ρ together Shew that the number of combinations of η things taken ρ together the number of combinations of η things taken ρ together tbe number of combinations of η things taken ρ together 12 Write down the expansion of -y and give the general term Find the coefficient of xn in the expansion of 2x 13 Prove logo logo -f- logo also loga logo logo Given logs 30103 Solve the equation Find the number of digits in 5100