Calendar: 1882-1883 Page 634

GENERAL LITERATURE AND SCIENCE 631 Find the value of χ χ Vl χ when χ and of xz 3x when -7rz V8 v- 3-V8 If four numbers are proportionals prove their reciprocals are proportional the greatest and least of them are together greater than the other two Sum to η terms ---- 3J 61 ---- and show that if be the sum of geometrical progression whose first term is and last term and sx the sum of the reciprocals of the terms of the same series then sxal Find the number of combinations of η things taken together and show that it is the same as the number taken η together have ten white and ten black balls in how many different ways can select from them set of ten balls of which five shall be white and five black What is meant by the base of system of logarithms Show that in any system the logarithm of the base is and the logarithm of is What are the advantages of 10 as base Given log 69897 and log 4771213 find log 360 log 36 and log Prove that sin2 cos2 and hence show that sin2 tan -f- cos2 cota 2sin cos tan cot sec cosec Find the trigonometrical ratios for angles of 30 45 780