Calendar: 1889-1890 Page 757

ENGINEERING DEPARTMENT Ill Shew that the amounts for successive vears of sum put out at compound interest are in continued proportion years is £455 and for η years it is iiCul find Γ and the rate per cent If scats are placed in row at table in how many ways may persons occupy them explain your mode of obtaining result In how many ways may the letters of the word plastic י be arranged without any restriction if ρ and come together if ρ and do not come together 1u Find the 10th term nd the middle term of 3a xj also the greatest term if χ Sum to η terms to η terms and- -I--- -I--to η terms and to infinity נ 33 55 Sum η terms oi the series of which the term is -f- also that of which the term is Enumerate briefly describing each the circles with which you are acquainted that have special relations to trinncfle Express in terms of the circumradius and the angles of triangle the length of the line joining the circumcentre to the orthocentre 10 If quadrilateral the sides of which arc be inscribed in circle of radius 71 and if £ prove that 11 If be the area of regular polygon of η sides the radii of the incircle and ciroumcircle prove that nrli sin Shew that this is less that nrJi What does it become when η oo