Calendar: 1865-1866 Page 539

GENERAL LITERATURE AND SCIENCE 541 15 If a0 av β2 0c3 αν ab be the digits of number of six figures show that it will be divisible by 13 if a0 a3 ae ad β2 αύ is multiple of 13 16 Define Geometrical Progression and find the sum of series to מ terms 17 If sv s2 i3 be the sums to η terms η terms and מ terms then $x s3 Sj s2 18 Prove that 20 392 20 γ 392 19 Find the coefficient of a2 42 c3 in ί and ex- pand to terms 20 The coefficients of χ in the 5th and 7th terms of 2x are 1120 and 1792 respectively find 21 If a1 b1 b2 a3 b3 &c then shall K2 ai &c έ i22 3" &c 22 Find the least number which is multiple of 13 but which when divided by or leaves remainder 23 If the diameter of florin be to that of half-crown as what should be the ratio of their thicknesses 24 boat's crew can row distance of miles miles up and miles down in 64 minutes However as they are rowing with the stream the breaking of an oar at miles from the starting point diminishes their pulling power by mile an hour at the end of the course the oar is replaced but is broken on the return at the same place as before and with the same effect on the rowing of the crew who now perform the row in minutes longer time than they expected Find the rate the men pulled at and the rate per hour the stream was flowing