Calendar: 1878-1879 Page 632

630 CLOTHWOBKEBS' SCIENCE EXHIBITION Find an such that the sum of the first five terms is one- fourth the sum of the following five terms the first term being unity 10 Find the number of combinations of מ things taken at time From company of 60 men committee of 12 is to be selected in how many ways can this be done so as always to exclude particular man so as always to include him 11 Prove the Binomial Theorem for positive integral indices Show that the middle term of זג can be written 2--ל- 15 12 Explain the advantages of the Napierian and common systems of logarithms respectively Given 10g2 30103 and log405 2607455 find log003 13 Define the sine cosine and tangent of an angle and prove the relations sin2 -f- cosaa sins sin 180 sin 90 cos sina tan2 tana 14 Prove by geometrical constructions the formulae ft &in smA cosi -f- cos sin tan tan Β UmtA -7- 1- -6 י י י י tan Λ tani 15 If Β 180 prove smZA sin2i sin2C 4sin sini s'mC cos2A cos2 cos2C 2cos cosi cost sin sin Β sin 16 Prove that in any triangle -- '-ς- ana -L e1 a2 cos --- also that if be the semi-perimeter Zbc the area of triangle Vs 17 Explain the ambiguous case in the solution of triangles 18 Show how to find the area of circle Three equal circles of radius touch each other show that the area of the space between them is '3