Calendar: 1899-1900 Page 768

CXV1 FACULTY OF SCIENCE sin cos β sin cos sin sin sin 10 Prove that the great circle bisecting two sides of spherical triangle cuts the base 90 from its middle point 11 Prove geometrically the formulae for solving right- angled spherical triangle given the angles Solve the triangle 37 35 Β 61 29' 90 12 Prove geometrically cos cos cos sin sin cos If the vertical angle of spherical triangle be bisected by great circle which also cuts the base the sines of the segments of the base are as the sines of the adjacent sides II -algebra anti fjcarg of qxiattons Prove the rule for finding the of two rational integral functions Find two rational integral functions such that Ρ Or3 hx χ2 χ If rational integral function be divided by χ-a find the remainder Use this theorem to find tests for the divisibility of any number by and by 11 Find the number of combinations of η things together Find the sum of all the different numbers of not more than five digits that can be formed with the digits where any of the digits may be used any number of times State and prove the Binomial Theorem for positive integral exponent Shew that if four geometric means be inserted between and 001 the common ratio is nearly 1Ό002 and more nearly 1Ό0019992 Sum the series to η terms 03 ii r2 v3 iii 22 3V