Calendar: 1848-1849 Page 269

APPLIED SCIENCES 2G7 If χ2 J2 a2 ןbx cos Θ ό2 e2 ζ sin find independently of Θ The product of the first η powers of find The sum of the squares of the diagonals of parallelo- pipedon the sum of the squares of the 12 edges In the arc Β of circle centre is taken sine Β then will sector CO Β segment CB 10 person at known distance from two towers observes that their apparent altitudes are the same he then walks given distance towards them till the angle of elevation of one is double that of the other find the heights of the towers 11 In the expansion of if η be integral every co-efficient is integral 12 If Ρ be the sum of the series formed by taking the 1st and every th term of an infinite geometric series first term unity the sum by taking the 1st and every qth term prove that pi Qp 13 The sides of triangle are in arithmetical progression and the distance between the centres of the inscribed and cir- cumscribed circles is mean proportional between the greatest and least find the sides 14 If the product of two numbers be square each of the numbers is the product of two factors and the four factors are proportionals 15 Solve the equation log 301030 8' 125224 16 Given the lines drawn from any point within square to of its angular points find side of the square 17 Sum the series Tan -1 tan -1 tan -1 a2 a2 &c to η terms sin χ a2 sin 2χ a3 sin 3x &c to infinity