Calendar: 1848-1849 Page 255

GENERAL LITERATURE AND SCIENCE 253 The difference between the second and fourth powers of prime number is divisible by 12 If r2 2ע bx cos θ A12 δ2 c2 -2 sin find independently of Θ The product ot the first 71 powers of find מ The sum of the squares of the diagonals of parallelo- pipedon the sum of the squares of the 12 edges In the arc Α Β of circle centre AC is taken sine then will sector COB segment Λ li 10 Λ 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 lit the expansion of χ if η be integral every co-efficient is integral 12 If Ρ be the sum of the series formed by taking the lit and every p'h term of an infinite geometric series first term unity the sum by taking the 1st and every q"1 term prove that P1 Q- P- 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 3010 50 1252 24 ז 16 Given the lines drawn from any point within η square to of its angular points find side of the square 17 Sum the series Tan ta tan -' γ &c to η terms sin a- sin sin &c to -צי infinity