Calendar: 1887-1888 Page 668

672 GENERAL LITERATURE AND SCIENCE State the laws of indices and interpret in accordance therewith a0 Write down the following logarithms 10g3 27 10g26 10g210 125 10 16 46 and the characteristics of the following log10127 Jog50 35 10g5 002 Ascertain the condition that ar px may be perfect square Prove that myf will be perfect square if i2a2 m2b2 p2 If β are the roots of ax2 £ form the equation of which the roots are a3 33 If ax2 by2 fy can be split into linear factors prove that ahc 2fgh af2 Find in order that r2 pvy ז may split into factors and find the factors If the cube root of ρ Ja rb can be expressed as the sum of two surds prove that p2a q2b must be perfect cube Prove that the sum of the squares of the cube roots of 2d 30 2d and 2d if rf 2rf is independent of If x2 y2 expand in powers of χ as far as Λ Hence expand sin in ascending powers of cos to four terms Given Λ τ4 24 720 expand y2 in powers of as far as Sum the following series 23 33 and find the series the sum of η terms of which is