Calendar: 1882-1883 Page 628

GENERAL LITERATURE AND SCIENCE 625 Prove that one of the roots of the equation xn pxxn1 ---- y1 tu is the coefficient of in the expansion of Prove that the roots of the equation x-a x- x-c -a x-a -b x-b -c x- -2a'b'c' are all real and find the condition that two of them may be equal Give an interpretation of this equation Of how many independent variables is the position of straight line in space function Shew that your answer is in harmony with the equation χ ν η fir c- shew that the points of contact lie on αχη-1 βτ η-l yzn an bn c71 10 Prove the following construction for the centre of gravity of right circular cone let AB be diameter of the AO 11 triangle ABC formed of three rods jointed together is supported by rough peg under the middle point of AB prove that the least angle of friction is that the sides AC BC are equally inclined to the vertical and that the stress at the joint is equally inclined to the horizon with the side AB 12 Over fixed pulley hangs string carrying at one end