(3) Find the value of √a2b3 +3 √✅a3 b3 +6√√/a2 b2 when a = 5, b = 25. Here b = a2 SECTION VI. (Three Questions.) = 5 = 755 Ans. Find the G. C. M. of 4+7x3 + 6x2 - 32x-32 and a2+9x+20. x2+9x+20)x+7x3+6x2 - 32x - 32(x2 - 2x + 4. x+9x3 +20x2 ..+4 is the G. C. M. required. 2 Find the L. C. M. of x2 - y2, x2 + xy − 2y2, and x2 + 3xy + 2y2. y2 x2-y2 = (x+y) (x-y) x2+xy − 2y2 = (x+2y) (x − y) x2 + 3xy + 2y2 = (x+2y) (x+y) Casting out Common Factors. L. C. M. (+2y) (x + y) (xy) = = (x+2y) (x2 − y2) = x2+2x2y-xy2-2y3 Ans. (3) What is the condition that a2+på+q may be divided by x-r ? Perform the actual division. x-r)x2+px+q(x+p+r Rem. = r2+rp + q, which should be equal to 0. SECTION VII. Solve the Equations. (1) 16-4x+8x = 5x + 14 (2) 8x-4y=5 | } SECTION VIII.-(a) The breadth of an oblong space is four yards less than its length; the area of the space is 252 square yards; find the length of its sides. (b) A regiment has sufficient food for m days; but if it were reinforced by p men, would have food enough for n days only, find the number of men in the regi ment. (These form one Question.) (a) Let x = length .. a - 4 breadth (b) Let x = number of men ..+p 2nd number .. Time food would support one man = m = n(x+p) MENSURATION. SECTION IX. (Two Questions.)-1. A triangular space whose sides are in the ratio, 5: 5: 6, contains 588 square yards; find the length of its sides. 2. A cottage which stands on a square plot of 729 feet, contains four rooms of equal size on the ground floor, and is divided into two equal parts by a passage four feet wide, having two rooms on each side; allowing one foot for the thickness of each wall, find the area of each of the four rooms. (1) Let 52, 5, 6x = sides. Calling the section parallel to passage the length, and the section perpendicular to passage the width, we have : 24 = 12 ft. Length of floor, minus walls = 27-3=24 ft. .. Width of one room = } =27-4-4-19 ft. = 19 = 93 ft. MALE AND FEMALE CANDIDATES. LANGUAGES. (Three hours allowed for this paper.) This paper is voluntary. Candidates examined in England, and Female Candidates in Scotland, may answer questions in one Language (only). Male Candidates in Scotland may answer questions in two (not more) Languages. FRENCH. 1. Translate into English : Mon malheureux frère n'avait pas besoin de cet ordre dès le premier moment, il s'était dit qu'il n'avait plus qu'un devoir: retrouver sa sœur et son amie, dût-il, pour accomplir son entreprise, affronter mille morts. Il eût voulu seulement emporter avec lui comme un gage de succês, comme une consécration divine, la bénédiction de son père; et loin de là, c'était sous le poids de l'anathème qu'il devait quitter l'auteur de ses jours, et courir le monde à la recherche de sa soeur chérie. Ce dernier coup du sort lui fut le plus cruel; mais, si tout d'abord il s'était senti écrasé sous ce comble d'infortune imméritée, il finit par puiser dans l'horreur même de sa situation une énergie sauvage et surhumaine. Désormais il était prêt à tout. 1. My unhappy brother had no need of this order: from the first instant he had said to himself that he had but one duty: to find his sister and his friend, even if it should be necessary to confront a thousand deaths to accomplish his enterprise. He would have wished only to carry away with him, as an earnest of success, as a Divine consecration, his father's blessing; and instead of that, it was under the weight of a curse that he had to leave the author of his being, and traverse the world in search of his beloved |