3. -(b−c)(c-a) (a − b)(a+b+c), (x−1)(x+1)(x+2)(x+3). H.C.F. x2 - 10x+21, L.C.M. (x2 – 10x+21) (x − 1)(x − 2)(x − 4) (x − 5). 4. 12. (i.); (ii.) Conservative 12944, Liberal 11120; (iii.) 21056 each. 13. 14. A parabola with same axis and vertex at the focus of the given parabola. A circle centre on the minor axis distant CS cot a from the centre and radius a cosec a, where a is the given angle. 1. (x2+1)(x-x2+2). 1. 2. (1+x) (1+x2) ( 1 − x − x2 − x3+x1). 3x2 -5x+7. 4. (i.) 61, 27; (ii.) x = ±1, ± ; y = }}, ± 4 3 N47 47 11. V. STATICS AND DYNAMICS. 3. (i.) 10 lbs. ; (ii.) 15 lbs. W W 6. Power is (i.) (ii.) √2 8. (i.) W; (ii.) ‡ W. 10. 12 ft., 4 ft. Its distances from AB, AC are 16, 32 ft., and it is moving in a direction equally inclined to AB, AC. 2. 7. VI. PURE MATHEMATICS. g'o (n+5)(n+10), − f(n+4)(n+9), &(n+3)(n+8), − (n+2)(n+7), o according as n is of the form 57, 5r+1, 5r+2, 5r+3, 5r+4. 2743.86 ft. 8. Taking centre of pentagon as origin, and a line joining it to one angular point as the axis of x, the equations are ; (ii.) x=y=z=−}; x=}, y=z=− }; y = }, x = z= =-}; 3 and z =},x=y= -3. 5. 6. In the larger, wine: water = p2 - 32p+ 1280 : 32p − p2, and in smaller, 32-p2: p2 - 32p+320. p=16. 1296 and 2025, 2025 and 3025, 3025 and 4356, etc., 133 = 912 – 782. 1. V. STATICS AND DYNAMICS. II lbs. 15 oz. and II lbs. at the ends; 11 lbs. 5 oz. and 11 lbs. 10 oz. |