2. 2x2 - 3x + 5, (x + 2y) (x + 7y) (x − 3y) (x — 51). 5. (1) 2, 3. a (2) x = ± 3, ± 2√√ — 3, ± 2√3, ± ±√{3( √−1±√47)}, ± √{3( − √−1±√47)} ; y=±1, ± - 13. Area of surface, 2130°7 sq. ft.; volume 12016'58 cub. ft. (3) (sin 2x) sin.{cos x log sin 2x + 2 sin x cot 2x). 9. Ratio of the masses e: I ; velocities e2u, (1 − e)e2u, where u is the original velocity. 12. Assuming the energy to vary as the number of lbs. of powder, the velocity would be doubled. 1. (1) 3(x2+ y2+82). 13a +5x (2) II.-ALG. MENS. 2. (a2 + b2) (a + b) (a - b) (2a - b) (a + 26). 3. 5. 4. (1) 1 − 2 a3 + a. (2) √2x + 1 + √x - 4. 5. (1) 20. (2) x, ± 2; y, ± 1. a+Arith. Series, 4th term = – 7. 2 5a+13x 6. 18 gallons. I 2√2+3 9. 1+4x+10x2+20x3+35x1+..... +}(r+6)(r+5)(r+4)x2+3 +. IV. CONICS, DIFF. CAL. 4. x 30, y4= = o. Area = 2. 5. x2+ y2 - 2 √ a2 — b2 . y = b2 (or x2 + y2 + 2 √ a2 − b2 . y = b2). 2N √a2 - b2 2 √x. √1 + x (1 + √√x) 22 - (1)* (1 + log x). IO. 13. - 2, m ± √m2 - 2. 3 1. 2√√6; (x2 + x + 1) (x2 −x + 1), (2x + 1) (x − 1) (x + 1) (x − 1), (x + 2y + 28) (x + 2y − 28). 3. H.C.F.2x2-3x, L.C.M. = x2(2x-3) (3x-2) (4x2-12x+9) ; 4771213, 602c600, 6989700, 7781513, 8450980, 9030900, *9542426. 13. 16125 sq. ft. 14. 41888, 5236 cu. in. 6. Sq. on diagonal = sum of sqq. on the III.-CONICS, DIFF. CAL. "2 4. 2(x" - x)x+2(y" − y)y = x2 - x2+y"2 - 2. x"2 below, and its distance from the 1st. II. W. 12. 88n R E July 1889. I. ALG. MENS. I. La Nô, 5x2+4. 2. I - 19+ 25, x3-3x+2. 3. (x-4) (x 6), (9x + 32) (3x – 16), 4(a – d) (b − c), (x2 + x + 1) (x2 − x + 1). - 4. Expression = (x − y) (y − 2) (≈ − x) (x + y + z). 6. (1) H.C.F. 3x2-5x-12; L.C.D. 244-10613+59x2+189x-180. (2) H.C.F.6(x2 — y2) ; L.C.D. 72(x2-y)2(x2+xy+y2)(x2-xy+y2)=72(x8-x®y? — x2y©+y®). 7. (1) 5. (2) 0,± 1. (3) x = = 21, y = 6. 8. A £1520, B £1760, C £720, D £1040. 12 2 9. 973; 4, 8, 16, 32, 64. IO. = 627264. II. 13. 816816, 13 ft. n(n − 1) (n − 2)... (n − r+1), 3.4.5...(+2) 1.3.5... (2r — 1) βπ-Υ. , 11. 7:589466; 18° 26′ 6′′, 108° 26′ 6′′, 53° 7′ 48′′. III. CONICS, DIFF. CAL. 3. x + y = 3. 7. x2 — y2 = a2 (referred to centre of circle as origin). along a line making an angle tan-1√2 with line due N. II. Time sec., at distance 54'6 ft. from A. 2. 1; (a+b+c+d) (a−b-c+d) (a+b-c-d) (a−b+c-d). 3. 2x2-3x+1; (x2+2x-2)(x2 -2x+2)(2x2−3x+1)=2x6-3x5-7x1 +28x3-36x2+ 20x −4. 4. (1) I. (2) I. 5. (1) a + b, and (a - b)2 (2) 4. 6. 20. 7. 8. |