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.