(a) Simplify : \(\frac{x^{2} - 8x + 16}{x^{2} - 7x + 12}\).

(b) If \(\frac{1}{2}, \frac{1}{x}, \frac{1}{3}\) are successive terms of an arithmetic progression (A.P), show that \(\frac{2 - x}{x - 3} = \frac{2}{3}\).

The diagram shows the cross- section of a railway tunnel. If |AB| = 100m and the radius of the arc is 56m, calculate, correct to the nearest metre, the perimetre of the cross- section.

Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the :

(a) distance of Z from Y ;

(b) bearing of Z from Y.

Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that :

(a) the first two are good and the third is bad ;

(b) all three are bad ;

(c) all the three are good.

(a) Simplify : \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}}\)

(b) If \(p = \frac{m}{2} - \frac{n^{2}}{5m}\) ; 

(i) make n the subject of the relation ;  (ii) find, correct to three significant figures, the value of n when p = 14 and m = -8.