P and Q are two points on latitude 55°N and their longitudes are 33°W and 23°E respectively. Calculate the distance between P and Q measured along 

(a) the parallel of latitude ;

(b) a great circle. 

[Take \(\pi = \frac{22}{7}\) and radius of the earth = 6400km].

(a) If \(9^{2x - 1} = \frac{81^{x - 2}}{3^{x}}\), find x.

(b) Without using Mathematical Tables, evaluate: \(\sqrt{\frac{0.81 \times 10^{-5}}{2.25 \times 10^{7}}}\)

(a) Solve the following pair of simultaneous equations: \(2x + 5y = 6\frac{1}{2} ; 5x - 2y = 9\)

(b) If \(\log_{10} (2x + 1) - \log_{10} (3x - 2) = 1\), find x.

(a) The angle of a sector of a circle radius 7cm is 108°. Calculate the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)]

(b) A boat is on the same horizontal level as the foot of a cliff, and the angle of depression of the boat from the top of the cliff is 30°. If the boat is 120m away from the foot of the cliff, find the height of the cliff correct to three significant figures.

(a) The sides PQ and PR of \(\Delta\) PQR are produced to T and S respectively, such that TQR = 131° and < QRS = 98°. Find < QPR.

(b) The circumference of a circular track is 400m. Find its radius, correct to the nearest metre. [Take \(\pi = \frac{22}{7}\)]