If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).

• A. \(\frac{24}{5}\)
• B. \(\frac{8}{5}\)
• C. \(\frac{5}{8}\)
• D. \(\frac{5}{24}\)

In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

• A. 160°
• B. 140°
• C. 120°
• D. 100°

Solve the equation (x - 2) (x - 3) = 12

• A. 2, 3
• B. 3, 6
• C. -1, 6
• D. 1, -6

Triangle OPQ above is the solution of the inequalities

• A. x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
• B. y + x ≤ 0, y - x ≥ 0, x -1 ≥ 0
• C. x - 1 ≤ 0, y - x ≥ o, y + x ≥ 0
• D. x - 1 ≤ 0, y + x ≤ 0, y - x ≤ 0

A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.

• A. 33°
• B. 32°
• C. 27°
• D. 26°

In a road worthiness test on 240 cars, 60% passed. The number that failed had faults in Clutch, Brakes and Steering as follows: Clutch only - 28, Clutch and Steering - 14; Clutch, Steering and Brakes - 8; Clutch and Brakes - 20; Brakes and Steering only - 6. The number of cars with faults in Steering only is twice the number of cars with faults in Brakes only.

(a) Draw a Venn Diagram to illustrate this information.

(b) How many cars had : (i) Faulty Brakes? (ii) Only one fault?

If log\(_{10}\)2 = 0.3010 and log\(_{10}\)7 = 0.8451, evaluate log\(_{10}\)280

• A. 3.4471
• B. 2.4471
• C. 1.4471
• D. 1.4071

If P and Q are two statements, under what condition would p|q be false?

• A. If p is true and q is true
• B. If p is true and q is false
• C. If p is false and q is false
• D. If p is false and q is true

If the heights of two circular cylinder are in the ratio 2 : 3 and their volumes?

• A. 27 : 32
• B. 27 : 23
• C. 23 : 32
• D. 27 : 23

Calculate the standard deviation of the distribution.

• A. 1.10
• B. 2.36
• C. 3.50
• D. 7.50