A flagstaff stands on the top of a vertical tower. A man standing 60 m away from the tower observes that the angles of elevation of the top and bottom of the flagstaff are 64^o and 62^o respectively. Find the length of the flagstaff.

• A. 60 (tan 62^o - tan 64^o)
• B. 60 (cot 64^o - cot 62^o)
• C. 60 (cot 62^o - cot 64^o)
• D. 60 (tan 64^o - tan 62^o)

PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters

• A. 7.3, 5.9
• B. 7.7, 12.5
• C. 12.5, 7.7
• D. 5.9, 7.3

Simplify \(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)

• A. tan x
• B. tanx secx
• C. sec²x
• D. cosec2x

Fifty boxes each of 50 bolts were inspected for the number which were defective. The following was the result

\(\begin{array}{c|c} \text{No. defective per box} & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No. of boxes} & 2 & 7 & 17 & 10 & 8 & 6\end{array}\)

The mean and the median of the distribution are respectively

• A. 6.7, 6
• B. 7.6, 5
• C. 5.7, 87
• D. 34, 6

If 3 gallons of spirit containing 20% water are added to 5 gallons of another spirit containing 15% water, what percentage of the mixture is water?

• A. 2\(\frac{4}{5}\)%
• B. 16\(\frac{7}{8}\)%
• C. 18\(\frac{1}{8}\)%
• D. 18\(\frac{7}{8}\)%

If cos x = \(\sqrt{\frac{a}{b}}\) find cosec x

• A. \(\frac{b}{\sqrt{b - a}}\)
• B. \(\sqrt{\frac{b}{a}}\)
• C. \(\sqrt{\frac{b}{b - a}}\)
• D. \(\sqrt{\frac{b - a}{a}}\)

If 2257 is the result of subtracting 4577 from 7056 in base n, find n

• A. 8
• B. 9
• C. 10
• D. 11

Find the total area of the surface of a solid cylinder whose base radius is 4cm and height is 5cm

• A. 56πcm²
• B. 72πcm²
• C. 96πcm²
• D. 192πcm²

At what value of x is the function y = x² - 2x - 3 minimum?

• A. 1
• B. -1
• C. -4
• D. 4

Find the volume of the figure

• A. \(\frac{a \pi^2}{3} (x + 3y) \)
• B. a\(\pi ^2\)y
• C. \(\frac{a \pi ^2}{3}\)(y + x)
• D. (\(\frac{1}{3} a \pi ^2 x + y\))