81). How many different triangles are there for which the length of the sides are 3.8, and n, where n is an integer and 3 < n < 8 ?
| A). Two |
| B). Three |
| C). Four |
| D). Five |
|
82). The speed of boat A in still water is 2 km/h less than the speed of the boat B in still water. The time taken by boat A to travel a distance of 20km downstream is 30 minutes more than time taken by boat B to travel the same distance downstream. If the speed of the current is \( \Large \frac{1}{3} \)rd of the speed of the boat A in still water, what is the speed of boat B ? (km/h)
|
83). A boat can travel 12.6 km downstream in 35 minutes. If the speed of the water current is \( \Large \frac{1}{4} \)th the speed of the boat in still water, what distance (in km) can the boat travel upstream in 28 minutes ?
| A). 7 |
| B). 7.5 |
| C). 8.5 |
| D). 6 |
|
84). A boat can travel 12.8 km downstream in 32 minutes. If the speed of the water current is \( \Large \frac{1}{5} \)th of the speed of the boat in still water, what distance (in km) the boat can travel upstream 135 minutes?
| A). 27.5 |
| B). 10.2 |
| C). 28.5 |
| D). 36 |
|
85). The sides of a quadrilateral are extended to make the angles as shown below. What is the value of x ? 
| A). \( \Large 100^{\circ} \) |
| B). \( \Large 90^{\circ} \) |
| C). \( \Large 80^{\circ} \) |
| D). \( \Large 75^{\circ} \) |
|
86). What is the area of the region in the cartesian plane whose points (x, y) satisfy \( \Large |x| + |y| + |x + y| \leq 2 \) ?
| A). 2.5 |
| B). 3 |
| C). 2 |
| D). 4 |
|
87). From a horizontal distance of 50 m, the angles of elevation of the top and the bottom of a vertical cliff face are \( \Large 45^{\circ} \) and \( \Large 30^{\circ} \) respectively. The height of the cliff face (in m) is
| A). \( \Large \frac{50}{\sqrt{3}} \) |
| B). \( \Large \frac{50}{\sqrt{2}} \) |
| C). \( \Large \frac{50}{2\sqrt{3}} \) |
| D). \( \Large 50 (1 - \frac{1}{\sqrt{3}}) \) |
|
88). If \( \Large G = H + \sqrt{\frac{4}{L}} \), then L equals
| A). \( \Large \frac{4}{(G - H)^{2}} \) |
| B). \( \Large 4 (G - H)^{2} \) |
| C). \( \Large \frac{4}{G^{2} - H^{2}} \) |
| D). \( \Large 4 (G^{2} - H)^{2} \) |
|
89). If \( \Large \frac{1}{x} = \frac{1}{y} + \frac{1}{z} \), then z equals
| A). \( \Large \frac{xy}{(x - y)} \) |
| B). \( \Large x - y \) |
| C). \( \Large \frac{xy}{(y - x)} \) |
| D). \( \Large \frac{(x - y)}{xy} \) |
|
90). If (x - 3) (2x + 1) = 0, then possible value of 2x + 1 are -
| A). Only 0 |
| B). 0 and 3 |
| C). \( \Large - \frac{1}{2} \) and 3 |
| D). 0 and 7 |
|
