71). The inequality \( \Large 2x^{2} + 9x + 4 < 0 \) is satisfied for which of the following values of 'x'?
| A). \( \Large - 4 < x - \frac{1}{2} \) |
| B). \( \Large \frac{1}{2} < x < 4 \) |
| C). 1 < x < 2 |
| D). - 2 < x < 1 |
|
72). Each inch on ruler A is marked in equal \( \Large \frac{1}{8} - inch units \) , and each inch on ruler B is marked in \( \Large \frac{1}{12} - inch units \) . When ruler A is used, a side of triangle measures 12 of the \( \Large \frac{1}{8} - inch units \) . When ruler B is used, how many \( \Large \frac{1}{12} - inch units \) will the same side measure?
| A). 8 |
| B). 12 |
| C). 18 |
| D). 20 |
|
73). The value of k for which x - 1 is a factor of \( \Large 4x^{3} + 3x^{2} - 4x + k \) is
| A). 3 |
| B). 1 |
| C). -2 |
| D). -3 |
|
74). Two straight lines can divide a circular disk into a maximum of 4 parts. Likewise into how many parts can four straight lines divide a circular disk ?
| A). 8 |
| B). 9 |
| C). 10 |
| D). 11 |
|
75). A person can row a boat d km upstream and the same distance downstream in \( \Large 5 \frac{1}{4} \ hours \). Also he can row the boat 2d km upstream in 7 hours. He will row the same distance downstream in
| A). \( \Large 3 \frac{1}{2} \ hours \) |
| B). \( \Large 3 \frac{1}{4} \ hours \) |
| C). \( \Large 4 \frac{1}{4} \ hours \) |
| D). 4 hours |
|
76). The rate at which a river flows is one-third the speed of a boat in still water. If that boat travels down the river for 2 hours and then back up river for 2 hours, it will be 16 km short of its starting point. The speed (km/hour) of the boat in still water is
|
77). If \( \Large a^{x} = b^{y} = c{z} \) and \( \Large \frac{b}{a} = \frac{c}{b} \) then \( \Large \frac{2z}{x + z} = ? \)
| A). \( \Large \frac{y}{x} \) |
| B). \( \Large \frac{x}{y} \) |
| C). \( \Large \frac{x}{z} \) |
| D). \( \Large \frac{z}{x} \) |
|
78). If \( \Large f(x) = 2x^{3} + 3x^{2} + 5 \) then f(2) = ?
| A). 31 |
| B). 32 |
| C). 33 |
| D). 35 |
|
79). For what value(s) of k, the roots of the equation \( \Large 9x^{2} + 2Kx + 4 = 0 \) will be equal ?
| A). 6 |
| B). -6 |
| C). \( \Large \pm 6 \) |
| D). \( \Large \pm 5 \) |
|
80). A 10 metre, long ladder is placed against a wall. It is inclined at an angle of \( \Large 30 ^{\circ} \) to the ground. The distance of the foot of the ladder from the wall is
| A). 7.32 m |
| B). 8.26 m |
| C). 8.66 m |
| D). 8.16 m |
|
