61). A man 6ft tall casts a shadow 4ft long. At the same time when a flag pole casts a shadow 50 ft long. The height of the flag pole is
| A). 80ft |
| B). 75ft |
| C). 60ft |
| D). 70ft |
|
62). The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds flight, the elevation changes to 30°, If the aeroplane is flying at a haight of \( \Large 1500\sqrt{3}\ m, \) find the speed of the plane.
| A). 300 m/sec |
| B). 200m/sec |
| C). 100m/sec |
| D). 150m/sec |
|
63). There are two temples, one on each bank of a river just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60" respectively. The length of the other temple is;
| A). \( \Large 18\ m \) |
| B). \( \Large 36\ m \) |
| C). \( \Large 36\sqrt{3}\ m \) |
| D). \( \Large 18\sqrt{3}\ m \) |
|
64). The angle of elevation of the top of a tower from the point P and Q at distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is
| A). \( \Large \sqrt{ab} \) |
| B). \( \Large \frac{a}{b} \) |
| C). \( \Large ab \) |
| D). \( \Large a^{2}b^{2} \) |
|
65). The angle of elevation of a tower from a distance 100 m from its foot is 30°. Height of the tower is
| A). \( \Large \frac{100}{\sqrt{3}}m \) |
| B). \( \Large 50\sqrt{3}m \) |
| C). \( \Large \frac{200}{\sqrt{3}}m \) |
| D). \( \Large 100\sqrt{3}m \) |
|
66). A pole stands vertically inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of'. the park is same, then in \( \Large \triangle ABC \), the foot of the pole is at the
| A). centroid |
| B). circumcentre |
| C). incentre |
| D). orthocentre |
|
67). If the angle of elevation of a balloon from two consecutive kilometre-stones along a road are 30° and 60° respectively.
| A). \( \Large \frac{\sqrt{3}}{2}km \) |
| B). \( \Large \frac{1}{2}km \) |
| C). \( \Large \frac{2}{\sqrt{3}}km \) |
| D). \( \Large 3\sqrt{3}km \) |
|
68). A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is
| A). 72 m |
| B). 60 m |
| C). 65 m |
| D). 70 m |
|
69). A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend and angle twice as before. The height of the tower is
| A). 80 m |
| B). 100 m |
| C). 160 m |
| D). 200 m |
|
70). The length of'the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from 45° to 30°. Then the height of the tower is
| A). \( \Large 5\sqrt{3}\small\ metre \) |
| B). \( \Large 10(\sqrt{3}+1)\small\ metre \) |
| C). \( \Large 5(\sqrt{3}+1)\small\ metre \) |
| D). \( \Large 10\sqrt{3}\small\ metre \) |
|
