1). The angle of elevation of the top of a tower at a point on the ground is \( \Large 30 ^{\circ} \). If on walking 20m towards the tower the angle of elevation becomes \( \Large 60 ^{\circ} \) then the heights of the tower is:
A). 10 m 
B). \( \Large \frac{10}{\sqrt{3}} m \) 
C). \( \Large 10\sqrt{3} m \) 
D). None of these 

2). When the elevation of sun changes from \( \Large 45 ^{\circ} \) to \( \Large 30 ^{\circ} \) the shadow of a tower increases by 60 m, The height of the tower is:
A). \( \Large 30\sqrt{3} m \) 
B). \( \Large 30 \left(\sqrt{2} + 1\right) m \) 
C). \( \Large 30 \left(\sqrt{3}  1\right) m \) 
D). \( \Large 30 \left(\sqrt{3} + 1\right) m \) 

3). A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \( \Large 60 ^{\circ} \) when he retire 40 m from the bank he finds the angle to be \( \Large 30 ^{\circ} \). The breadth of the river is:
A). 20 m 
B). 40 m 
C). 30 m 
D). 60 m 

4). A flagstaff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the tapes of the flagstaff and building are \( \Large 60 ^{\circ} \) and \( \Large 30 ^{\circ} \) respectively, then the height of the flagstaff is:
A). 46.19 m 
B). 50 m 
C). 25 m 
D). none of these 

5). A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, the distance between the two houses is:
A). 48 m 
B). 36 m 
C). 54 m 
D). 72 m 

6). From the top of a light house 60 m high with its base at the sea level the angle of depression of a boat is \( \Large 15 ^{\circ} \). The distance of the boat from the foot of light house is:
A). \( \Large \left(\frac{\sqrt{3}1}{\sqrt{3}+1}\right)60 m \) 
B). \( \Large \frac{\sqrt{3+1}}{\sqrt{31}} m \) 
C). \( \Large \left(\frac{\sqrt{3}1}{\sqrt{3}+1}\right)60 m \) 
D). none of therse 

7). Two poles of equal heights stand on either side of a 100 m wide road. At a point between the poles the angles of elevation of the tops of the poles are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \). The height of each pole is:
A). 25m 
B). \( \Large 25\sqrt{3} m \) 
C). \( \Large \frac{100}{\sqrt{3}} m \) 
D). none of these 

8). At a distance 2h metre from the foot of a tower of height h meter the top of the tower and pole at the top of tower subtend equal angles. Height of the pole should be
A). \( \Large \frac{5h}{3} m \) 
B). \( \Large \frac{4h}{3} m \) 
C). \( \Large \frac{7h}{3} m \) 
D). \( \Large \frac{3h}{3} m \) 

9). A kite is flying at an inclination of \( \Large 60 ^{\circ} \) with the horizontal. If the length of the thread is 120 m, then the height of the kite is:
A). \( \Large 60\sqrt{3} m \) 
B). 60 m 
C). \( \Large \frac{60}{\sqrt{3}} m \) 
D). 120 m 

10). If a flag staff of 6 m high placed on the top of a tower throws a \( \Large 2\sqrt{3} m\) along the ground, then the angle (in degrees) that the sun makes with the ground is:
A). \( \Large 60 ^{\circ} \) 
B). \( \Large 80 ^{\circ} \) 
C). \( \Large 75 ^{\circ} \) 
D). none of these 
