61)

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60° with the ground. When a man starts dimning on it, it slips and now ladder makes an angle of 30° with ground. How much did the ladder slip vertically?

A)

10(√3 - 1 ) ft.

B)

10(3 - √3) ft.

C)

20(3 - √3) ft.

D)

20(√3 - 1 ) ft.

62)

If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 meters . The height of the pillar is:

A)

20 (√3 - 1)m

B)

20 (√3 + 1)m

C)

10 (√3 - 1)m

D)

10 (√3 + 1)m

63)

The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45° to 30°. Then the height of the tower is

A)

20(√3 + 1) m

B)

24(√3 + 1) m

C)

30(√3 + 1) m

D)

30(√3 - 1) m

64)

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

A)

60 m

B)

65 m

C)

70 m

D)

72 m

65)

If a pole of 12 m height caste a shadow of 4√3 m long on the ground then the sun's angle of el­evation at that instant is

A)

30°

B)

45°

C)

60°

D)

90°

66)

The distance between two pillars of length 16 m and 9 m is x meters. If two angles of elevation of their respective top from the bottom of the other are complementary to each other, then the value of x in meters is

A)

9

B)

12

C)

15

D)

16

67)

The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h meter then, in meter, the height of the building is:

A)

\({h.cotx \over cotx + coty}\)

B)

\({h.cotx \over cotx - coty}\)

C)

\({h.coty \over cotx + coty}\)

D)

\({h.coty \over cotx - coty}\)

68)

Two poles of equal height are standing opposite to each other on either side of a road which is 100 m wide. From a point between them on road, angles of elevation of their tops are 30° and 60°. The height of each pole in meter, is:

A)

20√3 m

B)

25√3  m

C)

28√3  m

D)

30√3 m

69)

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meters) of the shorter post is

A)

\({x\sqrt{2}}\)

B)

\({x\over \sqrt{2}}\)

C)

\({x\over 2\sqrt{2}}\)

D)

\({x\over 4}\)

70)

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 ΔABC, the foot of the pole is at the

A)

centroid

B)

circumcentre

C)

incentre

D)

orthocentre