GATEWAY TO CGL MAINS 2015 : Advanced Quant Quiz

1.The angle of elevation of the top of a tower at a distance of 30 m from its foot is 45°. The height of the tower is : -   

(a) 20 m 

(b) 30 m 

(c) 15√2 m

(d) 15/√2 m 

2.If the ratio of the length of a pen to its shodow is 1 :√3 , the angle of elevation of the source of light is :- 

(a) 40°

(b) 30°

(c) 60°

(d) 90°

3.A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60° to the horizontal. Find the height of the balloon from ground. Assume that there is no slack in the cable:-

(a) 173.2 m 

(b) 17.35 m 

(c) 123.2 m 

(d) None of these 

4.One flies a kike with a thread 150 metre long. If the thread of the kite makes an angle of 60° with the horizontal line, then the height of the kite from the ground (assuming the thread to be in a straight line) is: 

(a) 50 metre

(b) 75√3

(c) 25√3

(d) 80 metre

5.From the top of h metres high cliff, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is : - 

(a) 2 h/3 

(b) h/3 

(c) 2h/√3

(d) h/√3

6.The angle of elevation of top of a tree on the bank of a river from its other bank is 60° and from a point 20 m further away from this is 30°. The width of the river is :- 

(a) 10 √3 m 

(b) 10 m 

(c) 20 m 

(d) 20 √3 m 

7.A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite side of the bank is 60°. When he moves 50 m away from the bank, the angle of elevation becomes 30°. The height of the tree and width of river respectively are : - 

(a) 25√3 m, 25 m 

(b) 25√3, 25√3 m 

(c) 25, 25√3 m 

(d) None of these

8.The angles of elevation of the top of a tower as observed from the bottom and top of a building of height 80 metre are 60° and 45° respectively. The distance of the base of the tower from the base of the building is: - 

(a) 40 (√3-1)m 

(b) 40 (3+ √3)m

(c) 40 (3- √3)m

(d) 40 (√3+1)m

9.A man on the top of a rock rising on a sea-shore observes a boat coming towards it. If it takes 20 minute for the angle of depression to change from 30° to 60°, how soon will the boat reach the shore? 

(a) 20 minute 

(b) 30 minute 

(c) 10 minute 

(d) 15 minute 

10.From the top of cliff 90 metre high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is : 

(a) 45 m 

(b) 60 m 

(c) 75 m 

(d) 30 m

Answers and Solution: