ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P i

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Question
ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P is the midpoint of AB, then the value of sin (?CPB) is :
Options
A. 3 5
B. 2 5
C. 3 4
D. 4 5

Correct Answer

4 5

Explanation

Height and Distance problems

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1.
From the top of a tower of height 108 meter the angles of depression of two objects on either sides of the tower are 30� and 45�. The distance between the objects are :
Options
A. 180 ( 3 + ?3 ) m
B. 180 ( 3 - ?3 ) m
C. 180 ( ?3 - 1 ) m
D. 180 ( ?3 + 1 ) m

2.
A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45� with the man's eye when at a distance of 60 meter from the tower. After 5 second, the angle of depression becomes 30�. What is the approximate speed of the boat, assuming it is running in still water?
Options
A. 32 Km/h
B. 42 Km/h
C. 38 Km/h
D. 36 Km/h

3.
A man is standing on the 8 m long shadow of a 6 m long pole. If the length of the shadow is 2.4 meter, then the height of the man is :
Options
A. 1.4 m
B. 1.6 m
C. 1.8 m
D. 2.0 m.

4.
The angle of elevation of the top of a TV tower from three points A, B, C in a straight line through the foot of the tower are ?, 2?, 3?, respectively. If AB = a, the height of the tower is :
Options
A. a tan ?
B. a sin ?
C. a sin 2?
D. a sin 3?

5.
If a flag staff of 6 m height placed on the top of a tower throws a shadow of 2 ?3 m along the ground, then the angle that the sun makes with the ground is :
Options
A. 60�
B. 30�
C. 45�
D. None of these

6.
The angles of elevation of the top of a tower from the points P and Q, at distances 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 :
Options
A. ?ab
B. a b
C. ab
D. a2b2

7.

The length of a shadow of a vertical tower is 1

?3

times of its height. The angle of elevation of the Sun is :
Options
A. 30 �
B. 45 �
C. 60 �
D. 90 �

8.
The banker's gain of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time and at the same rate is Rs. 30. The sum is?
Options
A. Rs. 1080
B. Rs. 180
C. Rs. 500
D. Rs. 300

9.
The banker's gain of a certain sum due 2 years hence at 5% per annum is Rs. 80. The present worth is?
Options
A. Rs. 800
B. Rs. 1600
C. Rs. 1200
D. Rs. 880

10.
The present worth of a certain due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is?
Options
A. Rs. 10
B. Rs. 16
C. Rs. 20
D. Rs. 24

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