#240.
A certain triangle have sides a = 42 cm, b = 51 cm and c = 64.05cm. Find the radius of the inscribed circle.
A
13.61 cm
B
12.63 cm
C
11.15 cm
D
10.81 cm
Answer: 13.61 cm
#241.
Two observing stations were set up 850 m apart. A structural building in between them was observed to have an angle of elevation at the top equal to 12.53 degrees and 10.21 degrees respectively from each stations. Find the height of the building.
A
88.50 m
B
82.25 m
C
89.50 m
D
84.50 m
Answer: 84.50 m
#242.
Two objects flies towards each other. When the distance between them is 1.2 km their velocities and acceleration are as follows. \(V_a = 40 m/s \), \(V_b = 5 m/s \) \( A_a = -0.5 \frac{m}{s^2}\) and \( A_b = 1.36 \frac{m}{s^2}\).A third object left object A and moves toward object B with velocity of 50m/s. Upon reaching B it then flies back to A and so on until A and B meets. What is the total distance traverse by the third object?
A
950m
B
1050m
C
850m
D
900m
Answer: 950m
#243.
Two side and an included angle of a triangular lot are measured as 2.56m, 3.54m and 48.8o respectively. What is the angle measure of the angle opposite to 2.56m?
A
40.10o
B
46.10o
C
47.22o
D
45.63o
Answer: 46.10o
#244.
Two side and an included angle of a triangular lot are measured as 2.56m, 3.54m and 48.8o respectively. What is the angle measure of the angle opposite to 3.54m?
A
85.10o
B
96.09o
C
80.32o
D
65.09o
Answer: 85.10o
#245.
A man fires a target with bullet’s velocity of 900 m/s. After 2.5 seconds, he hears the sound of the bullet that strikes the target. Assuming the sound has a constant velocity of 350 m/s. How far is the target from the man?
A
630m
B
530m
C
430m
D
330m
Answer: 630m
#246.
A distance of 15.94 m is measured with a tape. What is the correct distance if during the measurement, it was discovered that the other end is actually lower by 0.78m.
A
14.98
B
15.50
C
16.62
D
15.92
Answer: 15.92
#247.
There is a garden plot dimensions 12 m by 5 m. Determine the width of a footpath to be constructed around the perimeter of the garden if it has a total area of 112 sqm.
A
1.45 m
B
2.66 m
C
3.25 m
D
2.54 m
Answer: 2.54 m
#248.
In the given equation y = mx +b, m is the slope of the line and b is the y-intercept. If the coordinates of the two points is \(x_1 = 7.5\) and \(x_2 = 12.5\), \(y_2 = 20.6\), \(y_1 = 8.5\). What is the value of m?
A
1.42
B
0.42
C
2.42
D
3.42
Answer: 2.42
#249.
xy is inversely proportional to yz. When xy = 12.54, yz = 15, 000. Find xy if yz = 12, 900.
A
14.23
B
13.66
C
14.58
D
14.53
Answer: 14.58
#250.
AB is proportional to BC in the ratio 12 to 17. Also, BC is proportional to CD in the same ratio. How long is AB if CD is 280 m long?
A
160.73
B
162.37
C
153.74
D
163.74
Answer: 163.74
#251.
The sides of a triangle 33m, 45m and 64m respectively. Find the angle opposite to the 45m side.
A
64.37o
B
45o
C
55.67o
D
84.37o
Answer: 84.37o
#252.
An observer from third floor of a mall measures the angle of elevation and depression of a tall building to be 54 and 8.6o respectively. What is the height of the building if his eye level is 10.2 m above the ground which is on the same horizontal plane as the mall and the building?
A
62.4m
B
113.45m
C
103.3m
D
93.3m
Answer: 103.3m
#253.
The expression \(x^4+ax^3+bx+6\) when divided by x-2 leaves a remainder 16 and when divided by (x+1) leaves the remainder 10. Find the value of a and b.
A
a = 7 and b = -5
B
a = -5 and b = 7
C
a = -7 and b = 4
D
a = -4 and b = 7
Answer: a = -5 and b = 7
#254.
A cat is no 50 of her own leaps ahead of a dog which is pursuing her. How many more leaps will the cat take before it is overtaken if she take 5 leaps while the dog takes 4, but two of the dog’s leaps are equivalent to three of the cat’s leaps?
A
150 leaps
B
250 leaps
C
350 leaps
D
50 leaps
Answer: 250 leaps
#255.
It is between 3 and 4 o’clock and in 20 minutes the minute hand will be as much ahead of the hour hand as it is behind it. What is the time?
A
3: 15 00 o’clock
B
3: 10 3/11 o’clock
C
3: 6 4/11 o’clock
D
3: 5 4/15 o’clock
Answer: 3: 6 4/11 o’clock
#256.
Find the fraction such that if 2 is subtracted from its terms it becomes ¼; but f 4 is added to its terms it becomes ½.
A
3/14
B
4/14
C
5/14
D
6/14
Answer: 5/14
#257.
The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motors. If it takes 20 seconds for a 5-hp motor to lift 50kg through 40m, what size of the motor is required to lift 1200 kg in 30 seconds through 40m?
A
80hp
B
82hp
C
84hp
D
86hp
Answer: 80hp
#258.
To build a macadam road, 60 men must work 72 days. If all 60 men are employed at the start but the number working decreased by 5 men at the end of each 12-day period. How long will it take to complete the road?
A
108days
B
126days
C
132days
D
84days
Answer: 108days
#259.
Three numbers whose sum is 18, are in arithmetic progression. If the first is multiplied by 2, the second multiplied by 3, and the third by 6. The resulting numbers from a geometric progression. Find the number.