Basic Engineering Correlation (Algebra Reviewer)
1. Three transformers are directly proportional to
the KVA cost P30,000. The cost of each transformer
is directly proportional to the KVA rating and each
has a constant of proportionally of 0.9, 0.8 and 0.6,
respectively. Find the cost of the KVA transformer.
a. P7,500
b. P13,500
c. P15,500
d. P9,000
2. What is the sum of the following sequence of
terms 18, 25, 32, 39, . . . ,67?
a. 280
b. 380
c. 320
d. 340
3. A train, an hour after starting, meets with an
accident which detains it an hour, after which it
proceeds at 3/5 of its former rate and arrives three
hour after the time; but had the accident happened
50 miles farther on yhe line, it would have arrived
one and one-half hour sooner. Find the length of
the journey.
a. 850/9 miles
b. 800/9 miles
c. 920/9 miles
d. 910/9 miles
4. Ten less than four times a certain number is 14.
Determine the number.
a. 5
b. 7
c. 4
d. 6
5. The roots of a quadratic equation are 1/3 and
1/4. What is the equation?
a. 12x2 + 7x + 1=0
b. 12x2 - 7x - 1=0
c. 12x2 - 7x + 1=0
d. 12x2 + 7x - 1=0
6. The geometric mean of 4 and 64:
a. 30
b. 34
c. 24
d. 16
7. A certain company manufactures two products,
X and Y, and each of these products must be
processed on two different machines. Product X
requires 1 minute of work time per unit on
machine 1 and 4 minutes of work time on machine
2. Product Y requires two minutes of work time per
unit on machine 1 and 3 minutes of work time per
unit on machine 2. Each day, 100 minutes are
available on machine 1 and 200 minutes are
available on machine 2. To satisfy certain
customers, the company must produce at least 6
units per day of product X and at least 12 units of
product Y. If the profit of each unit of product X is
P50 and the profit of each unit of product Y is P60,
how many of each product should be produced in
order to maximize the company's profit?
a. X = 20 units, Y = 40 units
b. X = 30 units, Y = 40 units
c. X = 20 units, Y = 50 units
d. X = 40 units, Y = 60 units
8. If 4y3 + 18y2 + 8y - 4 is divided by 2y + 3, the
remainder is:
a. 10
b. 12
c. 11
d. 9
9. The square of a number increased by 16 is the
same as 10 times the number. Find the number.
a. 8, 2
b. 6, 2
c. 4, 2
d. 2, 2
10. The seating section in a coliseum has 30 seats
in the first row, 32 in the second row, 34 seats in
the third row and so on, until the tenth row is
reached, after which there are ten rows each
containing 50 seats. Find the total number of seats
in the section.
a. 1290
b. 1080
c. 890
d. 980
11. If the roots of an equation is zero, then they are
classified as
a. hypergolic solutions
b. trivial solutions
c. conditional solutions
d. extraneous solutions
12. An airplane went 360 miles in 2 hours with the
wind and, flying back the same route, it took 3 3/5
hours against the wind. What was its speed in still
air?
a. 120 mph
b. 150 mph
c. 140 mph
d. 130 mph
13. Find the fourth proportion to 3, 5 and 21.
a. 27
b. 65
c. 56
d. 35
14. Two jet planes travelling towards each other
take off at the same time from two airports located
3000 miles apart. If they passed each other after
two hours, determine the speed of each plane if
one plane is flying at a speed 100 mph faster than
the other.
a. 700 and 800 mph
b. 600 and 700 mph
c. 700 and 900 mph
d. 800 and 500 mph
15. Round off 0.003086 to three significant figures.
a. 0.0031
b. 0.00308
c. 0.003
d. 0.00309
16. It is sequence of numbers that successive terms
differ by a constant.
a. geometric progression
b. arithmetic progression
c. harmonic progression
d. finite progression
17. At 2:00 pm, an airplane takes off at 340 mph on
an aircraft carrier. The aircraft carrier moves due
south at 25 kph in the same direction as the plane.
At 4:05 pm, the communication between the plane
and aircraft carrier was lost. Determine the
communication range in miles between the plane
and the carrier.
a. 785 miles
b. 557 miles
c. 412 miles
d. 656 miles
18. A manufacturing firm maintains one product
assembly line to produce signal generators. Weekly
demand for the generators is 25 units. The line
operates for 7 hours per day, 5 days per week.
What is the maximum production time per unit in
hours required for the line to meet the demand?
a. 3 hours
b. 1 hour
c. 2.25 hours
d. 0.75 hour
19. Ana is 5 years older than Beth. In5 years, the
product of their age is 1.5 times the product of
their product ages. How old is Beth now?
a. 20
b. 25
c. 18
d. 27
20. A chemist of a distillery experimented on two
alcohol solutions of different strengths, 30%
alcohol and 60% alcohol, respectively. How many
cubic meters of each strength must be used in
order to produce a mixture of 50 cubic meters that
contain 40% alcohol?
a. 20, 30 m3
b. 33 1/3, 16 2/3 m3
c. 21 1/3, 28 2/3 m3
d. 10, 40 m3
21. Subtracting 2.6 x 103 from8.26 x 104 is:
a. 8.0 x 104
b. 10.86 x 104
c. 8.0 x 103
d. 10.86 x 103
22. The time requires by an evaluator 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 motor. If it takes 30
seconds for 10 hp motor to lift 100 lbs through 50
feet, what size of motor is required to lift 800 lbs in
40 seconds through a distance of 40 feet?
a. 56 hp
b. 50 hp
c. 58 hp
d. 48 hp
23. Find the 30th term of the arithmetic
progression 4, 7, 10, . . .
a. 94
b. 941
c. 81
d. 104
24. Convergent series is a sequence of decreasing
numbers or when the succeeding term is _______
than the preceding term.
a. equal
b. slightly more
c. greater
d. lesser
25. In the equation x2 + x = 0, one root is x equal
to:
a. 1
b. ¼
c. 5
d. none of these.
26. How many liters of water must be added to 35
liters of 89% hydrochloric acid solution to reduce
its strength to 75%?
a. 4.83 liters
b. 6.53 liters
c. 7.33 liters
d. 5.34 liters
27. Round off 34.2814 to four significant figures.
a. 34.8214
b. 34
c. 34.28
d. 34.281
28. Solve algebraiclly: 11y2 - 3x2 = 41 4x2 + 7y2 =
32.
a. (-2, 2) and (2, -2)
b. (± 1, ± 2)
c. (± 1, ± 4)
d. (2, 3)and ( -2, -3)
29. Determine the sum of the progression if there
are 7 arithmetic means between 3 and 35.
a. 98
b. 304
c. 214
d. 171
30. Crew No. 1 can finish installation of an antenna
tower in 200 man-hour while Crew No. 2 can finish
the same job in 300 man-hour. How long will it take
both crews to finish the same job, working
together?
a. 120 man-hour
b. 140 man-hour
c. 100 man-hour
d. 160 man-hour
31. In how many minutes after 3:00 P.M will the
minute hand of a clock coincide with the hour
hand?
a. 15.455
b. 17.273
c. 16.364
d. 18.182
32. In a class of 40 students, 27 students like
Calculus and 25 like Geometry. How many students
liked both Calculus and Geometry?
a. 12
b. 13
c. 11
d. 10
33. The electric power which a transmission line
can transmit is proportional to the product of its
design voltage and current capacity, and inversely
to the transmission distance. A 115 - kilovolt line
rated at 100 amperes can transmit 150 megawatts
over 150 km. How much power, in megawatts can
a 230 kilovolt line rated at 150 amperes transmit
over 100 km?
a. 595
b. 675
c. 485
d. 785
34. The electrical resistance of a wire varies as its
length and inversely as the square of its diameter.
If a 100 m long and 1.25 mm in diameter has a
resistance of 30 ohms, find the length of the wire
of the same material whose resistance and
diameter are 25 ohms and 0.74 mm respectively.
a. 25 m
b. 35 m
c. 30 m
d. 40 m
35. What time after 3 o'clock will the hands of the
clock be together for the first time?
a. 3:02.30
b. 3:17.37
c. 3:16.36
d. 3:14.32
36. A pump can pump out water from a tank in 11
hours. Another pump can pump out water from the
same tank in 20 hours. How long will it take both
pumps to pump out water in the tank?
a. 6 hours
b. 6 1/2 hours
c. 7 1/2 hours
d. 7 hours
37. If the sum is 220 and the first term is 10, find
the common difference if the last term is 30.
a. 3
b. 4
c. 5
d. 2
38. Equal volumes of two different liquids
evaporated at different but constant rates. If the
first is totally evaporated in 6 weeks and the
second in 5 weeks, when will the second be onehalf the volume of the first?
a. 3.5 weeks
b. 3 weeks
c. 4 weeks
d. 4 2/7 weeks
39. MCMXCIV is a Roman numeral equivalent to:
a. 1994
b. 2174
c. 3974
d. 2974
40. Find the 100th term of the sequence 1.01, 1.00,
0.99, . .
a. 0.01
b. 0.02
c. 0.03
d. 0.04
41. At what time after 12:00 noon will the hour
hand and minute hand of the clock first form an
angle of 120o?
a. 12:21.818
b. 12:22.818
c. 12:18.818
d. 12:24.818
42. Solve the simultaneous equations: 3x - y = 6 9x y = 12.
a. ( -1, 3 )
b. ( 1, -3 )
c. ( 1, 3 )
d. ( -1, -3 )
43. A merchant has three items on sale: namely, a
radio for P50, a clock fo P30, and a flashlight for P1.
At the end of the day, she has sold a total of 100 of
the three items and has taken exacly P1000 on the
total sales. How many radios did he sale?
a. 4
b. 80
c. 20
d. 16
44. What is the sum of the first 10 terms of the
geometric progression 2, 4, 8, 16, . . . ?
a. 1696
b. 2046
c. 1024
d. 1846
45. In a commercial survey involving 1000 persons
on brand preferences, 120 were found to prefer
brand x only, 200 persons prefer brand y only, 150
persons prefer brand z only, 370 prefer either
brand x or y but not z, 450 prefer brand y or z but
not x, and 370 prefer either brand z or x but not y,
and none prefer all the three brands at a time. How
many persons have no brand preference with any
of the three brands?
a. 200
b. 100
c. 280
d. 70
46. Which number has four significant figures?
a. 1.414
b. 0.0014
c. 0.141
d. 0.01414
47. A club of 40 executives, 33 likes to smoke
Marlboro and 20 likes to smoke Philip Morris. How
many like both?
a. 12
b. 13
c. 14
d. 11
48. The arithmetic mean of 80 numbers is 55. If
two numbers namely 250 and 850 are removed,
what is the arithmetic mean of the remaining
numbers?
a. 41.25
b. 42.31
c. 44.25
d. 40.21
49. There are 9 arithmetic means between 11 and
51. The sum of the progreesion is:
a. 374
b. 341
c. 320
d. 337
50. If a two digit number has X for its unit digit and
Y for its tenth digit, represent the number.
a. 10Y + X
b. X + Y
c. XY
d. 10Y + Y
51. In the series 1, 1, 1/2, 1/6, 1/24, . . . , determine
the 6th term.
a. 1/60
b. 1/120
c. 1/150
d. 1/90
52. Round off 149.691 to the nearest integer.
a. 149
b. 149.7
c. 149.69
d. 150
53. The sum of two numbers is 21, and one number
twice the other. Find the numbers.
a. 9 & 12
b. 7 & 14
c. 8 & 13
d. 65 & 70
54. The probability for the ECE board examinees
from a certain school to pass the Mathematics
subject is 3/7 and that for the Communication
subject is 5/7. If none of the examinees failed in
both subjects, how many examinees from the
school took the examination?
a. 30
b. 27
c. 29
d. 28
55. Solve for x that satisfies the equation 6x2 - 7x 5 = 0.
a. 3/5 or ¾
b. 3/2 or 3/8
c. 5/3 or -1/2
d. 7/5 or -7/15
56. Three transformers are rated 5 KVA, 10 KVA
and 25 KVA, respectively. The total cost of the
three transformers is P15, 000.00. If the cost of
each transformer is proportional to its KVA rating
multiplied by the factor 1, 0.8 and 0.6 respectively,
find the cost of the 10 KVA transformer.
a. P4,286
b. P4,075
c. P4,101
d. P4,393
57. Solve the simultaneous equations: 2x2 - 3y2 = 6
3x2 + 2y2 = 35.
a. x-3 or 3; y2 or -1
b. x3 or -3; y2 or -2
c. x3 or -3; y-2 or 1
d. x3 or -3; y-2 or 3
58. The sum of the progression 5, 8, 11, 14, . . . Is
1025. How many terms are there?
a. 25
b. 24
c. 28
d. 29
59. If x varies directly as y and inversely as z, and x
= 14 when y = 7 and z = 2, find the value of x when
y = 16 and z = 4.
a. 4
b. 8
c. 16
d. 14
60. The arithmetic means of 6 numbers is 17. If two
numbers are added to the progression, the new set
of the numbers will have an arithmetic mean of 19.
What are the two numbers if their difference is 4?
a. 18, 22
b. 23, 27
c. 10, 14
d. 31, 35
61. The sum of Kim's and Kevin's ages is 18. In 3
years, Kim will be twice as old as Kevin. What are
their ages now?
a. 5, 13
b. 7, 11
c. 6, 12
d. 4, 14
62. The intensity of sound varies directly as the
strength of the source and inversely as the square
of the distance from the source. Write the
equation to the describe relation.
a. I = 1/d2 + k
b. I=k/d2
c. I = kd2
d. I = d2/k
63. Determine the sum of the infinite series 1/3 +
1/9 + 1/27 +. . .
a. 1
b. ¾
c. ½
d. 2/3
64. For a particular experiment, you need 5 liters of
10% solution. You find 7% and 12% solutions on
the shelf. How much of the 7% solution you mix
with the appropriate amount of the 12% solution
to get 5 liters of 10% solution?
a. 2.5
b. 2
c. 1.5
d. 3
65. Find the sum of the roots of 5x2 - 10x + 2 = 0
a. -2
b. ½
c. -1/2
d. 2
66. Maria is 36 years old. Maria was twice as old as
Anna was when Maria was as old as Anna is now.
Jow old is Anna now?
a. 26
b. 31
c. 29
d. 24
67. Find the ratio of an infinite geometric
progression if the sum is 2 and the first term is 1/2.
a. 2/3
b. 1/6
c. ¾
d. ¼
68. A tank is fitted with two pipes. The first pipe
can fill the tank in 10 hours. But after it has been
open for 3 hours, the second pipe is opened and
the tank is filled up in 4 hours more. How long
would it take the second pipe alone to fill tha tank?
a. 12.67 hr
b. 10.55 hr
c. 14.89 hr
d. 13.33 hr
69. How many kg of cream containing 25% butter
fat should be added to 50 kg of milk containing one
percent butter fat to produce milk containing 2%
butter fat?
a. 4.17
b. 2.174
c. 5.221
d. 3.318
70. The electrical resistance offered by an electric
wire varies directly as the length and inversely as
the square of the diameter of the wire. Compare
the electrical resistance offered by two pieces of
wire of the same material, one being 100 m long
and 8 mm in diameter, and the other 50 m long
and 3 mm in diameter.
a. R1 = 0.28 R2
b. R1 = 0.84 R2
c. R1 = 0.57 R2
d. R1 = 0.95 R2
71. A stack of bricks has 61 bricks in the bottom
layer, 58 bricks in the second layer, 55 bricks in the
third layer, and so on until there are 10 bricks in
the last layer. How many bricks are there all
together?
a. 458
b. 639
c. 724
d. 538
72. A 100 g of water are mixed with 150 g of
alcohol (p = 790 kg/cu.m.). What is the specific
volume of the resulting mixtures? Assuming that
the two fluids mix completely.
a. 0.63 cu cm/g
b. 0.88 cu. cm/g
c. 0.82 cu cm/g
d. 1.20 cu cm/g
73. One number is 5 less than another. If the sum is
135, what are the numbers?
a. 65, 70
b. 60, 65
c. 75, 80
d. 70, 75
74. The denominator of a certain fraction is three
more than twice the numerator. If 7 is added to
both terms of the fraction, the resulting fraction is
3/5. Find the original fraction.
a. 8/5
b. 13/5
c. 5/13
d. 3/5
75. An inexperienced statistical clerk submitted the
following statistics to his manager on the average
rate of production of transistorized radios in an
assenbly line: "1.5 workers produced 3 radios in 2
hour." How many workers are employed in the
assembly line working 40 hours per week if weekly
production is 480 radios?
a. 12
b. 10
c. 13
d. 14
76. Find the mean proportion of 4 and 36.
a. 12
b. 8
c. 16
d. 9
77. An automobile is travelling at a velocity of 10
mph. If the automobile mileage meter already
reads 20 miles, find the mileage meter reading
after 3 hours.
a. 60 miles
b. 30 miles
c. 50 miles
d. 40 miles
78. Find the sum of 1, -1/5, 1/25, . . .
a. 6/7
b. 7/8
c. 5/6
d. 8/9
79. A man is 41 years old and his son is 9. In how
many years will the father be three times as old as
his son?
a. 7
b. 8
c. 6
d. 5
80. A tank is fitted with an intake pipe that will fill it
in 4 hours, and an outlet pipe that will empty it in 9
hours. If both pipes are left open, how long will it
take to fill the empty tank?
a. 7.2 hr
b. 6.8 hr
c. 6.2 hr
d. 7.4 hr
81. Find the 1987th digit in the decimal equivalent
to 1785/9999 starting from the decimal point.
a. 1
b. 5
c. 7
d. 8
82. A mechanical engineer who was awarded a
P450,000.00 contract to install the machineries of
an oil mill failed to finish the work on time. As
provided for in the contract, he has to pay a daily
penalty equivalent to one-fourth of one percent of
the contract price for the first ten days of the
delay, one-half percent per day for the next ten
days and one percent per day for every day
thereafter. If the total penalty paid was
P60,750.00, how many days was the completion of
the contract delayed?
a. 30 days
b. 26 days
c. 24 days
d. 28 days
83. A man started driving his car at a certain time
froma certain place. On arrival at his destination at
the precise appointed time, he said, "If I had
averaged 6 miles per hour faster, I would have
been 5 minutes early. But if I had averaged 5 mph
slower, I would have been 6 minutes late." Find
how far he had driven.
a. 20 miles
b. 10 miles
c. 25 miles
d. 15 miles
84. Pedro started running at a speed of 10kph. Five
minutes later, Mario started running in the same
direction and catches up with Pedro in 20 minutes.
What is the speed of Mario?
a. 12.5 kph
b. 17.5 kph
c. 20.5 kph
d. 15.0 kph
85. The equation whose roots are the reciprocal of
the solutions of 2x2 - 3x - 5 = 0.
a. 3x2 - 5x - 2=0
b. 5x2 - 2x - 3=0
c. 5x2 + 3x - 2=0
d. 2x2 + 5x - 3=0
86. In certain Board Examination, 119 examinees
too the Shop Machinery subjected, 104 examinees
took thye Power Plant Machinery subject and 115
examinees took the Industrial Plant Machinery
subject. Seventy-eight (78) conditioned examinees
took only Shop Machinery and Power Machinery
subjects. Seventy-one (71) conditioned examinees
took only the POwer Plant Machinery and
Industrial Plant Machinery subjects. Eighty-five (85)
conditioned examinees took only Industrial Plant
Machinery and Shop Machinery subjects. Fifty-four
took all the three subjects. How many examinees
took the Certified Plant Mechanic board
examination?
a. 153
b. 165
c. 158
d. 176
87. If a train passes as many telegraph poles in one
minute as it goes miles per hour, how far apart are
the poles?
a. 78 ft.
b. 98 ft.
c. 68 ft.
d. 88 ft.
88. A man 38 years old has a son of ten years old.
In how many years will the father be three times as
old as his son?
a. 2
b. 3
c. 4
d. 5
89. In Algebra, the operation of root extraction is
called as _____.
a. revolution
b. resolution
c. involution
d. evolution
90. Pedro can paint a fence 50% faster than Juan
and 20% faster than Pilar and together they can
paint a given fence in 4 hours. How long will it take
Pedro to paint the same fence if he had to work
alone?
a. 15
b. 13
c. 10
d. 11
91. There are 9 arithmetic means between 11 and
51. The sum of the progression is:
a. 374
b. 341
c. 320
d. 337
92. The number 1.123123123. . . Is
a. surd
b. transcendental
c. rational
d. irrational
93. Which of the following numbers should be
changed to make all the numbers from an
arithmetic progression when properly arranged?
a. 27/14
b. 45/28
c. 20/14
d. 3/28
94. How many significant digits do 10.097 have?
a. 4
b. 5
c. 2
d. 3
95. Find the sum of the infinite geometric
progression 6, -2, 2/3, . . .
a. 9/2
b. 7/2
c. 3/2
d. 11/2
96. The time required for two examinees to solve
the same problem differ by two minutes. Together
they can solve 32 problems in one hour. How long
will it take for the slower problem solver to solve
the problem?
a. 3 minutes
b. 5 minutes
c. 2 minutes
d. 4 minutes
97. An equipment installation job in the completion
stage can be completed in 50 days of 8 hours day
work, with 50 men working. With the contract
expiring in 40 days, the mechanical engineer
contractor decided to add 15 men on the job,
overtime not being permitted. If the liquidated
damages is P5,000 per day of delay, and they are
paid P150 per day, will the engineer be able to
complete the job on time? Would he save money
with the addition of workers?
a. No, P20,500 losses
b. Yes, P44,750 savings
c. Yes, P24,500 savings
d. No, P15,750 losses
98. An airplane flying with the wind, took 2 hours
to travel 1000 km and 2.5 hours in flying back.
What was the wind velocity in kph?
a. 40
b. 70
c. 60
d. 50
99. If a = b, then b = a. This illustrates which axiom
in Algebra?
a. Transitive Axiom
b. Reflexive Axiom
c. Symmetric Axiom
d. Replacement Axiom
100. The ten's digit of a certain two digit number
exceeds the unit's digit by four and is one less than
twice the unit's digit. Find the number.
a. 59
b. 95
c. 65
d. 85
101. One pipe can fill a tank in 6 hours and another
pipe can fill the same in tank in 3 hours. A drain
pipe can empty the tank in 24 hours. With all three
pipes open, how lomg will it take to fill in the tank?
a. 2.18 hrs
b. 2.23 hrs
c. 2.81 hrs
d. 2.32 hrs
102. An equipment installation job in the
completion stage can be completed in 40 days of 8
hours day work with 40 men working. With the
contract expiring in 30 days, the mechanical
engineer contractor decided to add 10 men on the
job, overtime not being permitted. If the liquidated
damages is P2,000 per day of delay, and the men
are paid P80 per day, will the engineer be able to
complete the job on time?
a. No, there would be no savings
b. No, P16,000 would be lost
c. Yes, there would just be break even
d. Yes, P16,000 would be saved
103. It takes Butch twice as it takes Dan to do a
certain piece of work. Working together they can
do the work in 6 days. How long would it take Dan
to do it alone?
a. 12 days
b. 9 days
c. 10 days
d. 11 days
104. Robert is 15 years older than his brother Stan.
However, "y" years ago, Robert was twice as old as
Stan. If Stan is now "b" years old b.y, find the value
of (b-y).
a. 18
b. 17
c. 15
d. 16
105. Mike, Loui and Joy can mow the lawn in 4, 6
and 7 hours, respectively. What fraction of the yard
can they mow in 1 hour if they work together?
a. 47/84 hr
b. 84/47 hr
c. 34/60 hr
d. 45/84 hr
106. The volume of hemisphere varies directly as
the cube of its radius. The volume of a sphere with
2.54 cm radius is 20.75 cm3. What is the volume of
a sphere with 3.25 cm radius of the same kind?
a. 4056 cm3
b. 45.98 cm3
c. 43.47 cm3
d. 39.20 cm3
107. Add the following and express in meters: 3 m
+ 2 cm + 70 mm.
a. 3.14 m
b. 2.90 m
c. 3.12 m
d. 3.09 m
108. From the time 6:15 PM to the time 7:45 PM of
the same day, the minute hand of a standard clock
describe an arc of:
a. 90o
b. 60o
c. 540o
d. 180o
109. A clock has dial face 304.80 mm in radius. The
minute hand is 228.60 mm long while the hour
hand is 152.40 mm long. The plane of rotation of
the minute hand is 50.80 mm above the plane of
rotation of the hour hand. Find the distance
between the tips of the hands of the clock at 5:40
AM.
a. 228 mm
b. 239 mm
c. 243 mm
d. 233 mm
110. A certain manufactured part can be defective
because it has one or more out of the three
possible defects: insufficient tensile strength, a
burr, or a diameter outside of tolerance limit. In a
lot of 500 pieces: 19 have a tensile strength
defects, 17 have a burr, 11 have an unacceptable
diameter, 12 have tensile strength and burr
defects, 7 have tensile strength and diameter
defects, 5 have burr and diameter defects and 2
have all three defects. Determine: How many of
the pieces have no defects? How many pieces have
only burr defects? How many pieces have exactly 2
defects?
a. 475, 2, 18
b. 490, 4, 10
c. 465, 3, 7
d. 480, 4, 6
111. Mary is 24 years old. Mary is twice as old as
Ana waswhen Mary was as old as Ana is now. How
old is Ana?
a. 18
b. 16
c. 20
d. 19
112. The electrical resistance of wire made of a
certain material varies as its length and inversely as
the square of the diameter. If the wire 200 meters
long and 1.25 mm in diameter has a resistance of
60 ohms, find the length of the wire of the same
material, whose resistance and diameter are 5
ohms and 0.65 mm, respectively.
a. 3.96 m
b. 4.51 m
c. 4.28 m
d. 5.72 m
113. A man leaving his office on one afternoon
noticed the clock at past two o'clock. Between two
three hours, he returned to his office noticing the
hands of the clock interchanged. At what time did
he leave the office and the time that he returned to
the office?
a. 2:27.08, 5:11.19 P.M.
b. 2:26.01, 5:10.01 P.M
c. 2:26.01, 5:10.01 P.M.
d. 2:26.01, 5:12.17 P.M.
114. A medium unshaded lamp hangs 8 m directly
above the table. To what distance should it be
lowered to increase the illumination to 4.45 times
the former value? Illumination intensity varies
inversely to the square of the distance.
a. 4.75 m
b. 4.55 m
c. 3.79 m
d. 3.95 m
115. Roberto is 25 years younger than his father.
However, his father will be twice his age in 10
years. Find their ages now.
a. 15 and 40
b. 10 and 35
c. None of the choices
d. 20 and 45
116. A storage battery discharges at a rate which is
proportional to the charge. If the charge is reduced
by 50% of its original value at the end of 2 days,
how long will it take to reduce the charge to 25% of
its original charge?
a. 6
b. 4
c. 3
d. 5
117. Prior to the last IBP elections, a survey was
conducted in a certain barangay in Metro Manila to
find out which of three political parties they like
best. The results indicated that 320 like KBL, 250
like LABAN and 180 liked INDEPENDENTS. But of
these, 160 like both KBL and LABAN, 100 liked both
LABAN and INDEPENDENTS and 70 like both KBL
and INDEPENDENTS. Only 30 said they like all the
three parties and none admitted that they did not
like any party. How many voters are there in the
barangay?
a. 474
b. 525
c. 450
d. 540
118. A man left his home at past 3:00 o'clock P.M
as indicated in his wall clock. Between 2 and 3
hours after, he returned home and noticed the
hands of the lock interchanged. At what time the
man leave his home?
a. 3:24.73 P.M
b. 3:18.52 P.M
c. 3:31.47 P.M
d. 3:28.65 P.M
119. Given: f(x) = ( x+ 3) (x - 4) +4. When f(x) is
divided by (x - k), the remainder is k. Find k.
a. 2
b. 6
c. 4
d. 8
120. A & B working together can finish painting the
house in six days. A working alone, can finish it in
five days less than B. How long will it take each of
them to finish the work alone?
a. 15 days for A 20 days for B
b. 10 days for A 25 days for B
c. 15 days for A 20 days for B
d. 10 days for A 15 days for B
121. A statistical clerk submitted the following
reports: "The average rate of production of radios
is 1.5 units for every 1.5 hours of work by 1.5
workers." How many radios were produced in one
month by 30 men working 200 hours during the
month?
a. 4000
b. 3500
c. 4500
d. 5000
122. A piece of paper is 0.05 in thick. Each time the
paper is folded into half, the thickness is doubled. If
the paper was folded 12 times, how thick in feet
the folded paper will be?
a. 15.2
b. 16.25
c. 17.06
d. 18.5
123. A job could be done by eleven workers in 15
days. Five workers started the job. They were
reinforced with four more workers at the beginning
of the 6th day. Find the total number of days it
took them to finish the job.
a. 22.36 days
b. 20.56 days
c. 23.22 days
d. 21.42 days
124. Six times the middle digit of a three-digit
number is the sum of the other two. If the number
is divided by the sum of its digits, the answer is 51
and the remainder is 11. If the digits are reversed
the number becomes smaller by 198, find the
number.
a. 825
b. 775
c. 725
d. 875
125. Given that "w" varies directly as the product
of x and y and inversely as the square of z and that
w = 4 when x = 2, y = 6 and z = 3. Find tha value of
"w" when x = 1, y = 4 and z = 2.
a. 5
b. 4
c. 3
d. 2
126. A man driving his car at a certain speed from
his house will reach his office in 6 hours. If he
increased his speed 15 mph, he would reach his
office 1 hour earlier. Find the distance from his
office to his house.
a. 350 miles
b. 450 miles
c. 520 miles
d. 250 miles
127. Determine x, so that x, 2x + 7, 10x - 7 will be a
geometric progression.
a. 7, -15/6
b. 7, -7/5
c. 7, -5/6
d. 7, -7/6
128. Solve for the values of x and y in 4x + 2y = 5
and 13x - 3y = 2.
a. (1, 3)
b. (3/2, 1/2)
c. (1, 2)
d. ( 1/2, 3/2 )
129. Determine the k so that the equation 4x2 + kx
+ 1 = 0 will have just one real root.
a. 5
b. 6
c. 4
d. 3
130. An airplane travels from points A and B with
the distance of 1500 km and a wind along its flight
line. If it takes the airplane 2 hours from A to B with
the tailwind and 2.5 hours from B to A with the
headwind, what is the velocity?
a. 700 kph
b. 675 kph
c. 450 kph
d. 750 kph
131. How many numbers between 10 and 200 are
exactly divisible by 7? Find their sum.
a. 2835
b. 2840
c. 283
d. 2830
e. 27 numbers; sum
f. 28 numbers; sum
g. 26 numbers; sum
h. 26 numbers; sum
132. A gasoline tank of a car contains 50 liters of
gasoline and alcohol, the alcohol comprising 25%.
How much of the mixture must be drawn off and
replaced by alcohol so that the tank will contain a
mixture of which 50% is alcohol?
a. 10.67 liters
b. 20.33 liters
c. 16.67 liters
d. 16.33 liters
133. In a pile of logs, each layer contains one more
log than the layer above and the top contains just
one log. If there are 105 logs in the pile, how many
layers are there?
a. 16
b. 14
c. 10
d. 12
134. Two thousand (2000) kg of steel containing 8%
nickel is to be made by mixing a steel containing
14% nickel with anothercontaining 6% nickel. How
much of each is needed?
a. 800 kg, 1200 kg
b. 500 kg, 1500 kg
c. 600 kg, 1500 kg
d. 400 kg, 1600 kg
135. A boat man rows to a place 4.8 miles with the
stream and black in 14 hours, but that he can row
14 miles with the stream in the same time as 3
miles against the stream. Find the rate of the
stream.
a. 1 mile per hour
b. 0.6 mile per hour
c. 0.8 mile per hour
d. 1.5 mile per hour
136. Gravity causes a body to fall 16.1 ft in the first
second, 48.3 ft in the 2nd second, 80.5 ft in the 3rd
second. How far did the body fall during the 10th
second.
a. 250.1 ft
b. 305.9 ft
c. 529.45 ft
d. 417.3 ft
137. Solve for x : 10x2 + 10 x2 + 1 = 0.
a. -0.331, 0.788
b. -0.311, -0.887
c. -0.113, -0.788
d. -0.113, -0.887
138. An airplane travels from points A and B with a
distance of 1500 km and a wind along its flight line.
If it takes the airplane 2 hours from A and B with
the tailwind and 2.5 hours from B to A with the
headwind, What is the velocity?
a. 700 kph
b. 675 kph
c. 750 kph
d. 450 kph
139. A jogger starts a course at a steady rate of 8
kph. Five minutes later, a second jogger starts the
same course at 10 kph. How long will it take the
second jogger to catch the first?
a. 22 min
b. 18 min
c. 21 min
d. 20 min
140. A rubber ball is made to fall from a height of
50 ft. and is observed to rebound 2/3 of the
distance it falls. How far will the ball travel before
coming to rest if the ball continues to fall in this
manner?
a. 300
b. 200
c. 350
d. 250
141. The resistance of the wire varies directly with
its length and inversely with its area. If a certain
piece of wire 10 m long and 0.10 cm in diameter
has a resistance of 100 ohms, what will its
resistance be if it is uniformly stretched so that its
length becomes 12 m?
a. 144
b. 80
c. 120
d. 90
142. Ten liters of 25% salt solution and 25 liters of
35% salt solution are poured into a drum originally
containing 30 liters of 10% salt solution. What is
the percent concentration of salt in the mixture?
a. 0.1955
b. 0.2572
c. 0.2215
d. 0.2705
143. A & B can do the job in 42 days, B & C for the
same job in 31 days, C & A also for the same job in
20 days. If A & C work together, how many days
can they do the same job?
a. 19
b. 17
c. 21
d. 15
144. A pipe can fill a tank in 14 hours. A second
pipe can fill the tank in 16 hours. If both pipes are
left open, determine the time required to fill the
tank?
a. 7.92 hr
b. 8.47 hr
c. 7.47 hr
d. 6.53 hr
145. A man rows downstream at the rate of 5mph
and upstream at the rate of 2mph. How far
downstream should he go if he is to return in 7/4
hours after leaving?
a. 2.5 miles
b. 3.3 miles
c. 2.7 mlies
d. 3.1 miles
146. Solve for the value of x. 2x - y + z = 6 x - 3y - 2z
= 13 2x - 3y - 3z = 16
a. 3
b. 1
c. 2
d. 4
147. Find the value of w in the following equations:
3x - 2y + w = 11 x + 5y - 2w = -9 2x + y - 3w = -6.
a. 4
b. 2
c. 3
d. -2
148. A boat travels downstream 2/3 of the time as
it goes going upstream. If the velocity of the river's
current is 8 kph, determine the velocity of the boat
in still water.
a. 70 kph
b. 60 kph
c. 30 kph
d. 40 kph
149. A survey of 100 persons revealed that 72 of
them had eaten at restaurant P and that 52 of
them had eaten at restaurant Q. Which of the
following could not be the number of persons in
the surveyed group who had eaten at both P and
Q?
a. 23
b. 22
c. 24
d. 25
Basic Engineering Correlation (Trigo Reviewer)
1. What will be the length of the two other sides of
a right triangle if the opposite side of a 60 degrees
angle is 4V cm _____"
a. 8cm, 4 cm
b. 4 cm, 3 cm
c. 2 cm, 1cm
d. 4cm, 5 cm
2. The expression sin16° sin14° + cos16° cos14° is
equivalent to
a. Cos 8°
b. Sin 30°
c. Sin 8°
d. Cos 2°
3. If tan a = 1/2 — and tan = -3/5, then the value of
tan(a +,8) is
a. 5/9
b. 7/9
c. 9/7
d. 11/7
4. What is the value of sin [3 if cos p = 3/5?
a. sec 0 = 0.8
b. sine=0.25
c. cot 0=0.5
d. tan@=2.5
5. A central angle of 45 degrees subtends an arc of
12 cm. What is the radius of the circle?
a. 12.58 cm
b. 15.82 cm
c. 12.82 cm
d. 15.28 cm
6. The exact radian measure of 180o is
a. π
.
.
d.
7. Solve for x by logarithm, log x2 - log (2x/5 = 7.58.
a. 189675888
b. 136783520
c. 15207576
d. 13678352
. If a ta x + a ta
______.
a. ½
b. 1/5
c. 1/3
d. ¼
/
=
/ , the alue of x is
9. A road is tangent to a circular lake. Along the
road and 12 miles from the point of tangency,
another road opens towards the lake. From the
intersection of the two roads to the periphery of
the lake, the length of the new road is 11 miles. If
the new road will be prolonged across the lake,
find the length of the bridge to be constructed.
a. 2.09 miles
b. 6.65 miles
c. 1.20 miles
d. 8.89 miles
10. A strip of 640 sq. m is sold from a tirangular
field whose sides are 96, 72 and 80 meters. The
strip is of uniform width "h" and has one of its sides
parallel to the longest side of the field. Find the
width of the strip.
a. 7.059 m
b. 5.89 m
c. 5.78 m
d. 6.679 m
11. The expression sin25x sin5x is equivalent to
a. 2sin10xcos5x
b. Sin20x
c. 2sin10xsin5x
d. 2sin15xsin10x
12. The area of the sector determined by an angle
of 60° in a circle of radius 5 cm is
a. 49.09 cm2
b. 2812.5 cm2
c. 312.5 cm2
d. 13.09 cm2
13. Three times the sine of a certain angle is twice
of the square of the cosine of the same angle. Find
the angle.
a. 60o
b. 45o
c. 10o
d. 30o
14. If sin A = 2.5x and cos A = 5.5x, find the value of
A in degrees.
a. 24.44
b. 32.47
c. 52.37
d. 42.47
15. One leg of a right triangle is 20 cm and the
hypotenuse is 10 cm longer than the other leg. Find
the length of the hypotenuse.
a. 10 cm
b. 15 cm
c. 20 cm
d. 25 cm
16. Which of the following is an even function?
a. f(x)=3sin x
b. f (x)=4 tan x
c. f (x)=5 COSx
d. f (x)=4 cot x
17. The sides of a triangle lot are 130m, 180m, and
190m. This lot is to be divided by a line bisecting
the longest side and drawn from the opposite
vertex. Find the length of the line (1) and the area
of each lot (A).
a. 1125 m, A6520 sq.m
b. 1128 m, A2879 sq.m
c. 1110 m, A1000 sq. m
d. 1125 m, A5620 sq. m
18. If A is in the III quadrant and cos A = -15/17,
find the value of cos (1/2)A.
a. -(8/17)1/2
b. -(2/17)1/2
c. -(1/17)1/2
d. -(5/17)1/2
19. Ship "A" started sailing N 40o 32' E at the rate of
3 mph. After 2 hours, ship "B" started from the
same port soing S 45o 18' E at the rate of 4 mph.
After how many hours wil the second ship be
exactly south of ship "A"?
a. 4.37 hours
b. 2.37 hours
c. 5.37 hours
d. 3.37 hours
20. Two speedboats simultaneously sailed out from
port A on a 10 km radius circle lake towards point B
directly opposite of port A. The first boat took the
shortest route and reached the destination in 1
hour. The boat has to pass by port C before
proceeding to port B. At what speed will it run in
order to arrive at port B at the same time with the
first boat?
a. 78.89 kph
b. 67.89 kph
c. 34.57 kph
d. 27.32 kph
21. The reference angle of 0 = 210° is
a. 15°
b. 45°
c. 60°
d. 30°
22. If A is in the III quadrant and cos A = -15/17,
find the value of cos (1/2)A.
a. -(2/17)1/2
b. -(8/17)1/2
c. -(5/17)1/2
d. -(1/17)1/2
23. The angle that is supplementary to 45o 15' 25"
is
a. 45.257o
b. 44.743o
c. 134.74o
d. 44o 45'
24. If 77o + 0.40x = arc tan (cot 0.25x), find x.
a. 30o
b. 10o
c. 20o
d. 40o
25. If A + B + C = 180o and tan A + tan B + tan C =
5.67, find the value of tan A tan B tan C.
a. 1.89
b. 5.67
c. 1.78
d. 6.75
26. The angle of elevation of the top point D of a
tower A is 23o30'. From another point B the angle
of elevation of the top of the tower is 55o30'. The
points A and B are 217.45 m. apart and on the
same horizontal plane as the foot (point C) of the
tower. The horizontal angle subtended by A and B
at the foot of the tower is 90o. Find the height of
the tower CD.
a. 69.59 m
b. 90.59 m
c. 59.90 m
d. 50.90 m
28. The simplified form of sin4 0 —cos4 0 is
a. 0
b. 1
c. 2sin2 0-1
d. 1+2cos2
29. The simplified form of cos(A— B)—cos(A + B) is
a. Cos2B
b. math012-1tc. Cos2A
d. 2sinAsinB
30. If cot 2A cot 68o = 1, then tan A is equal to
_______.
a. 0.194
b. 0.491
c. 0.491
d. 0.419
. The exa t deg ee
a. 45o
b. 90o
easu e of .
is
c. 180o
d. 145o
32. Solve for G if csc (11G - 16o) = sec (5G + 26o).
a. 5 degrees
b. 6 degrees
c. 4 degrees
d. 7 degrees
33. A ladder 5 m long leans against the wall of an
apartment house forming an angle of 50 degrees,
32 minutes with the ground. How high od the wall
does it reach?
a. 3.12 m
b. 2.00 m
c. 12.66 m
d. 3.86 m
34. A regular dodecagon is inscribed in a circle of
radius 24. Find the perimeter of the dodecagon.
a. 151.24
b. 153.25
c. 143.63
d. 149.08
35. The measure of 2.25 revolutions
counterclockwise is
a. 810 degrees
b. 835 degrees
c. 810 degrees
d. 805 degrees
36. Determine the amplitude and the phase shift
for the function f(t)= 2 sin (3x + 4)
a. 2 and 4/3
b. 2 and -4/3
c. 2 and ¾
d. 2 and -3/4
37. Solve angle A of an oblique triangle with
vertices ABC, if a = 25, b = 16 and C = 94 degrees
and 6 minutes.
a. 49 degrees and 37 minutes
b. 55 degrees and 32 minutes
c. 53 degrees and 40 minutes
d. 54 degrees and 30 minutes
. The te i al side of the a gle θ =
standard position is in quadrant.
o in
a. III
b. IV
c. I
d. II
39. Determine the period of the curve y = sin(1/2)x
a. 540o
b. 360o
c. 900o
d. 720o
40. Solve for x in the given equation: arc tan(x +1)
+arc tan (x - 1) = arc tan (12).
a. 1.5
b. 1.2
c. 1.34
d. 1.25
41. Two towers AB and CD are of equal height. At a
point between them in the line AC joining their
bases, the angle of elevation of the nearer tower
was observed to be 60o. Then at 24 m from the
same point in a direction perpendicular to AC, the
angle of elevation of the top of the towers are 45o
for the nearer tower and 30o for the other. Find the
height of the towers (h) and their distance apart
(x).
a. h=29.38 m, x=71.83 m
b. h=39.38m, x=61.83 m
c. h=49.83, x=61.83 m
d. h=29.38 m, x=61.83 m
42. If 3x = 9y and 27y = 81z, find x/z.
a. 4/3
b. 8/3
c. 3/8
d. 3/5
43. Which of the following is a co terminal angle
o?
of θ =
a. –95o
b. 615o
c. 585o
d. 65o
44. The terminal side of 0 if cote > 0 and sec() >0 is
in quadrant
a. III
b. I
c. II
d. IV
45. Given: x = (cos B tan B - sin B) / cos B. Solve for
x if B = D45 degrees.
a. 0.5
b. 0.577
c. 0.866
d. 0
46. The perimeter of an isosceles right triangle is
6.6824. Its area is
a. ½
b. 4
c. 2
d. 1
47. Simplify: 4 cos y sin y (1 - 2 sin 2y)
a. sec 4y
b. tan 4y
c. cos 4y
d. sin 4y
48. The angle of elevation of the top of the tower A
from the foot of tower B is twice the angle of
elevation of the top of tower B from the foot of
tower A. At a point midway between the two
towers, the angles of elevations of the top of the
towers are complimetary. If the two towers are 120
m apart, what are the heights of the towers?
a. 30 m and 50 m
b. 30 m and 40 m
c. 25 m and 35 m
d. 40 m and 90 m
49. Find the value of x in the equation csc x + cot x
= 3.
a. /
. /
. /
d. π /
50. Find the other parts of the triangle given a =
48°,1C = 57 degrees b = 47 units.
a. 75 °, 36.16 units
b. 75 °, 35.16 units
c. 75 °, 33.16 units
d. 75 °, 34.16 units
51. A clock has a dial face 12 inches in radius. The
minute hand is 9 inches long while the hour hand is
6 inches long. The plane of rotation of the minute
hand is 2 inches above the plane of rotation of the
hour hand. Find the distance between the tips of
the hands of the clock at 5:40 a.m.
a. 3.89 in
b. 8.67 in
c. 7.78 in
d. 9.17 in
52. The expression 2cos6x cos2x is equivalent to
a. cos10x + cos6x
b. cos5x + cos3x
c. Cos8x + cos4x
d. cos32x
53. The solution set of the equation(tan x) 2 — 1 =
0 on the interval [0°, 360°) is ~{30°,90°,150°1}
a. {45°,135°,225°,315°1
b. {0°,30°,330°
c. 160901
54. If the terminal side of angle 13 contains the
point (-5, -7) then 13 is equal to
a. — 35.54°
b. 35.54°
c. 234.46°
d. 54.47°
55. Simplify the expression: (sin B + cos B tan B) /
cos B.
a. tan B cos B
b. tan B + cos B
c. 2 sin B cos B
d. 2 tan B
56. A 40 m high tower stands vertically on a hillside
(sloping ground) which makes an angle of 18o with
the horizontal. A tree also stands vertically up the
hill from the tower. An observer on top of the
tower finds the angle of depression of the top of
the tree to be 26o and the bottom of the tree to be
38o. Find the height of the tree.
a. 59.89 m
b. 89.89 m
c. 35.67 m
d. 10.62 m
57. Triangle ABC is a right triangle with the right
angle at C. CD is perpendicular to AB. BC = 4, and
CD = 1. Find the area of the triangle ABC.
a. 2.7
b. 2.07
c. 2.11
d. 2.43
58. If sin A = 4/5, A is in quadrant II, sin B = 7/25, B
is in quadrant I. Find sin (A + B).
a. 2/5
b. ¾
c. 3/5
d. 4/5
59. A and B are summit of two mountains rise from
a horizontal plain, B being 1200 m above the plain.
Find the height of A, it being given that its angle of
elevation as seen from a point C in the plain (in the
same vertical plane with A and B) is 50o, while the
angle of depression of C viewed from B is 28o58'
and the angle subtended at B by AC is 50o.
a. 2890.89 m
b. 1002.33 m
c. 1309.90 m
d. 3002.33 m
60. 174 degrees is equivalent to _____ mils.
a. 2044
b. 2845
c. 3421
d. 3094
61. Which of the following is arccos(n)?
a. UNDEFINED
b. n
c. 0
d. 1
62. A cyclic quadrilateral has the sides AB = 8 cm;
and CD = 12 cm. The fourth side DA forms the
diameter of the circle. Find the area of the circle.
a. 467.89 sq. cm
b. 87.89 sq. cm
c. 657.89 sq. cm
d. 316.68 sq. cm
63. If tan 25 = m, find the value of tan (tan 155 - tan
115) / (1 + tan 115 x tan 155). ( Note: all angles are
in degrees).
a. (m2 + 1) / 2m
b. m2 + 1
c. (1 - m2) / 2m
d. (m2 - 1) / 2m
Basic Engineering Correlation (Solid Mensuration
Reviewer)
1. It is a quadrilateral two and only two of whose
sides are parallel
a. rectangle
b. rhombus
c. trapezoid
d. parallelepiped
2. Five pointed figure in a
a. rhombus
b. star
c. trapezoid
d. rectangle
3. The volume of any cone is equal to
a. Bh
b. 1/2 Bh
c. 1/3 Bh
d. 4/3Bh
4. It is a polyhedron whose six faces are all squares.
a. cube
b. square
c. frustum
d. parallelepiped
5. What is the length of the diagonal of a cube of
edge 7 cm
a. 12.12 cm
b. 18.52 cm
c. 9.9cm
d. 5.28cm
6. A section of a sphere when a plane passing
through the center and diameter. Creating the
largest section called
a. medium circle
b. great circle
c. big circle
d. short circle
7. Each of the faces of a regular hexahedron is a
a. square
b. hexagon
c. triangle
d. rectangle
8. A cone and a cylinder have the same heightand
the same volume. Find the ratio of the radius
of the cone to the radius of the cylinder.
a. 0.866
b. 1.732
c. 0.577
d. 1.414
9. The volume of a water in a spherical tank having
a diameter of 4 m is 5.236 m3. Determine the
depth of the water in the tank.
a. 1.0 m
b. 1.4 m
c. 1.2 m
d. 1.8 m
10. It is desired that the volume of the sphere be
tripled. By how many times will the raduis be
increased?
a. 31/3
b. 31/2
c. 33
d. 21/2
11. In Heron's formula, the symbol 's' stands for
a. (a+b+c)/3
b. side
c. slant height
d. (a+b+c)/2
12. Find the measure of the diagonal of a
rectangular parallelepiped of dimensions 2 x 3 x 8.
a. 48
b. 77
c. 0.07
d. 48
13. In a plane figure, diamond is also known as
a. square
b. rhombus
c. trapezoid
d. parallelogram
c. 21/2
d. 31/3
14. Find the weight of a snowball 1 ft. in diameter if
the wet compact snow of which the ball is made
weighs 25 lbs/ cu. ft.
a. 1.047 lb
b. 2.36 lb
c. 13.09 lb
d. 4.19 lb
21. The bounding cylindrical surface of a cylinder is
called
a. base edge
b. lateral surface
c. lateral edge
d. edge
15. The area for a trapezoid is represented by
a. (dic12)/2
b. (a+b)h/2
c. bh
d. (a+b÷c)/3
16. An Egyptians pyramid of the Giza has a square
base of edge 6miles. If its altitude is 15miles.,
determine the
a. 540 cu.mi
b. 90 cu.mi
c. 180 cu.mi
d. 270 cu.mi
17. The sum of the interior angles of a polygon is
540o. Find the number of sides.
a. 8
b. 5
c. 6
d. 11
18. Prisms are named according to their?
a. bases
b. vertices
c. sides
d. diagonal
19. The approximate surface area of an ellipse is
a. 211r
b. 11(ab)2
c. Fir2
d. FI(ab)
20. It is desired that the volume of the sphere be
tripled. By how many times will the raduis be
increased?
a. 33
b. 31/2
22. It is the perpendicular distance between the
two bases of a frustum of a cone.
a. lateral face
b. altitude
c. lateral edge
d. element
23. Points on the same
a. intersection
b. congruent
c. coplanar
d. collinear
24. What is the area, in inches2, of a parabola with
a base if 15 cm and height of 20 cm.
a. 200
b. 87
c. 78.74
d. 31
25. If a lateral area of a right circular cylinder is 88
cm3 and its volume is 220 cm3, find its radius.
a. 2 cm
b. 5 cm
c. 4 cm
d. 3 cm
26. A cone has a base area of 30in? and a lateral
area which is 4.5 times bigger than the base area.
The surface area of the cone in in' is
a. 135
b. 105
c. 75
d. 165
27. How many elements are needed in solving a
truncated cylinder?
a. 1
b. 4
c. 2
d. 3
28. It is a rectangle whose length is equal to its
width
a. square
b. rectangle
c. parallelepiped
d. cube
29. a solid bounded by a conical surface (lateral
surface) whose directrix is a closed curve, and a
plane (base) which cuts all the elements.
a. pyramid
b. cylinder
c. cone
d. prism
30. The lateral area of a cylinder with a
circumference of 50 cm and a height of 4 cm is
a. 228.2 units
b. 288.2 units
c. 238.2 units
d. 282.8 units
31. What is the distance, in cm, between two
vertices of a cube that are farthest from each other
if an edge measures 8 cm?
a. 16.93
b. 12.32
c. 14.33
d. 13.86
32. If the radius of the circle is decreased by 20%,
by how much is the area decreased?
a. 0.26
b. 0.46
c. 0.56
d. 0.36
33. Find the volume a right circular cone to be
obtained from a sector of radius 26 cm and whose
central angle measure 138.5°?
a. 900rt
b. 800n
c. 600n
d. 700 n
34. A quarter circle has a radius of 8 units. What is
its area?
a. 18n sq. units
b. 16n sq. units
c. 32n sq. units
d. 64n sq. units
35. A prism whose lateral edges are perpendicular
to its bases; its lateral faces are rectangles
a. right
b. truncated
c. frustum
d. prismatoid
36. A window glass is 5 ft by 7 ft. What is its area?
a. 17.5 ft
b. 35ft
c. 8.75 ft
d. 11.67 ft
37. A regular hexagon pyramid has a slant height of
4 cm and the length of each side of the base is 6
cm. Find the lateral area.
a. 72 cm
b. 82 cm2
c. 62 cm2
d. 52 cm2
38. A central angle of 45o subtends an arc 12 cm.
What is the ratio of the circle?
a. 15.28 cm
b. 12.58 cm
c. 12.82 cm
d. 15.82 cm
39. A portion of the prism included between the
base and a plane not parallel to the base cutting all
the edges.
a. truncated cylinder
b. frustum of a cone
c. truncated prism
d. frustum of a pyramid
40. It is a polyhedron having for bases two
polygons in parallel planes and for lateral faces
triangles or trapezoids
a. truncated
b. prismatoid
c. parallelepiped
d. frustum
41. It is a part of a circle bounded by a chord and
an arc.
a. sector
b. section
c. slab
d. segment
41. One of the diagonals of a rhombus is 25 units
and its area is 75 units2. Determine the length of
the side.
a. 15.47 units
b. 12.85 units
c. 18.25 units
d. 12.58 units
42. It is a solid bounded by a closed surface every
point of which is equidistant from a fixed point
called the center.
a. cone
b. vertex
c. sphere
d. circle
43. The area of a circle is 89.42 in2. What is the
length of the side of a regular hexagon inscribed in
a circle?
a. 6.335 in
b. 5.533 in.
c. 7.335 in.
d. 5.335 in.
44. It is a solid which is bounded by planes
a. lateral face
b. polyhedron
c. lateral area
d. plane
45. These are the intersections of the edges in a
polyhedron
a. Vertices
b. edges
c. lateral face
d. lateral edge
46. The area of the rhombus is 132 m2. If its shorter
diagonal is 12 m, find the longer diagonal.
a. 20 m
b. 38 m
c. 22 m
d. 34 m
47. A regular dodecagon is inscribed in a circle of
raduis 24. Find the perimeter of the dodecagon.
a. 151.24 units
b. 143.63 units
c. 149.08 units
d. 153.25 units
48. Every section of a cone made by a plane
passing through its vertex & containing two points
of base is a
a. triangle
b. square
c. circle
d. pyramid
49. Water flows in a pipe 1/4 ft in diameter and 24
ft in length. What is the volume of the water in the
pipe?
a. 8n/3 ft3
b. 3n/8 ft3
c. II/8 ft3
d. 2 n/8 ft3
50. Determine the volume of a right truncated
triangular prism. The base has sides loft, 9ft and
12ft. The sides perpendicular to the base have the
height of 8.6 ft, 7.1 ft, and 5.5 ft., respectively
a. 391 ft3
b. 311 ft3
c. 413 ft3
d. 313 ft3
51. A certain angle has a supplement 4 times its
complement. What is the angle
a. 60°
b. 30°
c. 45°
d. 90°
52. A regular dodecagon is inscribed in a circle of
radius 24. Find the perimeter of the dodecagon.
a. 151.24 units
b. 149.08 units
c. 153.25 units
d. 143.63 units
53. The lateral area of the right circular water tank
is 92 cm2 and its volume is 342 m3. Determine its
radius.
a. 6.05 cm
b. 7.28 cm
c. 5.56 cm
d. 7.43 cm
54. The mean proportional between bases is
a. bB
b. sort(bB)
c. 13.sort(b)
d. •s i t B
55. A metal washer 1-inch in diameter is pierced by
a 1/2-inch hole. What is the volume of the washer
if it is 1/8-inch thick?
a. 0.028-inch
b. 0.082-inch
c. 0.047-inch
d. 0.074-inch
56. Two triangles have equal bases. The altitude of
one triangle is 3 units more than its base while the
altitude of the other is 3 units less than its base.
Find the altitudes if the areas of the triangles differ
by 21 units2.
a. 4 and 10
b. 5 and 11
c. 3 and 9
d. 6 and 12
59. The volume of a water in a spherical tank
having a diameter of 4 m is 5.236 m3. Determine
the depth of the water in the tank.
a. 1.0 m
b. 1.4 m
c. 1.2 m
d. 1.8 m
60. It is a polyhedron of which two faces are equal
polygons in parallel planes and the other faces are
parallelograms.
a. frustum
b. prismatiod
c. prism
d. tetrahedron
61. A section of a sphere when a plane passing
through the center and diameter. Creating the
largest section called
a. great circle
b. short circle
c. medium circle
d. big circle
62. The ratio of the volume of the two spheres is
27:343 and the sum of their radii is 10. Find the
radius of the smaller sphere.
a. 5
b. 3
c. 4
d. 6
57. A right circular cone has a base radius of 10 m.
and an altitude of 20 m. Determine its volume.
a. 666n
b. 2000n
c. 1000n
d. 500n
63. Find the increase in volume of a spherical
balloon when its radius is increased from 2 to 3
inches.
a. 74.59 in3
b. 79.59 in3
c. 74.12 in3
d. 75.99 in3
58. In plane geometry, two circular arcs that
together make up a full circle are called?
a. coterminal arcs
b. congruent arcs
c. conjugate arcs
d. half arcs
64. Which formula cannot be used to compute the
area for a circle
a. if(ab); where a=b
b. Eld2/4
c. lid2
d. n r2
65. The circumference of a great circle of a sphere
is
. Fi d the olume of the sphere.
a. 3033.6 units3
b. 3023.6 units3
c. 3053.6 units3
d. 3043.6 units3
66. Assuming that the earth is a sphere whose
radius is 6400 km, find the distance along a 3o arc
at the equator of the earth's surface.
a. 353.10 km
b. 335.10 km
c. 533.10 km
d. 353.01 km
67. Find the area, in cm2, of a regular octagon
inscribed in a circle of raduis 10 cm.
a. 283
b. 238
c. 298
d. 289
68. The side of a triangle are 8 cm. 10 cm and 14
cm. Determine the raduis of the inscribed circle.
a. 2.35 cm
b. 2.25 cm
c. 2.45cm
d. 2.55 cm
69. The side of a triangle are 8 cm. 10 cm and 14
cm. Determine the raduis of the circumscribing
circle.
a. 7.74 cm
b. 7.14 cm
c. 7.54 cm
d. 7.34 cm
70. The side of a right triangle are 8, 15 and 17
units. If each side is doubled, how many units2 will
the area of the new rectangle?
a. 420
b. 320
c. 240
d. 300
71. What is the volume of a frustum of a cone
whose upper base is 15 cm in diameter and lower
base is 10 cm in diameter with an altitude of 25 cm
a. 3108.87 cm3
b. 3180.87 cm3
c. 3081.87 cm3
d. 3018. 87 cm3
72. A regular hexagonal pyramid has a slant height
of 4 cm and the length of each side of the base is 6
cm. Find the lateral area.
a. 72 cm2
b. 52 cm2
c. 62 cm2
d. 82 cm2
73. The area of the region bounded by two
concentric circles is called?
a. circular disk
b. annulus
c. washer.
d. ring
74. A cone and a cylinder have the same heightand
the same volume. Find the ratio of the radius of the
cone to the radius of the cylinder.
a. 1.414
b. 1.732
c. 0.577
d. 0.866
75. A piece of wire of length 50 m is cut into two
parts. Each part is then bent to form square. It is
found that the total area of the square is 100 m2.
Find the difference in length of the sides of the two
squares.
a. 6.62 m
b. 6.16 m
c. 5.32 m
d. 5.44 m
76. A rectangular octagon is inscribed in a circle of
radius 10. Find the area of the octagon.
a. 288.2 units
b. 282.8 units
c. 228.2 units
d. 238.2 units
77. A piece of wire is shaped to enclose a square
whose area is 169 cm2. It is then reshaped to
enclose a rectangle whose length is 15 cm. The
area of the rectangle is?
a. 175 cm2
b. 170 cm2
c. 156 cm2
d. 165 cm2
78. The apothem of a polygon is the ______ of its
inscribed circle.
a. circumference
b. diameter
c. length
d. radius
79. The lateral faces are equal isosceles trapezoids.
a. frustum of a cone
b. cone
c. frustum of pyramid
d. pyramid
80. The tangent and a secant are drawn to a circle
from the same external point. If the tangent is 6
inches and the external segment of the secant is 3
inches, then the length of the secant is ______
inches.
a. 14
b. 15
c. 12
d. 13
81. Find the increase in volume of a spherical
balloon when its raduis is increased from 2 to 3
inches.
a. 75.99 in3
b. 74.59 in3
c. 74.12 in
d. 79.59 in
82. The angle of a sector is 30o and the raduis 15
cm. What is the area of the sector in cm2
a. 58.9
b. 89.5
c. 85.9
d. 59.8
83. A rectangle ABCD, which measures 18 cm by 24
cm, is folded once perpendicular to diagonal AC so
that the opposite vertices A and C coincide. Find
the length of the fold.
a. 21.5 cm
b. 20.5 cm
c. 22.5 cm
d. 23.5 cm
84. If an equilateral triangle is circumscribed about
a circle of raduis 10 cm, determine the side of the
triangle?
a. 34.64 cm
b. 36.44 cm
c. 32.10 cm
d. 64.12 cm
85. If a regular polygon has 27 diagonal, then it is
a?
a. hexagon
b. heptagon
c. nonagon
d. pentagon
86. The volume of a sphere is 36 &#960 m3. The
surface area of this sphere in m2 is?
a.
.
.
d. π
87. Polygons are classified according to the number
of?
a. diagonals
b. sides
c. angles
d. vertices
88. One side of a regular octagon is 2. Find the area
of the region inside the octagon.
a. 31
b. 21.4
c. 19.3
d. 13.9
Basic Engineering Correlation (Analytic Geometry
Reviewer)
1. The graph of the polar equation: r = 2cos0 is a
a. Rose
b. Limacon with a loop
c. Circle
d. Cardioid
2. Classify the conic represented by the equation x2
+ 4xy + 5 y2 - x + 2y + 1 = 0
a. circle
b. ellipse
c. hyperbola
d. parabola
3. The graph of the polar equation: r = I l is
a. a circle
b. a parabola
c. an ellipse
d. a hyperbola
4. What is the slope of the line 4x-5y +6 = 0?
a. -5/4
b. 5/4
c. 4/5
d. -4/5
5. The point of intersection of the lines x — 2y+4 0
and —3x + y —2 =0 is
a. (0,2)
b. (-2,0)
c. (0,-2)
d. (2,0)
6. The conic given by the equation? +4xy+5y2 -x+
2y+1 =0 is
a. parabola
b. circle
c. ellipse
d. hyperbola
7. Find the slope of a line having a parametric
equation of y = 4t + 6 and x = t + 1.
a. 2
b. 1
c. 4
d. 3
8. Find the equation of a straight line with a slope
of 3 and a y-intercept of 1.
a. x + 3y + 1
b. 0
c. x - 3y - 1
d. 3x - y + 1
e. 3x + y - 1
f. 0
g. 0
h. 0
9. An equation of the line with x and y intercepts 7
and -7, respectively, is
a. x— y +7 =0
b. x —y-7 = 0
c. —x+y-7=0
d. x+y+7=0
10. The line joining the points (3, -1) and (-3, 2) has
equation
a. x+2y+1= 0
b. x+2y—l= 0
c. x+y-2=0
d. x-2y—I=0
11. The set of all points in a plane such that the
sum of the distances of a point from some fixed
points on the plane is a constant is a/an
a. parabola
b. ellipse
c. hyperbola
d. circle
12. The distance from the point (5, 2) to the line 8x
- 6y +2 = 0 is
a. 3
b. 4
c. 1
d. 2
13. If (3,-5) is the midpoint of (-1,-3) and (x, y), then
the values of x and y are
a. x=1, y=-4
b. x=7, y= -7
c. x=2, y= -1
d. x= 7, y= -1
14. The distance between the given lines 3x + 2y —
2 =0 and 3x +2y-6 =0 is
a. 1.39
b. 1.12
c. 0.28
d. 0.55
15. The major axis of the elliptical path in which the
earth moves around the sun is approximately
186,000,000 miles and the eccentricity of the
ellipse is 1/60. Determine the apogee of the earth.
a. 94,550,000 miles
b. 93,000,000 miles
c. 91,450,000 milse
d. 94,335,100 miles
16. A line 4x + 2y -2 = 0 is coincident with the line
a. 0
b. 0
c. 4x + 4y + 2
d. 4x + 3y + 3
e. 8x + 4y - 2
f. 0
g. 0
h. 8x + 4y - 4
17. The length of the semi-transverse axis of the
graph of --- 9 — 4 =1 is
a. 2
b. 3
c. 5
d. 4
18. The equation of the line through (1, 2) and
perpendicular to 6x - y +5 =0 is
a. 6x-y-11=0
b. 6x-y+5=0
c. x+6y-13=0
d. x+6y-8=0
19. If the distance between the points (h, 2) and (0,
4) is 2 then the value of h is
a. 3,J2
b. 0
c. 2,5
d. 2
20. The length of the latus rectum for the ellipse
16x2 + 25y2 = 400 is equal to1
a. 5
b. 4
c. 6.4
d. 12.5
21. The graph of the polar equation: r = 2 + 2cos9 is
a
a. limacon
b. Circle
c. cardioid
d. lemniscates
22. Find the angle formed by the lines 2x + y — 8 =
0 and x + 3y + 4 = 0
a. 30°
b. 60°
c. 45°
d. 35°
23. The equation of a line that intercepts the x-axis
at x = 4 and the y-axis at y = -6 is,
a. 3x + 2y
b. 12
c. 2x - 3y
d. 12
e. 2x - 3y
f. 3x - 2y
g. 12
h. 12
24. Find the distance between the lines 3x + y - 12
= 0 and 3x + y - 4 = 0
a. letter d) 8/the squareroot of 10
25. Find the polar coordinate of the point (-3,A/3 )
a. (J18, 60°)
b. (412, 30°)
c. (012, 150°)
d. (A118, 330°)
26. To simplify the equation x2 + 4y2 + 6x +16y +
21= 0 by translation of axes, the origin must be
moved to
a. (-3, -2)
b. (2, 3)
c. (3, 8)
d. (-3, -8)
27. Given the equation of the parabola x2 = 4y –
20 . Locate its vertex.
a. (4, 20)
b. (0, 5)
c. (0, 4)
d. (0, 20)
28. Find the equation of a straight line with a slope
of 1/2 and y-intercept 3.
a. x - 2y -3 = 0
b. 3x-y+2 =0
c. x-2y+ 6 =
d. 2x-y+3 =0
29. Determine the coordinates of the point which is
two-fifths of the way from the point (1,-5) to the
point (6,10)
a. (3, 1)
b. (4, 5)
c. (2, -2)
d. (3, 5)
30. Find the area of the circle whose equation is x2
+ y2 = 6x - 8y.
a. 25 &
b. 20 &
c. 30 &
d. 15 &
31. How far from the y-axis is the center of the
curve 2x2 +2y2 + 10x - 6y - 55 = 0?
a. -3.25
b. -3.0
c. -2.5
d. -2.75
32. Which of the following lines is parallel to the
line 6x — 4y = 7?
a. 6x + 4y = 6
b. 4x — 6y = 9
c. 3x - 2y = 15
d. 3x + 2y = 12
33. The slope of the line passing through (-2,2) and
(3,12).
a. -2
b. ½
c. 2
d. 10
34. A line 4x + 2y -2 = 0 is coincident with the line
a. 0
b. 4x + 3y + 3
c. 0
d. 8x + 4y - 2
e. 8x + 4y - 4
f. 0
g. 0
h. 4x + 4y + 2
35. The parabolic antenna has an eqaution of y2 +
8x = 0. Determine the length of the latus rectum.
a. 8
b. 12
c. 10
d. 9
36. 14. A line through (-5, 2) and (1, -4) is
perpendicular to the line through (x, -7) and (8, 7).
Find x.
a. -4
b. -19/3
c. -6
d. -5
37. Find the eccentricity of the curve 9x2 - 4y2 - 36x
+ 8y = 4
a. 1.92
b. 1.86
c. 1.8
d. 1.76
38. If the points (0,0), (2, 0), and (1, k) are vertices
of an equilateral triangle then a value of k is
a. I
b. 5
c. 0
d. 2
39. Find the inclination of the line passing through
(-5, 3) and (10, 7).
a. 14.63
b. 14.73
c. 14.83
d. 14.93
40. What is the equation of the line that passes
thru (4, 0) and is parallel to the line x - y - 2 = 0
a. x - y
b. 0
c. x + y + 4
d. 0
e. x - y - 4
f. 0
g. 0
h. x - y + 4
41. What are the coordinates of the center of the
curve x2 + y2 - 2x - 4y - 31 = 0
a. (2, 1)
b. (-1, -1)
c. (1, 2)
d. (3, 5)
42. If a line through (-5, 2) and (1, -4) is parallel to
the line through (x, -7) and (8, 7) then x =
a. -5
b. -6
c. 22
d. -4
43. Find the distance between the given lines 4x 3y = 23 and 4x - 3y = -7
a. 3
b. 4
c. 6
d. 5
44. The equation of the directrix of the parabola y2
= 20x is
a. x = -5
b. x = 5
c. x = 4
d. x = -4
45. The center of a circle is at (1, 1) and one point
on its circumference is (-1, -3). Find the other end
of the diameter through ( -1, -3).
a. (3, 6)
b. (2, 4)
c. (1, 3)
d. (3, 5)
46. Two vertices of a triangle are (2, 4) and (-2, 3)
and the area is 2 square units, the locus of the third
vertex is
a. x + 4y = 12
b. 4x - y =14
c. 4x + 4y = 14
d. x - 4y =-10
47. The focus of parabola y2 = 16x is at:
a. (0, 3)
b. (3, 0)
c. (0, 4)
d. (4, 0)
48. The diameter of a circle described by 9x2 + 9y2
= 16 is
a. 4/3
b. 16/9
c. 4
d. 8/3
49. Find the distance between the points A (4, 7)
and B (-1, -5).
a. 10
b. 5
c. 13
d. 12
50. The equation 25x2 + 16y2 - 150x + 128y + 81 =
0 has its center at
a. (3, -4)
b. (3, 5)
c. (3, 4)
d. (4, -3)
51. Find the equation of the line where x-intercept
is 2 and y-intercept is -2.
a. x - y - 2
b. 0
c. 2x + 2y +2
d. -2
e. 0
f. -2x +2y
g. 0
h. x - y - 1
52. Find the inclination of the line passing through
(-2,4) and (2,7)
a. 53.13
b. 90
c. 36.87
d. 70
53. A horizontal line has a slope of
a. zero
b. infinity
c. negative
d. possitive
54. To simplify the equation x2 + 4y2 + 6x +16y+
21= 0 by translation of axes, the origin must be
moved to
a. (-3, -2)
b. (-3, -8)
c. (3, 8)
d. (2, 3)
55. Find the eccentricity of the curve 9x2 –16y2 –
144 = 0
a. 0.66
b. 1.67
c. 0.88
d. 1.25
56. Find the eccentricity of the curve 9x2 —16y2 —
144= 0
a. 1.67
b. 0.66
c. 1.25
d. 0.88
57. In the equation y = x2 + x + 1, where is the
curve facing?
a. Downward
b. Facing left
c. Facing right
d. Upward
58. Find the acute angle of rotation such that the
transformed equation of 6x2 +31y + 4y2 + x y = 0
will have no x' y' term.
a. 16.85°
b. 28.15°
c. 53.13°
d. 53.13°
59. The equation of the line through (1, 2) and
perpendicular to 6x + y — 4 = 0 is
a. x+6y-4 =0
b. x+2y-4 =0
c. 6x+y+ 4 =0
d. x- 6y+ 11 =
60. The equation of the line with a slope 47 and yintercept -2 is
a. —4 5x—y+2=0
b. x+y-2 =0
c. 5x-4y-20=0
d. 4x-5y-20=0
61. The polar equation r = 1 when transformed into
a rectangular equation is cos° —4sin
a. x2 — 4y2 =I
b. 4x2 — y2 =1
c. 4x — y = 4
d. x —4y = I
62. Given three vertices of a triangle whose
vertices are A(1, 1), B(3, -3) and (5, -3). Find the
area of the triangle.
a. 6 sq. units
b. 5 sq. units
c. 4 sq. units
d. 3 sq. units
63. A line with slope equal to — 2 has an inclination
of
a. 116.57°
b. —116.57°
c. 63.43°
d. —63.43°
64. What is the distance between the centers of
the circle x2 + y2 + 2x + 4y - 3 = 0 and x2 + y2 - 8x 6y + 7 = 0?
a. 7.07
b. 7.77
c. 8.07
d. 7.87
65. The area of hexagon ABCDEF formed by joining
the points A(1, 4), B(0, -3), C(2, 3), D(-1, 2), E(-2, -1)
and F(3, 0) is _________ square units.
a. 15
b. 24
c. 22
d. 20
66. Determine B such that 3x + 2y -7 = 0 is
perpendicular to 2x - By + 2 = 0.
a. 4
b. 2
c. 5
d. 3
67. Find the distance between the A (4, -3) and B (2, 5).
a. 10
b. 8
c. 11
d. 9
68. The equation of a line that intercepts the x-axis
at x = 5 and the y-axis at y = -4 is
a. 88x- l0y = 40
b. 5x + 4y = 20
c. 10x - 8y = 20
d. 4x + 5y = 20
69. Find the value of k for which the equation x2 +
y2 + 4x - 2y - k = 0 represents a point circle.
a. 6
b. 5
c. -6
d. -5
70. What is the length of the latus rectum of the
curve x2 = 20y
a. 5
b. 20
.√
d. √
71. Find the acute angle of rotation such that the
transformed equation of 6x2 + 3xy+ 4y2 +x-y =0 will
have no x' y' term.
a. 16.85°
b. 28.15°
c. 36.86°
d. 53.13°
72. Find the coordinates of the point P(2, 4) with
respect to the translated axis with origin at (1,3).
a. (1, 1)
b. (-1, 1)
c. (1, -1)
d. (-1, -1)
73. Determine the equation of the circle whose
radius is 5, center on the line x = 2 and tangent to
the line 3x - 4y + 11 = 0.
a. (x - 2)2 + (y - 2)2=25
b. (x - 2)2 + (y - 2)2=5
c. (x - 2)2 + (y + 2)2=25
d. (x - 2)2 + (y + 2)2=5
a. (x - 3)2 + (y + 5)2
b. (x - 5)2 + (y - 3)2
c. 16
d. 16
e. (x
f. 3)2 + (y - 5)2
g. 16
h. 16
i. x2 + y2
76. The line passing through the focus and is
perpendicular to the directrix of the parabola.
a. axis of the parabola
b. latus rectum
c. directrix
d. tangent line
77. What is the equation of the line joining the
points (3, -2) and (-7, 6)?
a. 2x + 3y = 0
b. 4x + 5y - 0
c. 5x + 4y = 7
d. 4x - Sy 22= 0
78. The angle formed by the lines y = -2x +8 and y
=1x- -4 is
a. 45°
b. 35°
c. 60°
d. 30°
79. In general quadratic equation, if the
discriminant is zero, the curve is a figure that
represents a/an _______.
a. circle
b. hyperbola
c. ellipse
d. parabola
74. The equation x2 + y1- 8x – 2y + 1 = 0 describes
a. A. a circle of radius 4 centered at (4, 1)
b. a circle of radius 4 centered at (-4,-1)
c. an ellipse centered at (-4, -1)
d. an ellipse centered at (4, 1)
80. The directrix of a parabola is the line y = 5 and
its focus is at the point (4, -3). What is the length of
the latus rectum?
a. 18
b. 12
c. 14
d. 16
75. Find the equation of a circle whose center is at
(3, -5) and whose raduis is 4.
81. A line, which is perpendicular to the x-axis, has
a slope to
a. infinity
b. 1
c. -1
d. 0
82. A line passes thru (1, -3) and (-4, 2). Write the
equation of the line in slope-intercept form.
a. y - 4 - x
b. y - 2 - x
c. y- x - 2
d. y - x -4
83. The line segment connecting (x, 6) and (9, y) is
bisected by the point (7, 3). Find the values of x and
y.
a. 14, 6
b. 5, 0
c. 33, 12
d. 14, 3
84. Determine the coordinates of the point which is
three-fifths of the way from the point (2, -5) to the
point (-3, 5).
a. (1, -1)
b. (-1, 1)
c. (-1, -2)
d. (-2, -1)
85. Which of the following points lie on the fourth
quadrant?
a. (5, 57r/4)
b. (-4, 27r13)
c. (-4, -7rJ3)
d. (5, -77r16)
86. The midpoint of the line segment between
P1(x1, y1) and p2(-2, 4) is P(2, -1). Find the
coordinates of P1.
a. (-6, 6)
b. (6, -6)
c. (5, -6)
d. (6, 6)
87. A locus of a point which moves so that it is
always equidistat from a fixed point (focus ) to a
fixed line (directix) is a _______.
a. hyperbola
b. ellipse
c. circle
d. parabola
88. A parabola having a span of 30m and a height
of 20m has an area of
a. 540
b. 360
c. 400
d. 180
89. An equation of the line that is parallel to 3x-6y
= —land passes through the point (2, 2) is
a. 2x—y+2=0
b. x-2y-2=0
c. x-2y+2 =0
d. x+2y+2= 0
90. If the product of the slope of any two straight
line is negative 1, one of these lines are said to be
a. Skew
b. Non-intersecting
c. Parallel
d. Perpendicular
91. Find the slope of the line defined by y - x = 5.
a. -1/2
b. ¼
c. 1
d. 5 + x
Basic Engineering Correlation (Calculus Reviewer)
1. The depth of water in cylindrical tank 4 m in
diameter is increasing at the rate of 0.7 m/min.
Find the rate at which the water flows into the
tank.
a. 6.4
b. 2.5
c. 1.5
d. 8.8
2. The volume of the sphere is increasing at the
rate of 6 cm3 / hr. At what is its surface area
increasing (in cn2/hr) when the radius is 50cm?
a. 0.3
b. 0.24
c. 0.4
d. 0.5
3. Find the height of aright circular cylinder of
maximum volume, which can be inscribed in a
sphere of radius 10 cm.
a. 12.81 cm.
b. 11.55 cm.
c. 15.11 cm.
d. 14.12 cm.
4. find the area in the first quadrant bounded by
the parabola y2 = 4x, x = 1 and x = 3
a. 9.955
b. 5.955
c. 5.595
d. 9.555
d. 40 kph
10. A box is to be constructed from a piece of zinc
20 sq. in. by cutting equal squarea from each
corner and turning up the zinc to form the side.
What is the volume of the largest box that can be
so constructed?
a. 592.59 cu. in.
b. 622.49 cu. In
c. 579.50 cu. In
d. 599.95 cu. in.
5. Find the maximum point of y = x + 1/x
a. (1,2)
b. (2,3)
c. (-1, -2)
d. (2, 5/2)
11. Find the coordinates of the vertex of the
parabola y = x2 - 4x + 1 by making use of the fact
that at the vertex, the slope of the tangent is zero.
a. (-2, -3)
b. (3, -2)
c. (-1, -3)
d. (2, -3)
6. ___________ is the concept of finding the
derivative of composite functions.
a. Logarithmic differentiation
b. Implicit differentiation
c. Trigonometric differentiation
d. Chain Rule
12. Given the function f(x) = x3 - 6x +2. Fnd the first
derivative at x = 2
a. 3x2 - 5
b. 8
c. 6
d. 7
7. Find the area bounded by the curve defined by
the equation x2 = 8y and its latus rectum.
a. 22/3
b. 32/3
c. 16/3
d. 11/3
13. If the first derivative of the function is constant,
then the function is__________.
a. Linear
b. Logarithmic
c. Sinusoid
d. Exponential
8. If y = x lnx. Find
a. -1/x
b. 1/x
c. -1/x2
d. 1/x2
14. Using the two existing corner sides of an
existing wall, what is the maximum rectangular
area that can be fenced by a fencing material 30 ft.
long?
a. 250 sq. ft.
b. 225 sq.ft.
c. 200 sq. ft.
d. 216 sq. ft.
9. Car A moves due east at 30 kph, at the same
instant car B is moving S 30o E with the speed 60
kph. The distance from A to B is 30 km. Find how
fast is the distance between them separating after
1 hour
a. 38 kph
b. 36 kph
c. 45 kph
15. The velocity of a body is given by v(t) = sin(xt),
where the velocity is given in meters per second
and " t " is given in seconds. The distance covered
in meters between t =1/4 and 1/2 second is close
to
a. 0.5221 m
b. -0.5221 m
c. -0.2251 m
d. 0.2551 m
16. Differentiate y = ex cos x2
a. ex(cosx2 - 2x sinx2)
b. -2xex sinx2
c. -ex sinx2
d. ex cosx2 - 2x sinx2
17. Three sides of a trapezoid are each 8 cm. long.
How long is the fourth side when the area of the
trapezoid has the greatest value?
a. 10
b. 8
c. 16
d. 12
18. Differentiate y = sec(x2 + 2)
a. -cos(x2 + 2)cot(x2 + 2)
b. 2xcos(x2 + 2)
c. cos(x2 + 2)
d. 2xsec(x2 + 2)tan(x2 + 2)
19. A statue 3 m high is standing on a base of 4 m
high. If an observer's eye is 1.5 m above the
ground, how far should he stand from the base in
order that the angle subtended by the statue is a
maximum.
a. 3.41 m
b. 4.41 m
c. 3.51 m
d. 3.71 m
22. In the curve 2 + 12x - x3, find the critical points.
a. (-2,18) & (2, -14)
b. (-2,18) & (-2,14)
c. (2,18) & (2,-14)
d. (2,18) & (-2,-14)
23. A man on a wharf 3.6 m above sea level is
pulling a rope tied to a raft at 0.60 m/sec. How fast
is the raft approaching the wharf when there are 6
m of rope out?
a. -0.95 m/s
b. -0.75 m/sec
c. -0.65 m/sec
d. -0.85m/sec
24. Find of y = 3sin 2x
a. 3 cos 4x
b. 2 sin 2x
c. 6 cos x
d. 6 cos 2x
25. If the distance x from the point of departure at
a time t is defined by the equation x = -16t2 + 5000t
+ 5000, what is the initial velocity?
a. 2000
b. 5000
c. 0
d. 3000
26. Find the slope of the tangent to the curve x2 +
y2 - 6x + 10y + 5 = 0 at the point (1,0)
a. ¼
b. 2/5
c. 2
d. 1/5
20. What is the area of the largest rectangle that
can be inscribed in a semi-circle of radius 10?
a. √
b. 100
c. 1000
d. √
27. Differentiate y = arc sin cos x
a. -2
b. 1
c. 2
d. -1
21. Find the partial derivative with recpect to x of
the funcyion xy2 - 5y + 6
a. 2xy
b. xy - 5y
c. y2 - 5
d. y2
28. Evaluate the limit lnx/x as x approaches positive
infinity.
a. 0
b. -1
c. 1
d. infinity
29. Determine the diameter of a closed a closed
cylindrical tank having a volume of 11.3 cu. m. to
obtain minimum surface area.
a. 1.22
b. 2.68
c. 1.64
d. 2.44
30. Divide the number 120 into two parts such that
the product of one and the square of the other is
maximum.
a. 30 and 90
b. 60 and 60
c. 40 and 80
d. 50 and 70
31. Evaluate: Lim (2 a. b e
b. e π
.∞
d. 0
x)tan
cm. What is the maximum possible area for the
triangle?
a. 14.03 sq.cm.
b. 15.59 sq. cm.
c. 17.15 sq. cm.
d. 18.71 sq. cm.
36. The cost of a product is a function of the
quantity x of the product: C(x) = x2 - 400x + 50. Find
the quantity for which the cost is minimum.
a. 2000
b. 3000
c. 5000
d. 0
37. Find the slope of the line tangent to the curve y
= x3 - 2x + 1 at x = 1.
a. 1/3
b. 1
c. 1/4
d. 1/2
32. Water is running into a hemispherical bowl
having a radius of 10 cm. at a constant rate of 3 cu.
cm/ min. When the water is x cm. deep, the water
level is rising at the rate of 0.0149 cm./min. What is
the value of x?
a. 2
b. 4
c. 3
d. 5
38. Water is running out in a conical funnel at the
rate of 1 cu. In. per second. If the radius of the base
of the funnel is 4 inches and the altitude in 8
inches, find the rate at which the water level is
dropping when it is 2 inches from top.
a. in./sec
b. in./sec
c. - / πin./sec.
d. in./sec
33. Find the area bounded by the line x - 2y + 10 =
0, the x-axis, the y-axis and x = 10
a. 50
b. 75
c. 100
d. 25
39. What is the area between y = 0, y = 3x2, x = 0
and x = 2?
a. 24
b. 6
c. 8
d. 12
34. Find the area bounded by the y - axis and x = 4
= y2/3
a. 12.8
b. 25.6
c. 56.8
d. 30.6
40. If y = (t2 + 2)2 and t = x1/2, datermine
a. x5/2 + x1/2
b. 2(x + 2)
c. 3/2
d. letter b
35. A triangle has variable sides x, y, z subject to
the constaint such that the perimeter is fixed to 18
41. Find the area between the curve y = cosh x and
the x-axis from x = 0 and x = 1
Select one:
a. 1.667 sq. units
b. 1.333 sq. units
c. 1.125 sq.units
d. 1.175 sq. units
42. Find the second derivative of y by implicit
differentiation from the equation 4x2 + 8y2 = 36.
a. 9/4y3
b. -16/9y3
c. 32xy
d. 64x2
43. Find the area in sq. units bounded by the
parabolas x2 - 2y = 0 and x2 + 2y - 8 = 0
a. 9.7
b. 4.7
c. 10.7
d. 11.7
44. What is the second derivative of a function y =
5x3 + 2x + 1?
a. 30x
b. 18
c. 30
d. 25x
45. Evaluate the limit of lim(x2 + 3x - 4) as x
approaches 3.
a. 54
b. 14
c. 18
d. 72
46. The rate of change of function y with respect to
x equals 2-y and y = 8 when x = 0. Find y when x =
ln2
a. -2
b. -5
c. 2
d. 5
47. If y = 4 cos x + sin 2x, what is the slope of the
curve when x = 2 radians?
a. -4.94
b. -2.21
c. 2.21
d. -3.25
48. Differentiate y = log10(x2 + 1)2
a. 4x(x2 + 1)
b. log e(x)(x2 + 1)
c. None of the choices
None of the choices
d. 2x(x2 + 1)
49. Given a cone of diameter x and altitude of h.
What percent is the volume of the largest cylinder
which can be inscribed in the cone to the volume of
the cone?
a. 2.12
b. 2.25
c. 2.86
d. 2.51
50. Find the minimum distance from the point (4,2)
to the parabola y2 = 8x
a. √
b. √
.√
d. √
51. Find the area enclosed y the curve x2 + 8y + 16
= 0, the x - axis, the y-axis and the line x - 4 = 0
a. 8.67 sq. units
b. 9.67sq. units
c. 10.67 sq. units
d. 7.67 sq. units
52. Find the equation of the normal to x2 + y2 = 1 at
the point (2,1).
a. 2x +3y = 3
b. y = 2x
c. x + y = 1
d. x = 2y
53. A poster is to contain 300 cm. sq. of printed
matter with margins of 10 cm. at the top and
bottom and 5 cm at each side. Find the overall
dimensions if the total area of the poster is
minimum.
a. 22.24, 44.5
b. 27.76, 47.8
c. 25.55, 46.7
d. 20.45, 35.6
54. Find the equation of the normal to i>x2 + y2 = 5
at the point (2, 1)
a. x = 2y
b. x + y = 1
c. 2x +3y = 3
d. y = 2x
a. 1
b. 2/3
c. 2
d. ½
55. Find the equation of the curve at every point of
which the tangent line has a slope of 2x.
a. y = -x2 + C
b. y = x2 + C
c. x = -y2 + C
d. 1x = y2 + C
61. Find the area bounded by the parabola, x2 = 4y,
and y = 4.
a. 33.21
b. 21.33
c. 13.23
d. 31.32
56. The radius of spheres is r inches at time t
seconds. Find the radius when the rates of increase
of the surface area and the radius are numerically
equal.
a.
i
. / i
. 2 in
d. / π in
62. The area bounded by the curve y = 2x1/2, the
line y = 6 and the y-axis is to be revolved at y = 6.
Determine the centroid of the volume generated.
a. 1.24
b. 0.56
c. 1.8
d. 1.0
57. Given a cone of diameter x and altitude of h.
What percent is the volume of the largest cylinder
which can be inscribed in the cone to the volume of
the cone?
a. 0.56
b. 0.44
c. 0.65
d. 0.46
58. The area enclosed by the ellipse (image) is
revolved about the line x = 3. What is the volume
generated?
a. 365.1
b. 360.1
c. 370.3
d. 355.3
59. If y = 2x + sin 2x, find x if y' = 0
a. π/2
. π/
. π/
d. π/
60. A Norman window is in the shape of a rectangle
surmountedby a semi-circle. What is the ratio of
the width of the rectangle to the total height so
that it will yield a window admitting the most light
for a given perimeter?
63. Find the volume generated if the area between
y = cosh x and x - axis from x = 0 to x = 1 is is
revolved about the x - axis.
a. 3.43 cu. Units
b. 4.42 cu. Units
c. 3.83 cu. Units
d. 2.83 cu. Units
64. What is the area bounded by the curve y = x3,
the x-axis and the line x = -2 and x = 1?
a. 5.24
b. 2.45
c. 5.42
d. 4.25
65. Find the approximate increase by the use of
differentials, in the volume of the sphere if the
radius increases from 2 to 2.05 in one second.
a. 2.12
b. 2.51
c. 2.86
d. 2.25
66. The integral of cos x wuth respect to x is
a. csc x + C
b. sec x + C
c. -sin x + C
d. sin x + C
c. The graph is not a periodic function.
d. The following shows an odd function.
67. Evaluate: Lim
a. infinity
b. 1
c. 0
d. 2
68. The distance of a body travels is a function of
time t and is defined by: x(t) = 18t + 9t2.What is its
velocity at t=3?
a. 18
b. 54
c. 36
d. 72
Basic Engineering Correlation (Advance
Mathematics and Differential Equation Reviewer)
1. Solve the equation y"+6y+9y=0subject to the
conditions y(0) =-4 andy (0) = 5.
a. y = (11x-4) e-3x
b. y = (-7x-4) e-3x
c. y = (-7x-4) e3x
d. y = (-11x-4) e3x
2. Solve the homogenous equation (x2+y2)
dx+2xydy=0
a. x2(x2+3y2) = c
b. x(x2+2y2)=c
c. x2(x2+2y2)=c
d. x(x2<+3y2) =c
3. The exp ession e uivalent to ∫
equivalent to
a. -4+6i
b. -z+Zi
c. -3+3i
d. 4+4i
+I z dz is
4. What can be concluded about the function that
the graph below depicts?
5. If A = eπ/ i and B = CiS π\4 then A + B
is_____"
a. 39.68∠125.62o
b. 40∠75o
c. 53.26+ 32.11i
d. 32.26+23.11i
6. Which of the following power series is a solution
to the differential equation y" + y' = 0 ?
a.
b.
c.
d.
7. The differential equation dv = (y2 - 3vy)dy is said
to be
a. linear in y
b. non linear in V
c. linear in V
d. non linear in x
8. The laplace transform of t is
a. 1/s-1
b. 1/s
c. 2/s2
d. 1/s2
9. Determine the value of the Legendre's
polynomial function P2(2).
a. P2 (2) = 2.5
b. P2(2) = 5.5
c. P2 (2) = 4
d. P2(2)=1
a. The following shows an even function.
b. The graph shows symmetry with respect to x=0.
10. The rate at which a solid substance dissolves
varies directly has the amount of undissolved solid
present in the solvent and as the difference
between the saturation concentration of the
substance and the instantaneous concentration of
the solution Five grams of A are placed in solvent B
.the solution when saturated will hold ten grams of
A. If 2 grams of A dossolved in 1 hr, how many
grams of A will be in solution in 2 hrs?
a. 7 g
b. 5 g
c. 4 g
d. 3 g
c. second order homogenous linear different
equation
d. second order homogenous linear different
equation
11. Find the differential equation whose general
solution is y = C1x + C2 ex.
a. (x + 1)y" - xy' + y = 0
b. (x - 1)y" + xy' + y = 0
c. (x + 1)y" + xy' +y = 0
d. (x - 1)y" - xy' + y = 0
17. The expression (3+2i)6 is equivalent to
a. -2035- 828i
b. -352+ 936i
c. 729+ 64i
d. 2187-128i
12. A cylindrical tank is 12ft. In diameter and 8=9 ft
high. Water flows into the tank at the rate of /10
cuft/sec. It has a hole radius 1/2 inch at the bottom.
The time the tank will be full if initially it is empty is
a. 76 min
b. 65 min
c. 56 min
d. 50 min
13. The indicial equation of the Bessel's equation x2
y" + xy' + (x2 - 9) y =0 is
a. r2 - 9 = 0
b. r2 + 3 = 0
c. r2 + r - 9 = 0
d. r2 + r - 3 = 0
16. The series
equivalent to the function
a. f(x) = e3x
b. f(x) = 1/1-3x
c. f(x) = cos 3x
d. f(x) = sin 3x
is
18. What is the order of the differential equation (4
+ y")1/3 = e2x
a. three
b. one-third
c. one
d. two
19. The indicial equation of ODE 2xy"+(l+ x)y'-2y=o
is
a. 2r2 - r =0
b. r2 -2 +l=O
c. r2-2r =0
d. r2-r =0
14. The solution to the equation x2y'+xy'+x2y=0 if
x=0.5 is approximately equal to
a. 0.7652
b. 0.5118
c. 0.9385
d. 0.5
20. The population of a certain municipality
increases at a rate to the square root of the
population. If the present population is 90,000, how
long will it take for the population to reach
160,000?
a. 210 years
b. 150 years
c. 200 years
d. 180 years
15. The different equation y" + 3y' - 4y =2x is
a. first order linear different equation
b. second order non homogenous linear different
equation
21. Find the equation of the curve at every point at
which the tangent line has a slope of 2x.
a. y = x2 + C
b. y = -x2 + C
c. x = -y2 + C
d. x = y2 + C
22. The order of the different equation
. The exp essio ∫
a. 13.098
b. 23,097i
c. 13.097i
d. 11.55i
a. 2
b. 4
c. 3
d. 6
28. Solve (cos x cos y - cot x)dx - sin x sin y dy = 0
a. sin x cos y = -ln(C cos)
b. sin x cos y = ln (C sin x)
c. sin x cos y = -ln (C sin x)
d. sin x cos y = ln (C cos x)
23. A water container whose circular cross section
is 6 ft in diameter and whose height is 8 ft. is filled
with water. It has a hole at the bottom of radius 1
inch. The time it will take if the tank rests on
support so that its 8 ft height is in a horizontal
direction and the hole in its bottom is
a. 25.46 min
b. 29.4 min
c. 28.95 min
d. 24.95 min
24. Determine the values of the constants r in the
indicial equations of the given ordinary differential
equation (2x2 — 24"-2,942y = 0 when Frobenius'
method is applied.
a. ri 0,r2 = 2
b. r, = r2 = 2
c. = 1,r2= 2
d. = 0,r2 =1
25. Find a power series for the function
a. x-x3+x5 - +...
b. 1+x2+x4+...
c. 1- x2+x4+...
d. x+x3+x5+...
i os z dz is e ui ale t to
29. The ganeral solution of the ordinary different
equation with c = constant is
a. - In(1 - 2 y) = x 22 + c
b. In(1 - 2y) = x2 + c
c. - 1 In(1 - 2 y) = x22 + c
d. 2 y = 1 + ce-x2
30. The differential equation given is correctly
described by which one of the following choices:
d2y/dx2 + bxy dy/dx = f(x)
a. non-linear, second order, non homogenous
b. non linear, second order, homogenous
c. linear,second order homogenous
d. linear. Second order, non homogenous
31. Which of the following is true about the Fourier
coefficients of f(x)= x if -π ≤ x ≤ π the value of f π/
is
a.
b.
c.
26. The order of the differential equation is
d.
a. 3
b. 4
c. 1
d. 2
32. Sugar decomposes in water at a rate
proportional to the amount still unchanged. If there
were 50 kg of sugar present initially and at the end
of 5 hours this is reduced to 20 kg, how long will it
take until 90% os the sugar is decomposed.
a. 12.56 hr
b. 15.72 hr
c. 16.41hr
d. 14.12 hr
33. In the higher-order differential equation (4 — x2
)y'''-4y1+y = 0 , x = —2 is a/an point.
a. focal
b. ordinary
c. regular
d. singular
34. Evaluate cos(3 + 5i)
a. -.99 + 0.28i
b. 0.53-3.59i
c. -73.47 -10.47i
d. -3.72- 0.51i
35. A new water pump has a capacity of 60 cu
m/day. If its capacity goes down by 15% every year,
in how many years will the capacity go down to 20
cu m/day?
a. 4.72 yrs.
b. 7.32 yrs.
c. 8.6 yrs
d. 3.72 yrs.
37. A certain quantity increases at a rate
proportional to q itself. If q = 25 when t = 0 and q =
75 when t =2, find q when t = 6.
a. 675
b. 576
c. 756
d. 657
38. Calculate the time in hrs, that it will take to
reach the fatal conc. Of 40% methane in a kitchen
measuring 15 ft x 12.5 ft x8 ft for a leaking stove.
The rate of leak is 15 cuft of 100% methane/hr.
Assume no fresh air is coming in. The gas rate is
measured at the rate conditions prevailing in the
kitchen.
a. 40 hrs.
b. 50 hrs.
c. 30 hrs.
d. 45 hrs.
39. Determine the Fourier coefficient a() of the
function f (x) = 3x2 + 4, —1 < x <1.
a. ao = 5
b. ao = 1
c. a = 0
d. as=10
36. Which of the following is the solution to the
Bessel's equation x2 y" + xy' + (x2 - y2) y=0
40. The differential equation (x2 +4xy+y2)dx-xydy=0
is
a. variable separable
b. linear differential equation
c. exact
d. homogenous
a.
41. The differential equation
can be classified
b.
c.
d.
as
a. exact
b. variable separable
c. linear but not homogenous
d. linear and homogenous
42. A spherical tank whose inner diameter is 2
meters is filled with water (density 1 g/cc). If a tank
has a hole 1 cm in diameter at the bottom, the
time the tank will be totally empty is
a. 3.61 hrs.
b. 2.41 hrs.
c. 4.21 hrs.
d. 6.31 hrs.
d.
43. The simplified form of (3 + 2i) is
a. 2,034-1781i
b. -2,034+1781i
c. -2,035-828i
d. 2,035+828i
44. The radius of conversence of the power series
(not sure yet)
a.
b.
c.
d.
45. Which of the following is a differential equation
of the first order of degree one?
a.
46. Find the differential equations og the family of
lines through the origin.
a. xdy - ydx = 0
b. ydx + xdy = 0
c. xdx + ydy = 0
d. ydx - xdy = 0
47. Solve the equation
a.
b.
c.
48. Solve the different equation
a. y=(2x3 + 11)2)
b. y=(2x3 - 5)
c. y=(x3 -5)2)
d. y=(x3 +11)2
49. Determine the general solution of xdy + ydx = 0
a. ln (xy) = c
b. ln x + ln y = c
c. xy = c
d. x + y = c
50. Find the equation of the orthogonal trajectories
of the system of parabolas y2=2x+C.
a. y = C ex
b. y = C e-x
c. y = C e-2x
d. y = C e2x
51. The principal 4th root of 5 + 12i
a. 1.62 + 0.39i
b. 1.49 + 1.86i
c. 0.73 + 1.75i
d. 1.82 + 0.55i
52. Evaluate 143 - 41).
a. 1.28+ j0.98
b. 1.76+ j0.54
c. 2.23+ j0.21
d. 1.61- 0.931
53. Solve
a. y= -x5+cx6
b. y=x5+cx6
c. y=-x6+cx5
d. y=x6+cx5
54. What is the differential equation of a family of
parabolas having their vertices at the origin and
their vertices on the x-axis?
a. xdy + ydx = 0
b. 2ydx - xdy = 0
c. 2xdy - ydx = 0
d. dy/dx - x = 0
55. When a simple electric circuit, containing no
condensers but having inductance and resistance,
has the electromotive force removed, the rate of
decrease of current is proportional to the current.
The current is i amperes t seconds after the cutoff,
and i = 40 when t = 0. If the current dies down to
15 amperes in 0.01 sec, fid i after 0.1 sec.
a. 0.003amp
b. 0.001amp
c. 0.004amp
d. 0.002amp
(assumed uniform throughtout at any instant) and
the temperature of the surrounding air, the
proportionality constant being 2 Btu/minoF. If the
air temperature remains constant at 70oF and if the
initial temperature of the tank and its contents is
55oF, the temperature of the tank as a function of
the is
a. T=120+65et/25
b. T=12-6.5e-t/25
c. T=120-65e-t/25
d. T=-120+65e-t/25
61. Which of the following is a solution of the wave
56. Solve the differential equation : x(y - x =
1,determine y when x = 2.
a. 1.55
b. 1.63
c. 1.48
d. 1.8
57. How can the differential equation a d2x/dt2 +
B(t) dx/dt + c = D(t) best be described?
a. linear, homogenous and first order
b. second order and non homogenous
c. homogenous and first order
d. linear, second order and non homogenous
58. Evaluate sin ( 3 + 4i )
a. 0.14 -0.75i
b. 3.85 - 27.02i
c. -0.96 + 4i
d. -0.09 + 0.75i
59. A body weighing 1960 N is pulled by a constant
force of 492 N along a horizontal plane where in
the coefficient of friction between the body and
the plane id 0.20. Determine the velocity after 20
seconds.
a. 13.1 m/s
b. 10.57 m/s
c. 8.25 m/s
d. 9.06 m/s
60. A tank and its contents weigh 100 lbs. The
average heat capacity of the system is 0.5 Btu/ lb.F.
The liquid in the tank is heated by an immersion
heater which delivers 100 Btu/min. Heat is lost
from the system at a rate proportional to the
difference between the temperature of the system
equation
a. u=ex cos t
b. u =(x + at)6
c. u = ln(ax-t)
d. u = sin(kx)sin(at)
62. A low radioactive material is used in
biochemical process to induce biological mutation.
The isotope is made in the experimental reactor of
the Philippine Atomic Energy Commssion, now
Philippine Nuclear Research Institute, and ship to
the chemical plant. It has a half life of 8.06 days.
The plant receive the shipment of the radioactive
material which on arrival contain 1 gram of the
radioactive material. The plant uses the material at
the rate of 0.1 gram per week. The time it will take
for the radioactivity to last is
a. 4.74 weeks
b. 3.24 weeks
c. 5.4 weeks
d. 4.34 weeks
63. Solve the differential equation dy - xdx = 0, if
the curve passes through (1, 0).
a. 3x2 + 2y - 3 = 0
b. 2y + x2 - 1 = 0
c. 2x2 + 2y - 2 = 0
d. x2 - 2y -1 = 0
64. A 10-ohm resistor and a 5-henry inductor are
connected in series with to a 50-volt source at time
t = 0. Express the current I as a function of time.
a. i = 5(1 - e)2t
b. i = 5(e2t - 1)
c. i = 5(1 - e-2t)
d. i = 5(1 - e2t)
65. Evaluate cosh(5 + 6i)
a. 201.72 +74.21i
b. 57.22-193.43i
c. 71.25-2073i
d. 74.20 - 0.28i
66. A 50 lb iron ball is heated to 200oF and then
plunged immediately into a vessel containing 100b
lbs of water whose temperature is 40oF. The
specific heat of iron is 0.11 Btu/lboF. The common
temperature, approached by the iron and water as
time approaches infinity is
a. 68.5oF
b. 58.4oF
c. 48.34oF
d. 38.43oF
67. The rate f decay of radioactivity elements is
usually assumed to be proportional to the number
of atoms that have not decayed, where &#955 is
the proportionality consatnt. If at time t=0 there
are Xo atoms of a given elements, the expression
for the number of atoms, X, that have not decayed
(as a function of time,t,&#955, and Xo) is
a. Xo/ +λt
b. Xo(1-λt
c. Xoe-λt
d. Xoe(1-e-λt)
68. Which of the following is a term of the power
series representation solution of the higher order
differential equation 3 y" —2 x y = 0
a. a1
b. 4
c. 4a2
d. 1
69. The solution to the non homogeneous partial
differential equation
a. u(x,y)=f(y)e2x-4x
b. u(x,y)=f(x)e-2y+4y
c. u(x,y)=f(x)e-2y+2y-1
d. u(x,y)=f(y)e-2x-2x-1
70. Find the general solution of y' = ysec x.
a. y = C sec x tan x
b. y = C (sec2 x - tan y)
c. y = C (sec x - tan x)
d. y = C (sec x + tan x)
71. Determine the value of c such that the function
u(x,t) = e -256 sin 2x will be a solution of the heat
equation given by
a. 1
b. 4
c. 8
d. 2
72. The expression (5+2i)7 is equivalent to
a. -15939+ 1846C1
b. -703919-68880i
c. -116615+60422i
d. 78125+128i
73. Find the principal 5th root of 5+121.
a. 1.64 +1.38i
b. 1.38+1.641
c. 1.67+0.13i
d. 1.62+0.391
74. Evaluatecos(2+3i).
a. -2,034+17811
b. 2,035+828i
c. 2,034-1781i
d. -4.19-9.11i
75. A body whose temperature is 180o is immersed
in a liquid which is kept at a constant temperature
of 60o. In 10 minutes the temperature of the
immersed body decreased to 120o. How long will it
take for the body's temperature to decrease to 90o?
a. 15 min.
b. 20 min.
c. 25 min.
d. 18 min.
76. the equation y2 = cx is the general solution of
a. y' = x/2y
b. y' = 2y/x
c. y' = y/2x
d. y' = 2x/y
77. Find the radius of the convergence of the series
a. |x| < 2
b. |x| < ½
c. |x| < 8
d. |x| < 1/8
78. Radium decomposes at a rate proportional to
the amount at any instant. In 100 years, 100 mg of
radium decomposes to 96 mg. How many mg will
be left after 100 years?
a. 88.6
b. 90.72
c. 92.16
d. 95.32
79. A certain subxtance increases at a rate
proportional to the square of the instantaneous
amount. After 5 days the amount is doubled.
Determine the time before the amount is tripled.
a. 40/3
b. 45/3
c. 20/3
d. 25/3
80. Evaluate sinh(6 + 5i)
a. 57.22 –193.43i
b. 201.71+ 74.201
c. –20.74 + 71.25i
d. –0.27 – 0.96i
81. Which of the following is true about the Fourier
coefficients
of
a. ao=7
b. ao= 0
c. ao=10
d. ao=5
82. The solution to the homogeneous partial
differential equation
a. u(x,y)=A(y)cos 3x+B(y)sin 3x
b. u(x,y)=A(y)e3x +B(y)xe3x
c. u(x,y)=A(y)e3x +B(y)e-3x
d. u(x,y)=A(y) +B(y)e-9x
83. Solve xy'(2y -1) = y(1-x)
a. ln (xy) = x + 2y + C
b. ln (xy) = 2y - x + C
c. ln (xy) = x - 2y + C
d. ln (xy) = 2 (x - y) + C
84. A tank initialy contains 400 liters of water. Salt
solution, containing 1/8 kg of salt per liter of
solution flows into the tank at the rate of 8 li/min
and the solution, kept well-stirred, flows out of the
tank at the rate of 4 li/min. Find the amount of salt
in the tank after 100 minutes.
a. 80 kg
b. 85 kg
c. 75 kg
d. 70 kg
85. A mothball loses mass by evaporation at rate
that is proportional to the surface area. If half tha
mass is lost in 100 days, how long will it take the
radius to decreases to half its initial value?
a. 255 days
b. 275 days
c. 243 days
d. 234 days
86. The laplace transform of et is
a. 1/(s-1)2
b. 1/(s+1)
c. 1/(s-1)
d. 1/s
87. Evaluate cosh ( 3 + 5i)
a. 2.86 + 9.61i
b. 1.61 + 0.93i
c. 2.08 + 1.79i
d. 2.08 + 0.93 i
88. If dy = x2dx, what is the equation of y in terms
of x if the curve passes through (1,1)?
a. x3 - 3y + 2 = 0
b. x3 + 3y + 2 = 0
c. x2 - 3y + 3 = 0
d. 2y + x3 + 2 = 0
89. Evaluateln(5 +j3).
a. 1.28+ j0.98
b. 2.54+ j0.866
c. 2.23+ j0.21
d. 1.76+ j0.54
90. Which of the following power series is a
solution to the differential equation
a.
b.
c.
d.
91. Solve the equation
a. y =cIe5x+ c2e3x
b. y =cIe-5x+ c2e-3x
c. y =(cIx+ c2)e-5x
d. y =(cIx+ c2)e3x
Basic Engineering Correlation (Chemistry
Reviewer)
1. Uranium-235 and uranium-238 have the same
number of which of the following?
a. Protons and electrons
b. neutrons
c. protons
d. electrons
2. What is the valence (oxidation state) of carbon in
sodium carbonate (Na2CO3)?
a. -4
b. 4
c. 2
d. -2
3. Water and SO3 combine to sulfuric acid (H2SO4)
according to the following reaction. How many
grams of water must be added to 100 g of 20%
oleum (20% SO3 and 80% H2SO4by weight) to
produce a 95% solution ( byweight) of sulfuric acid?
a. 3.3 g
b. 14 g
c. 5.0 g
d. 7.5 g
4. During a laboratory experiment at 1.0 atm and
25oC, a student observed that oxygen gas was
produced by de-composition of 15 g of sodium
chlorate. What was the volume of oxygen?
a. 1.27 L
b. 6.54 L
c. 5.17 L
d. 3.85 L
5. Which of the following does a catalyst change?
a. the activation energy of a reaction
b. the equilibrium constant of areaction
c. the concentration of product at equilibrium
d. the heat of reaction of a reaction
6. What is an isomer?
a. a substance containing a hydroxyl ion
b. a single atom
c. different arrangement of the same atoms
d. a basic building block for large chemical chains
7. The reaction shown occurs in a gaseous phase.
Once equilibrium has been achieved in a particular
reaction vessel, additional HI gas is injected directly
into the reaction vessel. Compared to the initial
conditions, which of the following statemnets is
correct after the new equilibrium has been
achieved?
a. The amount of H2 will have decreased.
b. The partial pressure of H2 will have decreased.
c. The amount of I2 will have increased.
d. The partila pressure of HI will have decreased.
8. Which of the following compounds would be
ionic, considering the electronegativities of the
elements?
a. I2
b. NO
c. CO
d. KCI
9. An unknown gas with a temperature of 25oC and
a pressure of 740 mm Hg is collected in a sampling
bag. The volume and mass of the gas are 24.0 L and
34.9 g, respectively. Which chemical formula could
represent the gas?
a. N2
b. H2S
c. HCI
d. Ar
10. What is the percentage (by mass) of htdrogen
in glucose (C6H12O6)?
a. 0.067
b. 0.093
c. 0.17
d. 0.4
11. 2.00 g of a substance dissolved in 250 g of
water produces a boiling point elevation of
0.065oC. What is the molecular weight of the
substance?
a. 63
b. 92
c. 16
d. 8
12. A current of 0.075 A passes through a solution
of silver nitrate for 10 munites. How much silver is
deposited?
a. 0.040g
b. 0.035 g
c. 0.030 g
d. 0.050 g
13. How many grams of copper will be deposited at
an electrode if a current of 1.5 A is supplied for 2
hours to a CuSO4?
a. 7.1 g
b. 3.6 g
c. 48 g
d. 2.4 g
14. What is the order of reaction with respect to
reactant E and the overall order of the reaction
described by the following rate law?
a. second order with respect to E; second order
overall
b. first order with respect to E; second order
overall
c. second order with respect to E; fourth order
overall
d. first order with respect to E; fourth order overall
15. What is the term for a quantity of a susbstance
to which a chemical formula can be assigned and
whose mass is equal to its formula weight?
a. a mole
b. an equivalent
c. a molecule
d. a one-normal solution
16. The pH of a 0.001 M HCI solution is
a. 5
b. 3
c. 7
d. 1
17. The half-life of radioactive carbon is
approximately 5700 years. If a sample is found to
have 7000 atoms after 6000 years, how many
atoms were presents initially?
a. 13800 atoms
b. 14500 atoms
c. 14300 atoms
d. 14100 atoms
18. Given the following reversible chemical
reaction, assume all reactants and products are
ideal gases.
a. The amount of ammonia (NH3) would halve.
b. There would be no change in the amount of
ammonia (NH3) present.
c. More ammonia (NH3) would be generated.
d. The amount of ammonia (NH3) would double.
19. Which of the following statements concerning
reversible reactions is false?
a. Temperature affects the direction of the
reaction.
b. Concentration have no effect on the direction
of the reaction
c. Concentration remain constant once equilibrium
is reached.
d. Both reactants and products are always present.
20. Which of the following reactions are not
balanced?
a. IV only
b. I only
c. II and III
d. I and III
21. 2.00 g of a substance dissolved in 250 g of
water produces a boiling point elevation of
0.065oC. What is the molecular weight of the
substance?
a. 92
b. 16
c. 8
d. 63
22. Oxygen reacts stoichimetrically with methane
to form 14 g of carbon monoxide. How many moles
of methane are consumed?
a. 1 mol
b. 0.5 mol
c. 2 mol
d. 1.5 mol
23. Which o fthe following chemical formulas is
incorrect?
a. Na2CO3
b. KOH
c. Ca(OH)2
d. CaCI
24. What are the chemical formulas for the
following compounds: aluminum nitrate,
magnesium hydroxide, calcium oxide, and cupric
carbonate?
a. AINO3,Mg(OH),Ca2O3,CuCO3
b. AI(NO3)3,Mg(OH)2,CaO,CuCO3
c. AL2NO3,Mg(HO),CaO2,CuCO3
d. AINO3Mg(HO)2,CaO,Cu(CO3)2
25. Nitroglycerin is made by combining glycerol,
nitric acid, and sulfuric acid. What are the
minimum coefficients needed to balance the
equation of this reactions?
a. 4,2,1,1,3,1
b. 1,3,1,1,3,1
c. 1,3,3,1,3,2
d. 2,6,2,2,6,2
26. Which of the following occurs when table salt
(NaCI) is added to continuously heated boiling
water?
a. The water boils even more agitatedly.
b. The temperature of the water decreases but
boiling continues uninterrupted.
c. The water continues to boil.
d. The water momentarily stops boiling.
27. The final temperature of the hydrogen and
chlorine described in Prob. 8 is 30oC. What is the
final pressure in the reaction vessel?
a. 80 kPa
b. 320 kPa
c. 240 kPa
d. 160 kPa
28. A wastewater treatment plant uses chlorine gas
as a reactant. A tank is filled with 800 m3 of 20oC
water, and chlorine is added at a dosage of 125 g
per cubic meter of water. (Assume all of the
chlorine dissolves and none initially reacts
chemically.) If the atmospheric pressure is 1.0 atm,
what is the theoretical partial pressure of the
chlorine gas at the tank surface immediately after
the gas is added?
a. 2.3 x 10-4 atm
b. 0.11 atm
c. 3.1 x 10-5 atm
d. 0.039 atm
29. What family of compounds is produced from
the reaction between an alcohol and a carboxylic
acid?
a. ether
b. amine
c. ester
d. ketone
30. Which of the following statements pertaining
to acids and bases is incorrect?
a. Acids conduct electricity in aqueous solutions.
b. Bases have a pH between 7 and 14.
c. Bases have a sour taste.
d. Acids turn blue litmus paper red.
31. As the pressure of a gas increases, the solubility
of that gas in a liquid
a. always increases.
b. is not changed.
c. always decreases.
d. cannot be determined.
32. What is a distinguishing characteristic of the
halogens?
a. They are phosphorescent.
b. Next to the noble gases, they are the most
chemicallyinactive group.
c. They readily accept an electron from another
atom to form compounds.
d. They have a high electrical conductivity.
33. Enthalpy of formation is most closely defined as
the
a. potential energy of a substance.
b. energy absorbed during creation of 1 grammole
of a compound from pure elements.
c. energy absorbed or released during a chemical
reaction.
d. sum of the enthalpy of reactions.
34. Assuming all of the energy goes into the
reaction, what electrical power is required to
produce oxygen gas at a rate of 50 mg/s?
a. 9.2 kW
b. 0.89 kW%
c. 3.1 kW
d. 1.5 kW
35. What is the oxidation number for chromium
(Cr) in the compound BaCro?
a. 2
b. 4
c. 1
d. 6
36. A transportation company specializes in the
shipment of pressurized gaseous materials. An
order is received for 100 L of a particular gas at STP
(0oC and 1 atm). What minimum volume tank is
necessary to transport the gas at 25oC and a
maximum pressure of 8 atm?
a. 14 L
b. 12 L
c. 16 L
d. 10 L
37. In an experient, a compound was determined
to contain 68.94% oxygen and 31.06% of an
unknown element by weight. The molecular weight
of this compound is 69.7 g/mol. What is this
compound?
a. SiO4
b. NO2
c. F2O2
d. B2O3
38. 6 g of a substance are dissolved in 1000 g of
water. The solution freezes at -0.16oC. What is the
molecular weight of the substance?
a. 70 g/ mol
b. 60 g/mol
c. 75 g/mol
d. 100 g/mol
39. A gaseous mixture consists of 2 kg of oxygen, 5
kg of nitrogen, and 3 kg of xenon. What is the mole
fraction of the oxygen gas?
a. 0.24
b. 0.17
c. 0.11
d. 0.13
40. The diameter of a spherical mothball is
observed to halve in 200 days.approximately how
long will it take for its remaining volume to become
half of its volume at 200 days?
a. 67 days
b. 160 days
c. 130 days
d. 200 days
41. For a given isotope of an element, the atomic
number plus the atomic weight is 148, and their
difference is 58. how many protons does an atom
of the isotope contain?
a. 45
b. 90
c. 148
d. 58
42. 10 g of solid PCI5 is heated in a 0.5 m3 container
to 150oC, producing gaseous PCI3 and CI2 gas
according to the following decomposition reaction:
The molecule weights of the compound are What is
the increase in pressure in the container when 50%
(By weight) of the PCI5 is decomposed?
a. 0.250 kPa
b. 18 kPa
c. 0.120 kPa
d. 0.350 kPa
43. An alkyl radical is best defined as
a. an electron that is shared in a covalent bond.
b. any functional group that substitutes for a
hydrogen atom in an alkane.
c. the remaining portion of an alkane after it loses
a hydrogen atom.
d. cancer-causing molecules found in foods
44. It is known that ozone (O3) will decompose into
oxygen (O2) at a temperature of 100o. One mole of
ozone is sealed in a container at STP (0oC and 1
atm). What will be pressure of the container once
it is heated to 100oC?
a. 37 kPa
b. 1.4 kPa
c. 2.1 kPa
d. 210 kPa
45. How much water must be added to 100 mL of a
0.75 molar solution of KCI to make a 0.04 molar
solution?
a. 1.88 L
b. 0.188 L
c. 1.78 L
d. 1.98 L
46. While moving from left to right across the
second row of the periodic table (i.e., from Li to
Ne), the atomic radii tend to
a. first increase, then decrease.
b. uniformly increase.
c. remain the same.
d. uniformly decrease.
47. A solution is adjusted from pH 8 to pH 9. The
relative concentraation of the hydrogen [H+] ion
has changed by a factor of what?
a. 1100
b. 5
c. 110
d. 10
48. The solubility constant of stronyium sulfate,
SrSO4, is 2.8 x 10-7. How many grams of SrSO4 must
be dissolved in water to produce 1 L saturated
solution?
a. 0.1 g
b. 2 g
c. 0.00005 g
d. 0.0005 g
49. Which of the following elements has the largest
first ionazation energy?
a. CI (chlorine)
b. Ar (argon)
c. H (hydrogen)
d. Kr (krypton)
50. How many milliters of 1 M NaOH solution will
25 mL of 2 H2SO4neutralize?
a. 50 mL
b. 100 mL
c. 75 mL
d. 25 mL
51. What is the molarity of a solution obtained by
dis-solving 25 g of NaCI in enough water to produce
4 L of solution?
a. 6.25
b. 0.365
c. 0.428
d. 0.107
52. What is the half-life of a substance that decays
to 25% of its original amount in six days?
a. 3 days
b. 0.08 days
c. 8 days
d. 12 days
53. Two moles of sodium react with 2 moles of
water to produce which of the following?
a. 1 mole of sodium hydroxide and 1 mole of
hydrogen
b. 2 moles of sodium hydroxide and 1 mole of
hydrogen
c. 1 mole of sodium hydroxide and 2 moles of
hydrogen
d. 2 moles of sodium hydroxide and 2 mole of
hydrogen
54. When a deliquescent substance is exposed to
air, it
a. oxidizes.
b. becomes moist
c. crystallizes.
d. loses water of hydration.
55. Which of the following elements does not exists
as a diatomic molecule under normal (ambient)
conditions?
a. chlorine
b. oxygen
c. iodine
d. sulfur
56. A given sample of radioactive material has 80%
of the original substance remaining after 10 years.
How much will remain after 90 additional years?
a. 0.001
b. 0.017
c. 0.11
d. 0.13
57. The decay of U-238 to Pb-206 can be used to
estimate the age of inorganic matter. The half-life
of U-238 is 4.5 x 109 years. In a particular rock
sample, the ratio of the numbers of Pb-206 to U238 atoms is 0.66. Assume all of the Pb-206
present is due to the decay of U-238. What is the
age of the rock?
a. 3.3x 109 yr
b. 1.4 x 109 yr
c. 7.0 x 109 yr
d. 9.3 x 109yr
58. How much energy is needed to convert ozone
to oxygen?
a. 43 kcal/mol
b. 0 kcal/ mol
c. 68 kcal/mol
d. 140 kcal/mol
59. The group of metals that includes lithium,
sodium,potassium, rubidium, and cesium forms a
closely related family known as the
a. rare earth group.
b. halogens.
c. alkali metals.
d. alkaline earth metals.
60. Hydrogen and chlorine gas combine in a 35 m3
reaction vessel to produce hydrogen chloride. The
masses of hydrogen and chlorine are 4.5 kg and
160 kg, respectively. How much hydrogen chloride
gas is produced?
a. 41 kg
b. 21 kg
c. 82 kg
d. 160 kg
61. How many liters of 2M solution (i.e., a molarity
of 2) can be produced from 184 g of enthyl alcohol
(CH3CH2OH)?
a. 1.5 L
b. 5.0 L
c. 2.0 L
d. 2.5 L
62. If the current, I, is 100 A, at what rate is oxygen
produced?
a. 18.7 mg/s
b. 8.29 mg/s
c. 16.7 mg/s
d. 9.34 mg/s
63. What mass of lead nitrate, Pb(NO3)2, must be
dis-solved in 1 L of water to produce a solution that
contains 20 mg of lead ions? Assume 100%
ionazation.
a. 43 mg
b. 52 mg
c. 32 mg
d. 26 mg
64. A compound in gas form Has a mass of 0.377 g
and occupies 191.6 mL at standard conditions (0oC
and 760 mm Hg). What is the formula of the
compound?
a. C3H8
b. CH4
c. C5H12
d. C2H6
65. A gas mixture of N2(g) and CO2(g) contained in
a volume of 10.0 L has a total pressure of 0.750
atm at a temperature of 273K. The mixture is
known to contain 3.00 g N2(g). What is the partial
pressure of CO2(g) in the mixture?
a. 0.120 atm
b. 0.630 atm
c. 0.510 atm
d. 0.240 atm
66. Rank the following gas according to increasing
effusion rates relative to O2 (reference).
a. F2< CO24
b. F<2< CH<4< CO<2
c. CH42<CO2
d. CO22<2
67. What is the vapor pressure of 1000.0 g of a
water solution at 250C that contains 124.0 g of the
nonvolatile solute ethylene glycol, C2H6O2? The
vapor pressure of pure water at this temperature is
23.76 torr. Assume an ideal solution
a. 23.7 torr
b. 24.6 torr
c. 22.8 torr
d. 0.94 torr
68. "::Add_Chem_004:: Consider a solution of
water and a nonvolatile solute at some
temperature. What combination of conditions
would be sure to increase the vapor pressure of
the solution? _____"
a. Raise the temperature and add more water
b. Lower the temperature and add more solute
c. Raise the temperature and add more solute
d. Lower the temperature and add more water
69. What is the mass of 0.01 gram-moles of
Na2SO4?
a. 1.42 g
b. 1.19 g
c. 0.71 g
d. 2.38 g
70. An ideal gas occupies a volume of 4L and has a
pressure of 283.71kPa (1atm=101.325kPa). Under
22.50C, what most likely is the identity of the gas if
0.01293 Kg of gas is used.
a. O2
b. Cl2
c. F2
d. N2
71. The reaction shown proceeds in a gaseous
state. At equilibrium, the concentration of the
components X,Y, and Z are measured to be 5.73 x
10-2 mol/L, 2.67 x 10-2 mol/L and 4.59 x 10-2 mol/L,
respectively. What is the equilibrium constant for
this reaction?
a. 9.8 x 10-4mol/L
b. 1.7 x 10-2mol/L
c. 3.7 x 10-1 mol/L
d. 2.1 x 10-2mol/L
72. If 1.5 L of an ideal gas at 250C is heated, the
new volume increases 2.5 times the original
volume. The pressure and amount of substance are
held constant. What is the new temperature of gas
in 0F
a. 882 0F
b. 8800F
c. 820 0F
d. 8280F
73. "::Add_Chem_013::Following are three states
for fluorine:1s22s12p6 1s22s22p5 1s22s22p42d1
They are, respectively: _____"
a. ground, excited, impossible
b. ground, impossible, excited
c. excited, impossible, ground
d. excited, ground, impossible
74. At what temperature in 0C will O2 has under a
p essu e of . at ? of O = . g/L
a. 645.7510C
b. 3810C
c. 315.570C
d. 318.160C
75. Macro Vee collected hydrogen gas using water
displacement method. He measured the
temperature of water using a thermometer and
found out that it is 230C with the correponding
pressure of 21.1 mmHg. Calculate the pressure of
hydrogen gas under standard atmospheric
pressure.
a. 95.81 KPa
b. 98.51 Kpa
c. 98.15 Kpa
d. 95.18 Kpa
76. A sample of an unknown compound is found to
be 49.3% carbons, 9.6% hydrogen, 19.2% nitrogen,
and 21.9% oxygen by weight. What is its molecular
formula?
a. C3H7NO
b. C3H7NO
c. C4H<><>
d. C4H4NO
77. Balance the following reaction.
a. HBrO3 + 5HBr 3H2O + 3bR2
b. 3HBrO3 + HBr 2H2O + 2Br2
c. 2HBrO3 + 4HBr 3H2O + 3Br2
d. HBrO3 + 4HBr 3H2O + Br2
78. Which of the following is the correct electron
configuration of Pb?
a. [Xe]6s24f146s2
b. [Xe]6s25d104f146p2
c. [Xe]6s25d104f145d106p2
d. [Xe]5d104f146p2
79. The mole (mol) is the amount of a substance
that contains as many elementary entities as there
are atoms in exactly
a. 12.00 grams of C.
b. average atomic mass of isotopes of C.
c. 12.01 grams/mol of C.
d. 12.00 grams of 12C.
80. At STP the volume of 1.5 mole N2as compared
to 1.0 mole O2 is
a. higher to about three fourths
b. the same, 22.4L
c. different by about 11.2 L
d. differ by a factor of 1.25
81. "::Add_Chem_008:: How many grams of
glucose, C6H12O6, are necessary to prepare 656
mL of a solution with a concentration that is 0.550
molar? _____"
a. 0.00200 g
b. 151 g
c. 64.9 g
d. 214 g
82. n the following reaction, which elements are
the reducing and exidizing agents?
a. Mg is the reducing agents; O2 is the oxidizing
agent.
b. MgO is the reducing agent; Mg is the oxidizing
agent.
c. Mg is the reducing agent;MgO is the oxidizing
agent.
d. O2 is the reducing agent; Mg is the oxidizing
agent.
83. By decreasing the pressure of an ideal gas at
constant temperature and amount of substance
1/3 times the original pressure, the volume of gas
will
a. expands two thirds the original
b. increases three times the original
c. multiply by a factor of 1/3
d. decreases three times the original
84. What is the gravimetric (i.e.m.,mass)
percentage of oxygen in K2CrO4?
a. 0.33
b. 0.66
c. 0.57
d. 0.42
85. There are 500 g of zinc sulfide (ZnS) in a load of
zinc ore. The ZnS is roasted in excess air to form
zinc oxide (ZnO) and sulfer dioxide (S)2). How many
grams of zinc can be subsequently recovered if 5%
of the zinc is lost in the roasting process?
a. 340 g
b. 380 g
c. 320 g
d. 400 g
86. What is the enthalpy of reaction at 25oC for the
combustion of ethane ( C2H6)?
a. -680 kcal/mol (exothermic)
b. -340 kcal/mol ( exothermic)
c. 130 kcal/mol (endothermic)
d. 340 kcal/mol (endothermic)
Basic Engineering Correlation (Physics Reviewer)
(A Collaborative work of GaMbit, jay729, and
airsWTP)
1. The system shown is in static equilibrium. Find
W.
Select one:
a. 1000 N
b. 1700 N
c. 1500 N
d. 830 N
2. What is the force in member AF?
Select one:
a. 5000 N
b. 15 000 N
c. 10 000 N
d. O
3. A ball is dropped from rest at a point 12 m above
the ground into a smooth, frictionless chute. The
ball exist the chute 2 m above the ground and at
angle 45o from the horizontal. Air resistance is
negligible. Approximately how far will the ball
travel in the horizontal direction before hitting the
ground?
Select one:
a. 22 m
b. 20 m
c. 24 m
d. 12 m
4. The structure shown is formed of three separate
solid aluminum cylindrical rods, each with a 1 cm
diameter. What is the -coordinate of the centroid
of volume for the structure?
Select one:
a. 15.2 cm
b. 16.0 cm
c. 15.9 cm
d. 14.0 cm
5. A projectile has an initial velocity of 110 m/s and
a launch angle of 20o from the horizontal. The
surrounding terrain is level, and air friction is to be
disregarded. What is the maximum elevation
achived by the projectile?
Select one:
a. 350 m
b. 72 m
c. 140 m
d. 620 m
6. What are R1 and R2? (insert question #11)
Select one:
a. 1250 N
b. 1250 N; R2 /
c. 1000 N; R2 /
d. R1 /
e. 3750 N
f. 4000 N
g. 2500 N; R2 /
h. 1250 N
i. R1 /
j. R1 /
k. 3750 N; R2 /
l. R1 /
7. What is the reaction at point A?
Select one:
a. 710 N
b. O
c. 500 N
d. 290 N
8. A turntable capable of angularly accelerating at
12 rad/s2 needs to be given an initial angular
velocity if it is to rotate through a net 400 radians
in 6 seconds. What must its initial angular velocity
be?
Select one:
a. 33 rad/s
b. 21 rad/s
c. 200 rad/s
d. 28 rad/s
9. A 550 kg mass initially at rest acted upon by a
force of 50 et N. What are the acceleration, speed,
and displacement of the mass at t = 4 s?
Select one:
a. 4.96 m/s2,4.87 m/s,19.5 m
b. 4.96 m/s2,135.5 m/s,2466 m
c. 4.96 m/s2,271 m/s,3900 m
d. 4.96 m/s2,4.96 m/s,19.8 m
10. A constant force of 750 N is applied through a
pulley system to lift a mass of 50 kg as shown.
Neglecting the mass and friction of the pulley
system, what is the acceleration of the 50 kg mass?
Select one:
a. 20.2 m/s2
b. 16.2 m/s2
c. 8.72 m/s2
d. 5.20 m/s2
11. A child keeps a 1 kg toy airplane flying
horizontally in a circle by holding onto a 1.5 m long
string attached to its wing tip. The string is always
in the plane of the circular flight path. If the plane
flies at 10 m/s, what is the tension in the string?
Select one:
a. 15 N
b. 28 N
c. 7 N
d. 67 N
12. One newton is the force required to
Select one:
a. give a 1 g mass an acceleration of 1m/s2.
b. accelerate a 10 kg mass at a rate of 0.10 m/s2.
c. accelerate a 1 kg mass at a rate of 9.81 m/s2
d. accelerate a 1 kg mass at a rate of 1.00 cm/s2.
13. What is the approximate centroidal polar
moment of inertia of the area?
Select one:
a. 27.3cm4
b. 25.6 cm4
c. 16.2 cm4
d. 21.4 cm4
14. A 4-A current is maintained in a simple circuit
with a total resistance of 2 . How much energy is
delivered in 3 seconds
Select one:
a. 3J
b. 12J
c. 6 J
d. 96J
15. In the pin-jointed truss shown, what is the force
in member DE?
Select one:
a. 3500 N
b. 2500 N
c. O
d. 550 N
16. Link AB of the linkage mechanism shown in the
illustration rotates with an instantaneous
counterclockwise angular velosity of 10 rad/s.
What is the instantaneous angular velocity of link
BC when link AB is horizontal and link CD is
vertical?
a. 1.30 m/s
b. 0 m/s
c. 5.20 m/s
d. 1.73 m/s
20. Find the distance between position B and C.
Select one:
a. 3.25 rad/s (counterclockwise)
b. 2.25 rad/s (clockwise)
c. 12.5 rad/s (clockwise)
d. 5.50 rad/s (clockwise)
17. Why does a spinning ice skater's angular
velocity increase as she brings her arms in toward
her body?
Select one:
a. Her angular momentum is constant
b. Her radius of gyration is reduced.
c. Her mass moment of inertia is reduced.
d. all of the above
18. A flywheel rotates at 7200 rev/min when the
power is suddenly cut off. The flywheel decelerates
at a constant rate of 2.1 rad/s2 and comes to rest 6
min later. How many revolutions does the flywheel
make before coming to rest?
Select one:
a. 390 000 rev
b. 18 000 rev
c. 22 000 rev
d. 72 000 rev
19. Two 2 kg block are linked as shown. Assuming
that the surfaces are frictionless, what is the
velocity of block B if block A is moving at a speed of
3 m/s?
Select one:
Select one:
a. 3.23 m
b. 10.1 m
c. 4.78 m
d. 7.78 m
21. A weekend plumber, unable to loosen a pipe
fitting, slips a piece of scrap pipe (a "cheater") over
his wench handle. He then applies his full mass of
100 kg to the end of the cheater by standing on it.
The distance from the center of the fitting on the
point where the weight acts is 0.80 m and the
wrench handle and cheater make an angle of 19°
with the horizontal. Find the magnitude and
direction of the torque he applies about the center
of the pipefitting.
Select one:
a. 740 N
b. 120 N
c. 360 N
d.
520 N
22. A 1530 kg car is towing a 300 kg trailer. The
coefficient of friction between all tires and the road
is 0.80. How fast can the car and trailer travel
around an unbanked curve of radius 200 m without
either the car or trailer skidding?
Select one:
a. 143 km/h
b. 75.2 km/h
c. 40.0 km/h
d. 108.1 km/h
23. A rope passes over a fixed sheave as shown.
The two rope ends are parallel. A fixed load on one
end of the rope is supported by a constant force on
the other end. The coefficient of friction between
the rope and the sheave is 0.30. What is the ratio
of tensile forces in the two rope ends?
Select one:
a. 2.6
b. 1.6
c. 1.2
d. 1.1
24. If the sum of the forces on a particle is not
equal to zero,the particle is
Select one:
a. moving with a constant velocity opposite to the
direction of the resulatnt force.
b. accelerating in a direction opposite to the
resultant force.
c. accelerating in the same direction as the
resultant force.
d. moving with constant velocity in the direction of
the resultant force.
25. What is the -coordinate of the centroid of the
perimeter line?
Select one:
a. 1.66 cm
b. 1.56 cm
c. 1.75 cm
d. 1.80 cm
26. An angle bracket is subjected to the forces and
couple shown. Determine the equivalent forcecouple system at point A
Select one:
a. 292 N at -5.9o ; 103 N.m
b. 333 N at 42.9o ; 53 N.m
c. 114 N at 15.3o ; 50 N.m
d. 307 N at 10.4o ; 110 N.m
27. In the figure, a very small toy race car of mass
m is released from rest on the loop-the-loop track.
If it is released at a height 2R above the floor, how
high is it above the floor when it leaves the track,
neglecting friction?
Select one:
a. 1.33 R
b. 2.00 R
c. 1.67 R
d. 1.50 R
28. Find the acceleration of block A after the blocks
are released.
Select one:
a. 2.5 m/s
b. 0 m/s
c. 1.4 m/s
d. 5.6 m/s
29. Where can a couple be moved on a rigid body
to have an equivalent effect?
Select one:
a. along the perpendicular bisector joining the two
original forces
b. along the line of action
c. anywhere on the rigid body
d. in a parallel plane
30. What is the reaction at point B?
a. potential energy
b. total energy
c. angular velocity
d. linear momentum
Select one:
a. 20 000 N
b. 10 000 N
c. 15 000 N
d. 5000 N
35. A single force (not shown) is applied at point B
in the y-direction, in line with points A and B. What
should this force bein order for the frame to be in
equilibrium in that direction?.
31. Find the -and y-coordinates of the centroid of
wire ABC
Select one:
a. 0.43 m ; 1.29 m
b. 2.71 m ; 1.49 m
c. 3.33 m ; 2.67 m
d. 0.64 m ; 2.83 m
32. For a force to do work it must be ____ the
displacement
Select one:
a. shorter than
b. equal in magnitude to
c. paralllel or antiparallel to
d. perpendicular to
Select one:
a. -280 N (down)
b. 120 N (down)
c. 180 N (down)
d. -250 N (down)
36. A cable passes over a stationary sheave and
supports a 60 kg bucket, as shown. The coefficient
of friction between the cable abd the sheave is
0.10. The cable has a uniform mass per unit length
of 0.4 kg/m. The cable is in the shape of a catenary
due to its own weight. The tension o fthe cable at
the pulley is given by T = wy, where w is the weight
per unit lenght and the constant y (for this
configuration) is known to be 151 m. How much
more mass can be added to the4 bucket before the
cable slips over the pulley?
33. For which of the following situation is the net
force acting on a particle necessarily equal to zero?
Select one:
a. The particle has constant loinear momentum.
b. The particle has constant angular momentum.
c. The particle has constant kinetic energy.
d. The particle is traveling at constant velocity
around a circle.
34. A perfect sphere moves up a frictionless incline.
Which of the following quantities increases?
Select one:
Select one:
a. 12.1 kg
b. 11.6 kg
c. 10.0 kg
d. 0
37. The moment of inertia about the -axis o fthe
cross section shown is 245833 cm4. If the crosssectional area is 250 cm2 and the thickness of the
web and the flanges are the same, what is the
moment of inertia about the centroidal axis?
Select one:
a. 600 N
b. 300 N
c. 100 N
d. 400 N
40. What are the - and y-coordinates of the
centroid of the area?
Select one:
a. 2.1 x 104 cm4
b. 1.5 x 105 cm4
c. 2.5 x 105 cm4
d. 8.0 x 104 cm4
38. Assume that the centroidal moment of inertia
of area A2 with respect to the composite centroidal
-axis is 73.94 cm4. The moment of inertia of area
A2 with respect to the composite centroidal
horizontal axis is 32.47 cm4. What is the moment
of inertia o fthe composite area with respect to its
centroidal -axis?
Select one:
a. 560 cm4
b. 460 cm4
c. 480 cm4
d. 350cm4
39. Find the tension, T, that must be applied to
pulley A to lift the 1200 N weight.
Select one:
a. 3.0 cm ; 4.0 cm
b. 2.4 cm ; 3.4 cm
c. 3.0 cm ; 3.6 cm
d. 3.0 cm ; 3.8 cm
41. Determine the force in member FH for the piconnected truss shown.
Select one:
a. 4130 N (tension)
b. 0
c. 2320 N (compression)
d. 3840 N (tension)
42. What is the period of a pendulum that passes
the center point 20 times a minute.
Select one:
a. 0.2 s
b. 3 s
c. 6 s
d. 0.3 s
43. A 2kg block rests on 34o incline. If the
coefficient of static friction is 0.2, how much
additional force, F, must be applied to keep the
block from sliding down the incline?
Select one:
a. 14 N
b. 9.1 N
c. 7.7 N
d. 8.8 N
44. A uniform rod (AB) of length L and weight W is
pinned at point C. An initial impulse starts the rod
accelerating with an initial angular acceleration (in
rad/s2) of g/L. What is the initial reaction at point
C?
Select one:
a. w/3
b. w/4
c. 4w/7
d. 4w/7
45. What is the radius of gyration about a
horizontal axis passing through the centroid?
Select one:
a. 1.7 cm
b. 0.86 cm
c. 3.7 cm
d. 2.3 cm
46. A 153 kg car is towing a 300 kg trailer. The
coefiicient of friction between all tires and the road
is 0.80. The car and trailer are traveling at 100
km/h around a banked curve of radius 200 m. What
is the necessary banking angle such that tire
friction will not be necessary to prevent skidding?
Select one:
a. 36o
b. 78o
c. 21o
d. 8o
47. A 47.2-kg child is standing on the outer edge of
a merry-go-round that has moment of inertia 543
kg · m2 and radius 2.40 m. The entire system is
initially rotating at 0.180 rev/s. Find the angular
velocity if the child moves to a final position 1.10 m
from the center of the merry-go-round.
Select one:
a. 4.123 rev/s
b. 0.132 rev/s
c. 0.244 rev/s
d. 1.324 rev/s
48. A hollow cylinder has a mass of 2 kg, a height of
1 m, an outer diameter of 1 m, and an inner
diameter of 0.8 m. What is the cylinders mass
moment of inertia about an axis perpendicular to
the cylinders longitudinal axis and located at the
cylinders end?
Select one:
a. 0.79 kg m2
b. 0.87 kg m2
c. 1.49 kg m2
d. 0.41 kg m2
49. Rigid link AB is 12 m long. It rotates
counterclockwise about point A at 12 rev/min. A
thin disk with radius 1.75 m is pinned at its center
to the link at point B. The disk rotates
counterclockwise at 60 rev/min with respect to
point B. What is the maximum tangetial velocity
seen by any point on the disk?
53. A 2 kg mass swings in a vertical plane at the end
of a 2 m cord. When = 30o, the magnitude of the
tangential velo9city of the mass is 1 m/s. What is
the tension in the cord at this position?
Select one:
a. 45 m/s
b. 28 m/s
c. 33 m/s
d. 6 m/s
50. A car is pulling a trailer at 100 km/h. A 5 kg cat
riding on the roof of the car jumps from the car to
the trailer. What is the change in the cat's
momentum?
Select one:
a. -25 N s (loss)
b. 0 N s
c. 1300 N s(gain)
d. 25 N s (gain)
Select one:
a. 19.6 N
b. 29.4 N
c. 18.0 N
d. 24.5 N
54. What total torque is apllied to the pulley?
51. What is the magnitude o fthe couple that
exactly replaces the moment that is removed?
Select one:
a. 2.5 N m
b. 0.16 N m
c. 15 N m
d. 0.08 N m
52. Refer to a particle for which the position is
defined by s(t) = 2 sin tj [tin radians]. What is the
magnitude of the particles velocity at t = 4 rad?
Select one:
a. 3.30
b. 4.12
c. 2.75
d. 2.61
Select one:
a. O
b. 230 N m
c. 300 N m
d. 280 N m
55. A fisherman cuts his boats engine as it is
entering a harbor. The boat comes to a dead stop
with its front end touching the dock. The
fisherman's mass is 80 kg. He moves 5 m from his
seat in the back to the front of the boat in 5 s,
expecting to be able to reach the dock. if the empty
boat has a mass of 300 kg, how far will the
fisherman have to jump to reach the dock?
Select one:
a. 1.3 m
b. 0.0 m
c. 5.0 m
d. 1.9 m
56. A cannonball of mass 10 kg is fired from a
cannon of mass 250 kg. The initial velocity of the
cannonball is 1000 km/h. All of the cannon's recoil
is absorbed by a spring with a spring constant of
250 N/cm. What is the maximum recoil distance of
the cannon?
Select one:
a. 0.59 m
b. 0.35 m
c. 0.92 m
d. 0.77 m
57. The cylinder shown is acted on by couple M.
Wall A is frictionless (&#181s = 0), but the
coefficeint of static friction between the cylinder
and wall B is &#181s = 0.3. The cylinder has a weigh
of 200 N. What is the largest value of the couple M
for which the cylinder will not turn?
If the forces are in equilibrium, and F2 is 11 N, what
is the magnitude of F1?
Select one:
a. 10 N
b. 8 N
c. 12 N
d. 11 N
60. If the car described in Prob.72 moves along a
track that is banked 5o, what is the smallest radius
it can travel without skidding?
Select one:
a. 47 m
b. 6 m
c. 26 m
d. 18 m
61. Find the force in member BC.
Select one:
a. 96 N m
b. 31 N m
c. 72 N m
d. 48 N m
58. Whatb is the polar radius of gyration?
Select one:
a. 4.2 m
b. 4.9 m
c. 3.6 m
d. 4.0 m
59. Three concurrent forces act as shown.
Select one:
a. 50 000 N (compression)
b. 50 000 N (tension)
c. 52 700 N (compression)
d. 16 700 N (tension)
62. A projectile is fired from a cannon with an
initial velocity of 1000 m/s and at an angle of 30o
from the horizontal. What distance from the
cannon will the projectile strike the ground if the
point of impact is 1500 m below the point of
release?
66. Three forces act on a hook. Determine the
magnitude of the resultant of the forces. Neglect
hook bending.
Select one:
a. 90 800 m
b. 78200 m
c. 67300 m
d. 8200 m
63. Quantity of inertia possessed by an object or
the proportion between force and acceleration
Select one:
a. Mass
b. Moment of inertia
c. Velocity
d. Momentum
64. A varying force acts on a 40 kg weight as shown
in the following force versus time diagram. What is
the object's velocity at t = 4 s if the object start
from
Select one:
a. 0.30 m/s
b. 0.075 m/s
c. 0.15 m/s
d. 0 m/s
65. A I kg uniform rod 1 m long is suspended from
the ceiling by a frictionless hinge. The rod is free to
pivot. What is the product of inertia of the about
the pivot point?
Select one:
a. 0 kg m2
b. 0.045 kg m2
c. 0.13 kg m2
d. 0.33 kg m2
Select one:
a. 1250 N
b. 989 N
c. 1510 N
d. 1140 N
67. The support force exerted on an object in
contact with another stable object
Select one:
a. Normal force
b. Weight
c. Tension
d. Gravity
68. Refer to a particle whose curvilinear motions is
represented by the equation s = 20t + 4t2 - 3t3.
What is particles initial velocity?
Select one:
a. 25 m/s
b. 20 m/s
c. 32 m/s
d. 30 m/s
69. What is the tension in cable AB?
Select one:
a. 250 N
b. 430 N
c. 870 N
d. 500 N
70. A 100 kg block is pulled along a smooth, flat
surface by an external 500 N force. If the
coefficient of friction between the block and the
surface is 0.15, what acceleration is experienced by
the block due to the external force?
Select one:
a. 4.33 m/s2
b. 3.23 m/s2
c. 5.00 m/s2
d. 3.80 m/s2
71. A motorist is travelling at 70 km/h when he
sees a traffic light in an intersection 250 m ahead
turn red. The light's red cycle is 15 s. The motorist
wanst to enter the intersection without stopping
his vehicle, just as the light turns green. What
uniform deceleration of the vehicle will just put the
motorist in the intersection when the light turns
greens?
Select one:
a. 0.18 m/s2
b. 1.3 m/s2
c. 0.37 m/s2
d. 25 m/s2
a. 358 rad/s2
b. 794 rad/s2
c. 126 rad/s2
d. 901 rad/s2
74. A 6.0-kg block is released from rest 80m above
the ground. When it has fallen 60m its kinetic
energy is approximately:
Select one:
a. 4800 J
b. 1176 J
c. 3528 J
d. 120 J
75. A particle starting from rest experienced an
acceleration of 3 m/s2 for 2 s. The particle then
returned to rest in a distance of 8 m. Assuming all
accelerations were uniform, what was the total
time elapsed for the particles motion?
Select one:
a. 5.33 s
b. 4.67 s
c. 2.67 s
d. 4.00 s
72. The nuts on a collar are each tightened to 18 N
m torque. 17% of this torque is used to overcome
screw thread friction. The bolts have a nominal
diameter of 10 mm. The threads are a simple
square cut with a pitch abgle of 15o. The
coefficient of friction in the threads is 0.10. What is
the approximate tensile force in each bolt?
76. A rope passes over a fixed sheave as shown.
The two rope ends are parallel. A fixed load on one
end of the rope is supported by a constant force on
the other end. The coefficient of friction between
the rope and the sheave is 0.30. What is the ratio
of tensile forces in the two rope ends?
Select one:
a. 203 N
b. 1620 N
c. 405 N
d. 132 N
Select one:
a. 1.6
b. 1.2
c. 1.1
d. 2.6
73. During the time a compact disc (CD) accelerates
from rest to a constant rotational speed of 477
rev/min, it rotates through an angular
displacement of 0.250 rev. What is the angular
acceleration of the CD
Select one:
77. In an isolated system it does not change with
time when there are no forces acting on the system
Select one:
a. displacement
b. force
c. momentum
d. position
78. The coeffecicient of friction between the
brqake pad and drum is 0.3. Assuming that the
beam supporting the cable drum is more than
adequate for the loads involved, what load,W, can
be held stat5ionary?(Insert question #12)
Select one:
a. 100 N
b. 180 N
c. 33 N
d. 90 N
79. The elevator in a 12--story building has a mass
of 1000 kg. Its maximum velocity and maximum
acceleartion ar 2 m/s and 1 m/s2, respectively. A
paasenger with a mass of 75 kg stands on a
bathroom scale in the elevator as the elevator
ascends at its maximum acceleration. what is the
scale reading just as the elevator reaches its
maximum velocity?
Select one:
a. 886 N
b. 150 N
c. 75 N
d. 811 N
80. The braced frame shown is constructed with
pin-connected members and supports. All applied
forces are horizontal. What is the force in the
diagonal member AB?(Insert question #10)
Select one:
a. 160 N
b. 250 N
c. 0
d. 200 N
81. An automobile travels on a perfectly horizontal,
unblanked circular track of radius r. The coefficient
of friction between the tires and the track is 0.3. If
the car's velocity is 10 m/s, what is the smallest
radius it may travel without skidding?
Select one:
a. 10 m
b. 50 m
c. 34 m
d. 68 m
82. A 10 kg block is resting on a horizontal circular
disk (e.g., turntable) at a radius of 0.5 m form the
center. The coefficient of friction between the
block and disk is 0.2. the disk begins to rotate with
a uniform angular acceleration. What is the
minimum angular velocity of the plate that will
cause the block to slip?
Select one:
a. 4.43 rad /s
b. 1.98 rad/s
c. 3.92 rad /s
d. 1.40 rad/s
83. A rigid body is subjecyed to three cfoncurrent,
coplanar forces. What is the minimum number of
independent equations that are necessary to
establish the equilibrium conditions?
Select one:
a. 3
b. 2
c. 1
d. 0
84. Two meshing spur gears are arranged such that
neither gear is turning and both are in equilibrium.
Gear 1 has a radius of 4 cm. Gear 1's shaft carries a
torsional moment of 65 N m from an external
motor. Gear 2 has a radius of 6 cm. Assuming a
100% transmission efficiency, what torque is
transmitted by the shaft of gear 2?
Select one:
a. 97.5 N m
b. 65 N m
c. 107 N m
d. 101 N m
85. Determine the force in member AG for the pinconneted truss shown.
Select one:
a. 37 500 N (tension)
b. 31 500 N (compression)
c. 25 000 N (compression)
d. 50 000 N (tension)
86. What are the -and y-coordiantes of the centroid
of the area?
Select one:
a. 3.50 cm ; 5.50 cm
b. 3.93 cm ; 4.79 cm
c. 4.00 cm ; 5.00 cm
d. 3.40 cm ; 5.60 cm
87. An ideal spring is hung vertically from the
ceiling. When a 2.0-kg block hangs at rest from it
the spring is extended 6.0 cm from its relaxed
length. A upward external force is then applied to
the block to move it upward a distance of 16 cm.
While the block is moving upward the work done
by the spring is
Select one:
a. -2.09 J
b. -1.75 J
c. -1.05 J
d. -0.52 J
88. Refer to a particle for which the position is
defined by s(t) = 2 sin tj [tin radians]. What is the
ag itude of the pa ti le's a elea tio at t = ?
Select one:
a. 2.00
b. 2.56
c. 4.00
d. 3.14
89. A satellite is placed in a circular orbit to observe
the surface of Mars from an altitude of 144 km.
The equatorial radius of Mars is 3397 km. If the
speed of the satellite is 3480 m/s, what is the
magnitude of the centripetal acceleration of the
satellite?
Select one:
a. 2.99 m/s2
b. 2.17 m/s2
c. 3.42 m/s2
d. 2.60 m/s2
90. A motorist is travelling at 70 km/h when he
sees a traffic light in an intersection 250 m ahead
turn red. The light's red cycle is 15 s. The motorist
wanst to enter the intersection without stopping
his vehicle, just as the light turns green. What
uniform deceleration of the vehicle will just put the
motorist in the intersection when the light turns
greens?
Select one:
a. 0.37 m/s2
b. 25 m/s2
c. 0.18 m/s2
d. 1.3 m/s2
91. The location of a particle moving in the -y plane
is given by the parametric equations = t2 + 4t and y
=(1/4)t4 - 60t, where and y are in meters and t is in
seconds. What I sthe particles velocity at t = 4 s?
Select one:
a. 16.0 m/s
b. 8.95 m/s
c. 11.3 m/s
d. 12.6 m/s
92. The two cables shown carry a 100 N vertical
load. What is the tension in cable AB?
Select one:
a. 80 N
b. 60 N
c. 50 N
d. 40 N
93. The pedestrian bridge truss shown has 10 000
N applied loads at points I,J, and K. What is the
force in member IJ?
Select one:
a. 18 000 N (compression)
b. 8000 N (tension)
c. 8000 N (compression)
d. 18 000 N (tension)
94. A projectile whose mass is 10 g is fired directly
upward from ground level with an initial velocity of
1000 m/s. Neglect the effects of air resistance,
what will be speed of the projectile when it
impacts the ground?
Select one:
a. 981 m/s
b. 1414 m/s
c. 1000 m/s
d. 707 m/s
95. The 285 kg plate shown is suspended
horizontally by four wires of equal loenght, and the
tension of each wire is equal. If wire D snaps, the
tension in the three remaining wires is
redistributed. Determined the tension in each wire
after wire D snaps.
Select one:
a. TA /= 699 N ; TB /= 699 N ; TC /= 1398 N
b. TA /=1398 N ; TB /= 1398 N ; TC /= 0 N
c. TA /
d. TA /= 1398 N ; TB /= 0 N ; TC /= 1398 N
e. TA = 699 N ; TB = 1398 N ; TC = 699 N
96. Identfy the zero-force members in the truss
shown.
Select one:
a. AB,GH,GI,HI,EG
b. AB,GH
c. AB,HI,GI
d. GI,HI
97. Three coplanar forces are in equilibrium on the
surface of a steel plate, as shown. Two of the
forces are known to be 10 N. What is the angle, , of
the third force?
Select one:
a. 82.5o
b. 26.7o
c. 53.8o
d. 7.50o
98. A signal arm carries two traffic signals and a
sign, as shown. The siognals and sign are rigidly
attached to the arm. Each traffic signal is 0.2 m2 in
frontal area and weighs 210 N. The sign weighs 60
N/m2. The design wind pressure is 575 N/m2. The
maximum moment that the connection between
the arm and pole can withstand due to wind is
6000 N m , and the maximum permitted moment
due to the loads is 4000 N m. As limited by
moment on the connection, what is the maximum
area of the sign?
a. 300 000N (tension)
b. 50 000 N (tension)
c. 37 500 N (tension)
d. 350 000 N (tension)
Select one:
a. 5.65 m2
b. 1.15 m2
c. 8.03 m2
d. 1.04 m2
99. A uniform thin disk has a radius of 30 cm and a
mass of 2 kg. A constant force of 10 N is applied
tangentially at a varying, but unknown, distance
from the center of the disk. The disk accelerates
about its axis at 3t rad/s2. What is the distance
from the center of the disk at which the force is
apllied at t = 12 s?
Select one:
a. 108 cm
b. 32.4 cm
c. 54.0 cm
d. 36.0 cm
101. A projectile has an initial velocity of 110 m/s
and a launch angle of 20o from the horizontal. The
surrounding terrain is level, and air friction is to be
disregarded. What is the horizontal distance
traveled by the projectile?
Select one:
a. 1200 m
b. 80 m
c. 800 m
d. 400 m
102. QUEST032::Figure shows a uniform disk, with
mass M = 2.5 kg and radius R = 20 cm, mounted on
a fixed horizontal axle. A block with mass m = 1.2
kg hangs from a massless cord that is wrapped
around the rim of the disk. Find the acceleration of
the falling block. The cord does not slip, and there
is no friction at the axle.
Select one:
a. -4.8 m/s2
b. 4.8 m/s2
c. -3.2 m/s2
d. 3.2 m/s2
103. Find the velocity of block A 2.5 s after the
blocks are released.
100. Four bolts (not shown) connect support A to
the ground. Determine the design load for each o
fthe four bolts.
Select one:
a. 3.5 m/s
b. 0 m/s
c. 4.4 m/s
d. 4.9 m/s
Select one:
104. A box has uniform density and a total weight
of 600 N. It is suspended by three equal-length
cables, AE,BE, and CE, as shown. Point E is 0.5 m
directly above the center of the box's top surface.
What is the tension in cable CE?
Select one:
a. 400 N
b. 200 N
c. 128 N
d. 370 N
Select one:
a. 41 kg mo
b. 16 kg mo
c. 150 kg mo
d. 4.1 kg mo
108. A rope is wrapped over a 6 cm diameter pipe
to support a bucket of tools being lowered. The
coefficient of friction between the rope and the
pipe is 0.20. The combined mass of bucket and
tools is 100 kg. What is the range of force that can
be applied to the free end of the rope such that the
bucket remains stationary?
105. The five forces shown act at point A. What is
the magnitude of the resultant force?
Select one:
Select one:
a. 720 N to 1360 N
b. 560 N to 1360 N
c. 720 N to 1510 N
d. 670 N to 1440 N
a. 234 N
b. 182 N
c. 156 N
d. 32 N
109. A model T-beam is constructed from five balsa
boards. Refer to the illustration for the as-built
dimensions. What is the approximate centroidal
moment of inertia about an axis parallel to the axis?
106. Determine the reaction at point C.
Select one:
a. -417 N (down)
b. + 83 N (down)
c. +333 N (up)
d. -83 N (down)
107. A 50 kg cylinder has a height of 3 m and a
radius of 50 cm. The cylinder sits on the -axis and is
oriented with its major axis parallel to the y-axis.
What is the mass moment of inertia about the axis?
Select one:
a. 660 cm4
b. 600 cm4
c. 500 cm4
d. 560 cm4
110. A 3 kg disk with a diameter of 0.6 m is rigidly
attached at point B to 1 kg rod 1 m in length. The
rod-disk combination rotates around point A. What
is the mass moment of inertia about A for the
combinanation
Select one:
a. 1530 m4
b. 1020 m4
c. 2410 m4
d. 1260 m4
114. An area is a composite of a semicircle and a
triangle, as shown. What is the distance between
the -axis an dthe centroid?
Select one:
a. 0.56 kg m2
b. 0.87 kg m2
c. 047 kg m2
d. 3.7 kg m2
111. A 2.5-kg ball and a 5.0-kg ball have an elastic
collision. Before the collision, the 2.5-kg ball was at
rest and the other ball had a speed of 3.5 m/s.
What is the kinetic energy of the 2.5-kg ball after
the collision?_____"
Select one:
a. 27 J
b. 14 J
c. 5.8 J
d. 8.1 J
112. A spring has a constant of 50 N/m. The spring
is hung vertically, and a mass is attached to its end.
The spring end displaces 30 cm from its equilibrium
position. The same mass is removed from the first
spring and attached to the end of a second
(different) spring, and the displacement is 25 cm.
What is the spring constant of the second spring?
Select one:
a. 63 N/m
b. 56 N/m
c. 60 N/m
d. 46 N/m
113. What is the polar moment of nertia about the
composite centroid?
Select one:
a. 3.46 mm
b. 3.68 mm
c. 5.35 mm
d. 4.28 mm
115. Find the velocity at position B.
Select one:
a. 9.83 m/s
b. 6.95 m/s
c. 2.41 m/s
d. 4.12 m/s
116. In the structure shown, the beam is pinned at
point B. Point E is a roller support. The beam is
loaded with a distributed load from point A to
point B of 400 N/m, a 500 N m couple at point C,
and a vertical 900 N force at point D. If the
distributed load and the vertical load are removed
and replaced with a vertical upward force of 1700
N at point F, what moment at point F would be
necessary to keep the reaction at point E at the
same?.
Select one:
a. -6500 N m (counterclockwise)
b. 12 000 N m (clockwise)
c. 3500 N m (clockwise)
d. -9000 N m (counterclockwise)
117. What is the magnitude of the forces that
constitute the moment?
Select one:
a. 8.3 N
b. 6.3 N
c. 4.2 N
d. 2.1 N
118. A 28 mm diameter circuit area is reduced by a
21 mm diameter circular area that is cut out. Both
circles are tangent to the y-axis. What is the
moment of inertia about the y-axis of the
remaining (shaded) area?
Select one:
a. 103 000 mm4
b. 330 000 mm4
c. 1340 000 mm4
d. 20 600 mm4
A gle θ of the incline is 30°. Block A slides down
the incline at constant speed. What is the mass of
block B
Select one:
a. 2.1 kg
b. 5.0 kg
c. 3.7 kg
d. 3.3 kg
121. The center of gravity of a roller coaster car is
0.5 m above the rails. The rails are 1 m part. What
is the maximum speed that the car can travel
around an unbanked curve of radius 15 m without
the inner wheel losing contact with the top of the
rail?
Select one:
a. 8.58 m/s
b. 17.2 m/s
c. 24.2 m/s
d. 12.1 m/s
122. Two particles are fixed to an x axis : particle 1
of charge -2.00 x 10-7 C at x=6.00 cm and particle 2
of charge +2.00 x 10-7 C at x=21.0 cm. Midway
between the particles, what is their net electric
field in unit vector notation?
Select one:
a. -3.20 X 10 N/C i ̂
b. - . x
N/C i ̂
.- . x
N/C i ̂
d. - . x
N/C i ̂
119. What is the coefficient of friction between the
plane and the block?
Select one:
a. 0.15
b. 0.78
c. 0.22
d. 0.85
123. Find the force in member DE.
120. Two blocks are connected over a pulley. The
mass of block A is 10 kg and the coefficient of
kinetic friction between A and the incline is 0.20.
Select one:
a. 8800 N (tension)
b. 10 000 N (compresiion)
c. 0
d. 6300 N (tension)
124. A force is defined by the vector A = 3.5 i - 1.5 j
+ 2.0k. i,j, and k are unit vectors in the -,y-, and zdirection, respectively. What is the angle that the
force makes with the positive y-axis?
b. mg
c. –mx2
d. None of the choices
128. A car with a mass of 1530 kg tows a trailer
(mass of 200 kg) at 100 km/h. What is the total
momentum of the car-trailer combination?
Select one:
a. 46 000 N s
b. 22 N s
c. 37 N s
d. 48 000 N s
129. If W = 80 N, what are the reactions
at pont A?
Select one:
a. 69.6o
b. 20.4o
c. 110o
d. 66.4o
125. The position (in radians) of a car travelling
around a curve is described by the following
function of time (in seconds). What is the angular
velocity at t = 3 s?
Select one:
a. -16 rad/s
b. -4 rad /s
c. 15 rad/s
d. 11 rad/s
126. A stone is dropped down a well. 2.47 s after
the stone is realeased, a splash is heard. If the
velocity of sound in air is 342 m/s, find the distance
to the surface of the water in the well.
Select one:
a. 38 m
b. 2.4 m
c. 28 m
d. 7.2 m
127. The maximum kinetic and potential energy of
a spring when stretched at various displacements is
equal to
Select one:
a. 1 /2Kx2
Select one:
a. 27 i N - 100j N
b. -27 i N - 100j N
c. 0 i N+ 180j N
d. 0 i N + 100j N
130. A parallel-plate air capacitor is made from two
plates 0.070 m square, spaced 6.3 mmapart. What
must the potential difference between the plates
be to produce an energydensity of 0.037 J/m3?
Select one:
a. 470 V
b. 370V
c. 270 V
d. 570 V
131. Block d side freely on the homogeneous bar
and experiences a gravitation force of 50 N.
Homogeneous bar AB experiences a gravitational
force of 25 N. What is the force between the bar
and block D?
Select one:
a. 21 N
b. 19 N
c. 15 N
d. 28 N
132. A motorist is travelling at 70 km/h when he
sees a traffic light in an intersection 250 m ahead
turn red. The light's red cycle is 15 s. The motorist
wanst to enter the intersection without stopping
his vehicle, just as the light turns green. If the
vehicle decelerates at a constant rate of 0.5 m/s2,
what will be its speed when the light turns green?
Select one:
a. 52 km/h
b. 63 km/h
c. 43 km/h
d. 59 km/h
133. Which of the structures shown is statically
determinant and stable?
Select one:
134. The rotor of a steam turbine is rotating at
7200 rev/min when the steam supply is suddenly
cut off. The rotor decelerates at a constant rate
and comes to rest after 5 min. What was the
angular deceleration of the rotor?
Select one:
a. 2.5 rad/s2
b. 5.8 rad/s2
c. 0.40 rad/s2
d. 16 rad/s2
135. A 6 kg sphere moving at 3m/s collides with a
10 kg sphere traveling 2.5 m/s in the same
direction. The 6 kg ball comes to a complete stop
after the collision. What is the new velocity of the
10 kg ball immediately after the collision?
Select one:
a. 0.5 m/s
b. 5.5 m/s
c. 2.8 m/s
d. 4.3 m/s
136. Which type of load is not resisted by a pinned
joint?
Select one:
a. compression
b. moment
c. shear
d. axial
137. What is the resultant R of the system of forces
shown?
Select one:
a. I and III
b. I and IV
c. I only
d. II and III
d. 890 N m
a.
b.
c.
d.
138. If the frame is pinned so that it rotates around
point B, what counteracting moment must be
applied at point A to put the frame in equilibrium?
Select one:
a. 1150 N m
b. 1240 N m
c. 650 N m
140. An isolated parallel-plate capacitor (not
connected to a battery) has a charge of Q = 2.9 ×
10-5 C. The separation between the plates initially
is d = 1.2 mm, and for this separation the
capacitance is 3.1 × 10-11 F. Calculate the work
that must be done to pull the plates apart until
their separation becomes 5.3 mm, if the charge on
the plates remains constant. The capacitor plates
are in a vacuum
Select one:
a. 5 J
b. 46 J
c. 48 J
d. 47 J
141. A wheel with a radius of 80 cm rolls along a
flat surface at 3 m/s. If arc AB on the wheels
perimeter measures 90o, what is the velocity of
point A when point B contacts the ground?
Select one:
a. 3.39 m/s
b. 3.75 m/s
c. 4.24 m/s
d. 3.00 m/s
142. A disk-shaped bofy with a 4 cm radius has a
320 N force acting through the center at an
unknown angle , and two 40 N loads acting as a
couple, as shown. All of these forces are removed
and replaced by a single 320 N force at point B,
parallel to the original 320 N force. What is the
angle ?
Select one:
a. 0o
b. 7.6o
c. 15o
d. 29o
143. A block with a mass of 150 kg is pulled over a
horizontal surface by a cable guided by a pulley as
shown. The coefficients of friction are 0.58
between the surface and the block, and 0.90
between the cable and the pulley. What force,F,
must be applied to the cable for the block to
move?
Select one:
a. 2500 N
b. 900 N
c. 1700 N
d. 2200 N
144. Refer to a particle whose curvilinear motions
is represented by the equation s = 20t + 4t2 - 3t3.
What is the acceleration of the particle at time t =
0?
Select one:
a. 2 m/s2
b. 5 m/s2
c. 3 m/s2
d. 8 m/s2
145. A playground merry-go-round has a radius of
3.0m and a rotational inertia of 600 kg m2.It is
initially spinning at 0.80 rad/s when a 20-kg child
crawls from the center to the rim. When the child
reaches the rim the angular velocity of the merrygo-round is
Select one:
a. 0.80 rad/s
b. 1.04 rad/s
c. 0.73 rad/s
d. 0.62 rad/s
146. Traffic travels at 100 km/h around a banked
high-way curve with a radius of 1000m. What
banking angle is necessary such that friction will
not be required to resist the centrifugal force?
Select one:
a. 46o
b. 2.8o
c. 4.5o
d. 1.4o
147. Resolve the 300 N force into two components,
one along line p and the other along line Q. (F, P
and Q are coplanar.)
Select one:
a. Fp = 126 N ; FQ /= 272 N
b. Fp = 226 N ; FQ = 135 N
c. Fp = 186 N ; FQ /= 232 N
d. Fp = 226 N ; FQ /=212 N
148. Determine the force in member BC.
Select one:
a. 1000 N (compression)
b. 2500 N (tension)
c. 1500 N (tension)
d. 0
. The state e t A o je t ith o sta t
o e tu is i a state of e uili iu is
Select one:
a. Insufficient data
b. False
c. Partly true
d. True
150. The velocity (in m/s) of a falling ball is
described by the equation v = 32 + t + 6t2. What I
sthe acceleration at time t = 2 s?
Select one:
a. 25 m/s2
b. 9.8 m/s2
c. 58 m/s2
d. 32 m/s2
151. A particle has a tangential acceleration of at
(represented by the equation given) when it moves
around a point in a curve with instantaneous radius
of 1 m. What is the instantaneous angular velocity (
in rad/s) of the particle?
Select one:
a. t2+cost+ 3 In |csct|
b. t2-cost+ 3 In |csct|
c. t2-cost+ 3 In |sint|
d. t2+cost+ 3 In |sint|
152. A golfer on level ground attempts to drive a
gof ball across a 50 m wide pond, hitting the ball so
that it travels initially at 25 m/s. The ball travels at
an initial angle of 45o to the horizontal plane. How
far will the golf ball travel, and does it clear the
pond?
Select one:
a. 58 m; the ball clears the pond
b. 32 n; the ball does not clear the pond
c. 45 m; the ball does not clear the pond
d. 64 m ; the ball clears the pond
153. A 2000 kg car pulls a 500 kg trailer. The car
and trailer accelerates from 50 km/h to 75 km/h at
rate of 1 m/s2. What linear impules does the car
impart on the trailer?
Select one:
a. 12 500 N s
b. 3470 N s
c. 17400 N s
d. 8680 N s
pulley. The mass of block A is 10 kg and the
coefficient of kinetic friction between A and the
incline is 0.20. Angle θ of the i li e is °. Blo k A
slides down the incline at constant speed. What is
the mass of block B
Select one:
a. 3.7 kg
b. 3.3 kg
c. 2.1 kg
d. 5.0 kg
156. A mass of 10 kg is suspended from a vertical
spring with a spring constant of 10 N/m. What is
the period of vibration?
Select one:
a. 6.3 s
b. 0.30 s
c. 0.60 s
d. 0.90 s
157. What is the reaction at point A for the simply
supported beam shown?
Select one:
a.
b. None of the choices
154. What are R1 and R2? (insert question #11)
Select one:
a. 1250 N
b. 4000 N
c. R1 /
d. 1000 N; R2 /
e. R1 /
f. R1 /
g. 3750 N; R2 /
h. 1250 N
155. QUEST029::Two blocks are connected over a
c.
d.
158. A bent beam is acted upon by a moment and
several concentrated forces, as shown. Find the
missing force F and distance that will maintain
equilibrium on the member shown.
45o from the horizontal. What is the velocity of
point P at that instant?
Select one:
a. 10.0 m/s15.0 m/s16.2 m/s
b. 18.5 m/s
Select one:
a. F = 20 N ; = 0.2 m
b. F = 10 N ; = 0.6 m
c. F = 20 N ; = 0.4 m
d. F = 5 N ; = 0.8 m
159. A car travels around an unbanked 50 m radius
curve without skidding. The coefficient of friction
between the tires and road is 0.3. What is the car's
maximum speed?
Select one:
a. 54 km/h
b. 25 km/h
c. 44 km/h
d. 14 km/h
160. A force that is directed away or towards the
origin
Select one:
a. Frictional force
b. Uniform force
c. Central force
d. Normal force
161. QUEST030::The small piston of a hydraulic lift
has a cross-sectional area of 3.00 cm2, and its large
piston has a cross-sectional area of 200 cm2 . What
force must be applied to the small piston for it to
raise a load of 15.0 kN? (In service stations, this
force is usually generated with the use of
compressed air.)
Select one:
a. 1.00 X 102 N
b. 40 N
c. 1.00 x 103 N
d. 225 N
162. A disk rolls along a flat surface at a constant
speed of 10 m/s. Its diameter is 0.5 m. At a
particular instant, point P on the edge of the disk is
163. For the reciprocating pump shown, the radius
of the crank is r = 0.3 m, and the rotational speed is
n = 350 rpm. What is the tangetial velocity of point
A on the crank corresponding to an angle of = 35o
from the horizontal?
Select one:
a. 10 m/s
b. 1.1 m/s
c. 0 m/s
d. 11 m/s
164. What is the -coordinate of the centroid of the
curve y = cos between = 0 = /2?
a. pi/4
b. pi/6
c. 1 – 2/pi
d. pi/2 – 1
165. QUEST031::Two particles are fixed to an x axis
: particle 1 of charge -2.00 x 10-7 C at x=6.00 cm
and particle 2 of charge +2.00 x 10-7 C at x=21.0
cm. Midway between the particles, what is their
net electric field in unit vector notation?
Select one:
a. - . x
N/C i ̂
b. - . x
N/C i ̂
.- . x
N/C i ̂
d. - . X
N/C i ̂
166. Refer to a particle whose curvilinear motions
is represented by the equation s = 20t + 4t2 - 3t3.
What is the maximum speed reached by the
particle?
Select one:
a. 34.6 m/s
b. 27.9 m/s
c. 48.0 m/s
d. 21.8 m/s
167. A torsional pendulum consists of a 5 kg
uniform disk with a diameter of 50 cm attached at
its center to a rod 1.5 m in length. The torsional
spring constant is 0.625 N.m/rad. Disregarding the
mass of the rod, what is the natural frequency of
the torsional pendulum?
Select one:
a. 1.0 rad/s
b. 1.4 rad/s
c. 1.2 rad/s
d. 2.0 rad/s
168. The position (in radians) of a car travelling
around a curve is described by the following
function of time (in seconds). What is the angular
acceleration at t = 5 s?
Select one:
a. 4 rad/s2
b. 26 rad/s2
c. 30 rad/s2
d. 6 rad/s2