multiple choice questions in engineering mathematics by perfecto b. padilla jr
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MULTIPLE CHOICE QUESTIONS IN
MATHEMATICS
PERFECTO B. PADILLA JR
AND
DIEGO INOCENCIO TAPANG GILLESANIA
ENCODED BY: BAUTISTA, HEZZIELEEN F.
1. What is the allowable error in measuring the edge of a cube that is intended to hold 8 cu.m, if the error of the compound volume is not to exceed 0.03m3? a. 0.002 b. 0.001 c. 0.0025 d. 0.0001
2. Find the area bounded by the parabola
and its latus rectum. a.10.67 sq. units b. 32 sq. units c. 48 sq. units d. 16.67 sq. units
3. The effective rate of 14% compounded semi-annually is: a. 14.49% b. 12.36% c. 12.94% d. 14.88%
4. is the equation of
_______? a. Parallel sides b. Parabola c. Circle d. Ellipse
5. A section in a coliseum has 32 seats in
the 1st row, 34 in the 2nd row, 36 in the 3rd row, . . and 48 in the 9th row. From the 10th up to the 20th row, all have 50 seats. Find the seating capacity of this section of the coliseum. a. 908 b. 900 c. 920 d. 910
6. Smallest term that can be factored from a number a. Greater b. None of these c. equal d. lesser
7. How many horsepower are there in 800 kW? a. 2072.4 hp b. 746 hp c. 1072.4 hp d. 3072.4 hp
8. A man roes downstream at the rate of 5
mph and upstream at the rate of 2 mph. how far downstream should he go if he is to return 7/4 hour after leaving? a. 2.5 mi b. 3.3 mi c. 3.1 mi d. 2.7 mi
9. Find the angular velocity of a flywheel
whose radius is 20 ft. if it is revolving at 20 000 ft/min a. 500 rad/min b. 750 rad/min c. 1000 rad/min d. 800 rad/min
10. Find the area of parabolic segment
whose base is 10 and height of 9 meters. a. 60 m2 b. 70 m2 c. 75 m2 d. 65 m2
11. A line which a curve approach infinity
but will never intersect. a. Parallel line
b. Assymptote c. Inclined line d. Skew line
12. An organization that aims to block the
entry of a new comer. a. Monopoly b. Cartel c. Competitor d. Proprietor
13. The tens digit of a two-digit number is 1
less than twice the unit’s digit. They differ by 4. Find the number. a. 65 b. 95 c. 84 d. 73
14. At the surface of the earth g=9.806 m/s2. Assuming the earth to be a sphere of radius 6.371x106m. Compute the mass of the earth. a. 5.97x1024 kg b. 5.62 x1024 kg c. 5.12 x1024 kg d. 5.97 x1023 kg
15. A material has a modulus of elasticity of
200 GPa. Find the minimum cross sectional area of the said material so as not to elongate by more than 5mm for every 2m length when subjected to 10 kN tensile force. a. 20 mm2 b. 10 mm2 c. 30 mm2 d. 40 mm2
16. At what temperature is the ˚C and ˚F
numerically the same? a. 40˚ b. 32˚ c. -40˚ d. -32˚
17. On ordinary day, 400 m3 of air has a
temperature of 30˚C. During El Nino drought, temperature increased to 40˚C. Find the volume of air of k=3670x10-6. a. 416.86 m3 b. 418.86 m3 c. 414.68 m3 d. 416.48 m3
18. A sphere has a volume of 36π cubic
meters. The rate of change in volume is 9π cubic meters per minute. Find the rate of change in area of the sphere. a. 6 π m2/min b. 2 π m2/min c. 3 π m2/min d. 4 π m2/min
19. Sin A=2.5x, cos A= 5.5x. Find A.
a. 34.44˚ b. 24.44˚ c. 44.44˚ d. 64.44˚
20. A ladder 5 meter long leans on a wall and makes an angle of 30˚ with the horizontal. Find the vertical height from the top to the ground. a. 2.5 meter b. 1.5 meter c. 2.0 meter d. 2.75 meter
21. A rectangular lot is bounded on its two
adjacent sides by existing concrete walls. If it is to be fenced along two remaining sides and the available fencing material is 30 meters long, find the largest possible area of the lot. a. 200 sq. m b. 225 sq. m
c. 175 sq. m d. 250 sq. m
22. A tangent line intersects a secant line to
a circle. If the distance from the point of tangency to the point of intersection is 6, and the external distance of the secant line is 4, find the length of the secant line. a. 5 b. 7 c. 8 d. 9
23. In an oblique triangle, a=25, b=16, angle
C=94˚06’. Find the measure of angle A. a. 54.5˚ b. 45.5˚ c. 24.5˚ d. 54.5˚
24. Q=25 when t=0. Q=75 when t=2. What
is Q when t=6? a. 185 b. 145 c. 150 d. 175
25. Pipes A and B can fill an empty tank in 6
and 3 hours respectively. Drain C can empty a full tank in 24 hours. How long will an empty tank be filled if pipes A and B with drain C open? a. 1.218 hours b. 2.182 hours c. 5.324 hours d. 3.821 hours
26. Find the tangential velocity of a flywheel whose radius is 14 ft. if it is revolving at 200 rpm. a. 17 593 ft/min b. 18 593 ft/min c. 19 593 ft/min
d. 12 593 ft/min
27. A ball is thrown vertically upward at a velocity of 10 m/s. What is its velocity at the maximum height? a. 10 m/s b. 0 c. 5 m/s d. 15 m/s
28. The volume of a sphere is tripled. What
is the increase in surface area if the radius of the original sphere is 50 cm.? a. 34 931.83 sq. units b. 33 931.83 sq. units c. 35 931.83 sq. units d. 36 931.83 sq. units
29. Given a right triangle ABC. Angle C is the
right triangle. BC=4 and the altitude to the hypotenuse is 1 unit. Find the area of the triangle. a. 2.0654 sq. units b. 1.0654 sq. units c. 3.0654 sq. units d. 4.0645 sq. units
30. Find the equation of a parabola passing
through (3, 1), (0, 0), and (8, 4) and whose axis is parallel to the x-axis. a. b. c. d.
31. Pedro runs with a speed of 20 kph. Five
minutes later, Mario starts running to catch Pedro in 20 minutes. Find the velocity of Mario. a. 22.5 kph b. 25 kph c. 27.5 kph d. 30 kph
32. How much do ten P2000 quarterly
payments amount at present if the interest rate is 10% compounded quarterly. a. P17 771.40 b. P17 504.13 c. P18 504.13 d. P71 504.13
33. A man bought a machine costing P135
000 with a salvage value of P20 000 after 3 years. If the man will sell it after 2 years, how much is the loss or gain (i.e. the cost of equipment) if i=10%. a. P134 350 b. P143 350 c. P153 350 d. P163 350
34. P1000 becomes P1500 in three years.
Find the simple interest rate. a. 16.67% b. 15.67% c. 17.67% d. 18.67%
35. Form of paper money issued by the
central bank. a. T-bills b. Check c. Cash d. Stocks
36. _________ is the concept of finding the
derivative of an exponential expression. a. Logarithmic derivative b. Chain rule c. Trigonometric derivative d. Implicit derivative
37. The line y=5 is the directrix of a
parabola whose focus is at point (4, -3). Find the length of the latus rectum. a. 8 b. 4
c. 16 d. 24
38. 2.25 revolutions are how many
degrees? a. 810˚ b. 730˚ c. 190˚ d. 490˚
39. The sum of two numbers is 21 and their product is 108. Find the sum of their reciprocals.
a.
b.
c.
d.
40. What is the accumulated amount of
five years annuity paying P 6000 at the end of each year, with interest at 15% compounded annually? a. P40 454.29 b. P41 114.29 c. P41 454.29 d. P40 544.29
41. Ana is 5 years older than Beth. In 5
years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now? a. 25 b. 20 c. 15 d. 30
42. In , x=
distance in meters, and t= time in seconds. What is the initial velocity? a. 2000 m/s b. 3000 m/s c. 4000 m/s d. 5000 m/s
43. The highest point that a girl on a swing
reaches is 7 ft above the ground, while the lowest point is 3 ft above the ground. Find its tangential velocity at the lowest point. a. 16.05 ft/sec b. 12.05 ft/sec c. 20.05 ft/sec d. 12.05 ft/sec
44. If m=tan25˚, find the value of
in terms of m.
a. -1/m
b.
c.
d. –m
45. A VOM has a current selling price of P400. If it’s selling price is expected to decline at the rate of 10% per annum due to obsolence, what will be its selling price after 5 years? a. P236.20 b. P200.00 c. P213.10 d. P245.50
46. Evaluate ∫
dx
a. 1.051 b. 1.501 c. 3.21 d. 2.321
47. Fin the eccentricity of an ellipse when
the length of the latus rectum is 2/3 the length of the major axis. a. 0.577 b. 0.477 c. 0.333 d. 0.643
48. What is the book value of an electronic test equipment after 8 years of use if it depreciates from its original value of P120 000 to its salvage value of 13% in 12 years. Use straight line method. a. P20 794.76 b. P50 400 c. P40 794.76 d. P50 794.76
49. What is the book value of an electronic
test equipment after 8 years of use if it depreciates from its original value of P120 000 to its salvage value of 13% in 12 years. Use declining balance method. a. P20 794.76 b. P30 794.76 c. P40 794.76 d. P50 794.76
50. A balloon is released from the ground
100 meters from an observer. The balloon rises directly upward at the rate of 4 meters per second. How fast is the balloon receding from the observer 10 seconds later? a. 1.4856 m/s b. 2.4856 m/s c. 3.4856 m/s d. 5 m/s
51. Divide 120 into two parts so that product of one and the square of another is maximum. Find the small number. a. 60 b. 50 c. 40 d. 30
52.
. What is the period?
. π .2 π .4 π .3 π
53. A horizontal force of 80 000 N is applied
unto a 120 ton load in 10 seconds. Find its acceleration. a. 0.67 m/s2 b. 0.75 m/s2 c. 1.05 m/s2 d. 1.35 m/s2
54. A plane is headed due to east with
airspeed 240 mph. if a wind at 40 mph from the north is blowing; find the groundspeed of the plane. a. 342 mph b. 532 mph c. 243 mph d. 4123 mph
55. The ratio of radii of cone and cylinder is
1:2 while the ratio of radius of cone to its altitude is 1:3. If lateral surface area of cylinder equals volume of cone, find the radius of the cone if the altitude of cylinder is 4. a. 5 b. 4 c. 3 d. 6
56. If a derivative of a function is constant,
the function is: a. First degree b. Exponential c. Logarithmic d. Sinusoidal
57. 2700 mils is how many degrees?
a. 151.875˚ b. 270˚ c. 180˚ d. 131.875˚
58. An air has an initial pressure of 100kPa absolute and volume 1 m3. If pressure will be increased to 120 kPa, find the new volume. a. 1.2 m3
b. 0.83 m3 c. 0.63 m3 d. 1.5 m3
59. The pistons (A&B) of a hydraulic jack are
at the same level. Pistol A is 100 cm2 while piston B is 500 cm2. Piston A carries a 500 kg load. Find the required force F at piston B to carry the load. a. 3.5 tons b. 2.5 tons c. 4.5 tons d. 1.5 tons
60. A rectangular dodecagon is inscribed in a circle whose radius is 1 unit. Find the perimeter. a. 5.21 b. 6.21 c. 7.21 d. 8.21
61. In a box, there are 52 coins, consisting
of quarters, nickels, and dimes with a total amount of $2.75. If the nickel were dimes, the dimes were quarters and the quarters were nickels; the total amount would be $3.75. How many quarters are there? a. 16 b. 10 c. 5 d.12
62. A stone is thrown vertically upward at 12 m/s. Find the time to reach the ground. a. 2.45 secs. b. 1.35 secs. c. 2.15 secs. d. 1.95 secs.
63. A regular polygon has 27 diagonals.
Then it is a : a. Pentagon b. Heptagon
c. Nonagon d. Hexagon
64. A 50 meter cable is divided into two parts and formed into squares. If the sum of the areas is 100 sq. meter, find the difference in length? a. 21.5 b. 20.5 c. 24.5 d. 0
65. What theorem is used to solve for
centroid? a. Pappus b. Varignon’s c. Castiglliano’s d. Pascal’s
66. ∫
a. tan x – x + c b. x - tan x + c c. sec x d. sec x tan x
67. A hyperbola has its center at point (1,
2), vertex at (2, 2) and conjugate vertex at (1, 0). Find the equation. a. 4x2-y2-8x+4y-4=0 b. x2-4y2-8x+4y-4=0 c. 4x2-y2-8x-4y-4=0 d. x2-4y2+8x-4y-4=0
68. A pipe can fill a tank in 2 hours. A drain
can empty a full tank in 6 hours. If the pipe runs with the drain open, how long will take to fill-up an empty tank? a. 2.5 hrs b. 4 hrs c. 3 hrs d. 3.5 hrs
69. Fin the 7th term in the series:
,
,
, . .
a.
b.
c.
d.
70. Find the length of the larger base of the largest isosceles trapezoid if the legs and smaller base measure 8 units. a. 8 b. 16 c. 10 d. 20
71. y=arctan ln x. Find y’.
a.
b.
c.
d.
72. The general equation of a conic section whose axis is inclined is given by Ax2+Bxy+Cy2+Dx+Ey+F=0. When B2-4 Ac=0, the curve is a/an _____. a. Hyperbola b. Parabola c. Ellipse d. Circle
73. The time required for two examinees to
solve the same problem differs 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. 2 min b. 3 min c. 4 min d. 5 min
74. cos4 θ – sin4 θ= ? a. sin 2θ b. cos 2θ c. cos 4θ d. cos 3θ
75. A function wherein one variable is not yet readily expressed as function of another variable is said to be: a. symmetric b. implicit c. explicit d. exponential
76. Given an ellipse
+
=1. Determine the
distance between directrix: a. 3 b. 4 c. 2 d. 8
77. Three forces 20N, 30N, and 40N are in
equilibrium. Find the angle between 30N and 40N forces. a. 28.96˚ b. 25.97˚ c. 40˚ d. 30˚15’25”
78. At the inflection point where x=a
a. f”(a) > 0 b. f”(a) < 0 c. f”(a) = 0 d. f”(a) is no equal to zero
79. A merchant has three items on sale
namely: a radio for $50.00, a clock for $30.00 and a flashlight for $1.00. At the end of the day, she has sold a total of 100 of the three sale items and has taken in exactly $1, 000.00 on the total sales, how many radios did she sell? a. 4
b. 80 c. 16 d. 20
80. Which of the following is true?
a. sin(-θ)= sin θ b. tan(-θ)= tan θ c. cos(-θ)= cos θ d. csc(-θ)= csc θ
81. _______ is the loss of value of the
equipment with use over a period of time. It could mean a difference in value between a new asset and the used asset currently in service. a. Loss b. Depreciation c. Gain d. Extracted
82. Find the area bounded by the curve
defined by the equation x2=8y and its latus rectum. a. 11/3 b. 32/3 c. 16/3 d. 22/3
83. The height of a right circular cylinder is
50 inches and decreases at the rate of 4 inches per second. While the radius of the base is 20 inches and increases at the rate of one inch per second. At what rate is the volume changing? a. 11 130 cu. in/sec b. 11 310 cu. in/sec c. 1 275 cu. in/sec d. 1 257 cu. in/sec
84. This occurs in a situation where a
commodity or service is supplied by a number of vendors and there is nothing to prevent additional vendors entering the market. a. Elastic demand b. Perfect competition
c. Monopoly d. Oligopoly
85. The graphical representation of the
cumulative frequency distribution in a set statistical data is called? a. Frequency polygon b. Mass diagram c. Ogive d. Histogram
86. If the product of the slopes of two
straight lines is negative 1, one of these lines are said to be: a. Skew b. Non-intersecting c. Parallel d. Perpendicular
87. Pedro can paint a fence 50% faster than
Juan and 20% faster that 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. 10 hrs b. 13 hrs c. 11 hrs d. 15 hrs
88. If you borrowed money from your
friend with simple interest of 12%, find the present worth of P50 000, which is due at the end of 7 months. a. P46 200 b. 44 893 c. P46 729 d. 45 789
89. The amount of P12 800 in 4 years at 5% compounded quarterly is? a. P14 785.34 b. P15 614.59 c. P16 311.26
d. P15 847.33
90. What is the effective rate corresponding to 18% compounded daily? Take 1 year =365 days. a. 17.35% b. 19.72% c. 17.84% d. 16.78%
91. In how many ways can 2 integers be
selected from the integers 1 to 100 so that their difference is exactly 7? a. 74 b. 81 c. 69 d. 93
92. A 2 lbs liquid has an specific heat of 1.2
Btu/ lb-˚F. How much heat is required to increase its temperature by 10˚C? a. 100BTU b. 110BTU c. 120 BTU d. 130 BTU
93. A machine costing P100 000 depreciates
at 10% annually. What is its book value after 5 years? a. P59 049 b. P69 049 c. P49 049 d. P79 049
94. Find the length of the latus rectum of
the parabola y2=-8x? a. 8 b. 9 c. 7 d. 6
95. The property by virtue of which a body tends to return to its original size and shape after a deformation and when the deforming forces have been removed. a. Elasticity b. Malleability c. Ductility d. Plasticity
96. A man wants to make 14% nominal
interest compounded semi-annually on a bond investment. How should the man be willing to pay now for 12% -P10 000 bond that will mature in 10 years and pays interest semi-annually? a. P2 584.19 b. P3 118.05 c. P8 940.60 d. P867.82
97. Evaluate ∫
a. -3/2 cos 2 + C b. -3 cos 2 c. 3/2 cos 2 + C d. 3 cos 2 + C
98. Find the maximum height which a
cannonball fired at an initial velocity of 100 m/s at 30˚ above the horizontal. a. 127.42 m b. 172.42 m c. 137.42 m d. 177.42 m
99. A man expects to receive P20 000 in 10
years. How much is that money worth now considering interest at 6% compounded quarterly.
a. P 12 698.65 b. P11 025.25 c. P17 567.95 d. P15 678.45
100. The area of a rhombus is 24. One
diagonal measures 6 units, find the length of the other diagonal.
a. 9 b. 7 c. 6 d. 8
101. The area of a rhombus is 24. One diagonal measures 6 units, find the length of a side. a. 5 b. 6 c. 7 d. 8
102. The sum of the coefficients in the
expansion of (x+y-z)8 is: a. From 2 to 5 b. From 5 to 10 c. Above 10 d. Less than 2
103. A banca traveled at an average speed of
15 kph downstream and then back at an average speed of 12 kph upstream. If the total time of travel is 3 hours, find the total distance traveled by the banca.
a. 40 km b. 30 km c. 60 km d. 50 km
104. A father is now 41 and his son 9. After
how many years will his age be just triple his son’s age?
a. 6 b. 5 c. 4 d. 7
105. Find the area of the largest rectangle
which you can inscribe in a semi-circle whose radius is 10.
a. 1000 sq. units
b. √ sq. units c. 100 sq. units
d. 2√ sq. units
106. Given y = 4 cos 2x. Determine its amplitude.
a. 2 b. 4 c. 8
d. √
107. A central angle of 45˚ subtends an arc of 12cm. What is the radius of the circle?
a. 12.58 cm b. 15.28 cm c. 15.82 cm d. 12.85 cm
108. The volume of two spheres is in the
ratio of 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere.
a. 6 b. 3 c. 5 d. 4
109. The integral of any quotient whose
numerator is the differential of the denominator is the:
a. Product b. Derivative c. Cologarithm d. Logarithm
110. Find the sum of the roots 5x2 -10x + 2 =
0 a. -2 b. 2 c. 1/2 d. -1/2
111. Determine the vertical pressure due to a
column of water 85 cm high. a. 8.33 x 103 N/m2 b. 8.33 x 104 N/m2
c. 8.33 x 105 N/m2 d. 8.33 x 106 N/m2
112. A rectangular 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. 52 cm2 b. 62 cm2 c. 72 cm2 d. 82 cm2
113. If a =b, the b = a. This illustrates which
axiom in algebra? a. Replacement axiom b. Symmetric axiom c. Transitive axiom d. Reflexive axiom
114. If arc tan x + arc tan 1/3 = π/4, find the
value of x. a. 1/2 b. 1/3 c. 1/4 d. 1/5
115. It is the measure of relationship between two variables.
a. Correlation b. Function c. Equation d. Relation
116. It is a polyhedron of which two faces are
equal, polygons in parallel planes and the other faces are parallelograms.
a. Cube b. Pyramid c. Prism d. Parallelepiped
117. What is the distance in cm. between
two vertices of a cube which are farthest
from each other, if an edge measures 8 cm?
a. 12.32 b. 13.86 c. 8.66 d. 6.93
118. A loan of P5000 is made for a period of
15 months at a simple interest rate of 15%. What future amount is due at the end of the loan period?
a. P 5 842.54 b. P5 900.00 c. P5 637.50 d. P5 937.50
119. To compute for the value of the
factorial, in symbolic form (n!) where n is a large number, we use a formula called:
a. Matheson formula b. Diophantine formula c. Stirlings Approximation formula d. Richardson-Duchman formula
120. Find the distance of the directrix from
the center of an ellipse if its major axis is 10 and its minor axis is 8.
a. 8.1 b. 8.3 c. 8.5 d. 8.7
121. A 200 gram apple is thrown from the edge of a tall building with an initial speed of 20 m/s. What is the change is kinetic energy of the apple if it strikes the ground at 50 m/s?
a. 100 joules b. 180 joules c. 81 joules d. 210 joules
122. When two planes intersect with each other, the amount of divergence between the two planes is expressed by the measure of:
a. Polyhedral angle b. Dihedral angle c. Reflex angle d. Plane angle
123. The median of a triangle is the line
connecting a vertex and the midpoint of the opposite side. For a given triangle, the medians intersects at a pint which is called the:
a. Circumcenter b. Incenter c. Orthocenter d. Centroid
124. A five-pointed star is also known as:
a. Quintagon b. Pentagon c. Pentatron d. Pentagram
125. The altitudes of the sides of a triangle
intersect at the point, which is known as: a. Centroid b. Incenter c. Orthocenter d. Circumcenter
126. The arc length equal to the radius of the
circle is called: a. 1 grad b. 1 radian c. π radian d. 1 quarter circle
127. One gram of ice at 0˚C is placed on a
container containing 2,000,000 cu. m of water at 0˚C. Assuming no heat loss, what will happen?
a. The volume of ice will not change
b. Ice will become water
c. Some part of ice will not change d. All of the above
128. The angular bisector of the sides of a
triangle at a point which is known as: a. Centroid b. Incenter c. Orthocenter d. Centroid
129. A pole cast a shadow of 15 meters long
when the angle of elevation of the sun is 61˚. If the pole has leaned 15˚ from the vertical directly toward the sun, what is the length of the pole?
a. 53.24 m b. 54.25 m c. 52.43 m d. 53.25 m
130. Each side of a cube is increased by 1%.
By what percent is the volume of the cube increased?
a. 3% b. 23.4% c. 33.1% d. 34.56%
131. MCMXCIV is a Roman numeral
equivalent to: a. 2174 b. 3974 c. 2974 d. 1994
132. The sum of the digits of a two digit
number is 11. If the digits are reversed, the resulting number is seven more than twice the original number. What is the original number?
a. 44 b. 83 c. 38 d. 53
133. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon.
a. 288.2 b. 282.8 c. 228.2 d. 238.2
134. Find the probability of getting exactly 12
out of 30 questions on the true or false question.
a. 0.04 b. 0.15 c. 0.12 d. 0.08
135. Find the length of the vector (12, 4, 4).
a. 8.75 b. 5.18 c. 7 d. 6
136. According to this law, “The force
between two charges varies directly as the magnitude of each charge and inversely as the square of the distance between them”.
a. Newton’s law b. Inverse Square law c. Coulomb’s law d. Law of Universal Gravitation
137. Mr. J. Reyes borrowed money from the
bank. He received from the back P1842 and promised to pay P2000 at the end of 10 months. Determine the simple interest.
a. 15.7% b. 16.1% c. 10.29% d. 19.45%
138. Evaluate the expression (1 + i2 )10 where
I is an imaginary number. a. -1 b. 10 c. 0
d. 1
139. The amount of heat needed to change solid to liquid.
a. Latent heat of fusion b. Solid fusion c. Condensation d. Cold fusion
140. Solve for x in the equation: 2 log4 x –
log4 9 = 2 a. 12 b. 10 c. 11 d. 13
141. Two post, one 8m and the other 12 m
high are 15 m apart. If the posts are supported by a cable running from the top of the first post to a stake on the ground and then back to the top of the second post, find the distance from the lower post to the stake to use the minimum amount of wire.
a. 4 m b. 6 m c. 8 m d. 9m
142. A 40 gm rifle bullet is fired with a speed of 300 m/s into a ballistic pendulum of mass 5 kg suspended from a chord 1 m long. Compute the vertical height through which the pendulum arises.
a. 29.88 cm b. 28.89 cm c. 28.45 cm d. 29.42 cm
143. If the roots of an equation are zero,
then they are classified as: a. Trivial solution b. Hypergolic solution c. Zeros of function d. Extraneous roots
144. Of what quadrant is A, if secA is positive and cscA is negative?
a. IV b. II c. III d. I
145. The reciprocal of bulk modulus of any
fluid is called ______. a. Volume stress b. Compressibility c. Shape elasticity d. Volume strain
146. Assuming that the earth is a sphere
whose radius is 6,400 km. Find the distance along 3 deg arc at the equator of the earth’s surface.
a. 335.10 km b. 533.10 km c. 353.10 km d. 353.01 km
147. Equations relating x and y that cannot
readily solved explicitly for y as a function of x or for x as a function of y. Such equation may nonetheless determine y as a function of x or vice versa, such as function is called _____.
a. Logarithmic function b. Implicit function c. Continuous function d. Explicit function
148. What is the integral of (3t-1)3 dt?
a. 1/12 (3t-1)4 + c b. 1/12 (3t-1)3 + c c. ¼ (3t-1)3 + c d. ¼ (3t-1)4 + c
149. If 16 is 4 more than 4x, find x-1 a. 14 b. 3 c. 12 d. 5
150. A frequency curve which is composed of a series of rectangles constructed with the steps as the base and the frequency as the height.
a. Histogram b. Ogive c. Frequency distribution d. Bar graph
151. It is a sequence of numbers such that
successive terms differ by a constant a. Arithmetic progression b. Infinite progression c. Geometric progression d. Harmonic progression
152. If the second derivative of the equation
of a curve is equal to the negative of the equation of that same curve, the curve is:
a. A paraboloid b. A sinusoid c. A cissoids d. An exponential
153. Determine x, so that: a, 2x + 4, 10x – 4
will be a geometric progression. a. 4 b. 6 c. 2 d. 5
154. The angular distance of a point on the
terrestrial sphere from the north pole is called its:
a. Co-latitude b. Altitude c. Latitude d. Co-declination
155. If one third of the air in a tank is
removed by each stroke of an air pump, what fractional part of the air removed in 6 strokes?
a. 0.7122 b. 0.9122 c. 0.6122
d. 0.8122
156. The linear distance between -4 and 17 on the number line is
a. 13 b. 21 c. -17 d. -13
157. Determine the angle of the super
elevation for a 200 m highway curve so that there will be no side thrust at a speed of 90 kph.
a. 19.17˚ b. 17.67˚ c. 18.32˚ d. 20.11˚
158. A ball is dropped from a building 100 m
high. If the mass of the ball is 10 grams, after what time will the ball strike the earth?
a. 4.52s b. 4.42s c. 5.61s d. 2.45s
159. Centrifugal force is _____
a. Directly proportional to the radius of the curvature
b. Directly proportional to the square of the tangential velocity
c. Inversely proportional to the tangential velocity
d. Directly proportional to the square of the weight of the object
160. Each of the faces of a regular hexahedron is a _____
a. Triangle b. Square c. Rectangle d. Hexagon
161. Find the mean proportion of 4 and 36 a. 72 b. 24 c. 12 d. 20
162. Simplify the expression i1999 + i1999
where I is an imaginary number. a. 0 b. -1 c. 1+1 d. 1-i
163. In a club of 40 executives, 33 likes to smoke Marlboro and 20 like to smoke Philip Moris. How many like both?
a. 13 b. 10 c. 11 d. 12
164. The graph of r=a+bcos θ is a :
a. Lemniscates b. Limacon c. Cardioids d. Lituus
165. Solve for A in the equation: cos2A = 1-
cos2A a. 15˚, 125˚, 225˚, 335˚ b. 45˚, 125˚, 225˚, 315˚ c. 45˚, 135˚, 225˚, 315˚ d. 45˚, 150˚, 220˚, 315˚
166. Momentum is the product of velocity
and a. Acceleration b. Mass c. Force d. Time
167. If 15 people can win prices in a estate lottery (assuming that there are no ties). How many ways can these 15 people win first, second,, third, fourth and fifth prizes?
a. 4,845 b. 116,280 c. 360,360 d. 3,003
168. Find the 30th term of the A.P 4, 7, 10,…
a. 75 b. 90 c. 88 d. 91
169. Mary is 24. She is twice as old as Ann
was when Mary was as old as Ann now. How old is Ann now?
a. 16 b. 17 c. 12 d. 15
170. Find the ratio of an infinite geometric series if the sum is 2 and the first term is ½
a. 1/3 b. 1/2 c. 3/4 d. 1/4
171. 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. 44% b. 46% c. 56% d. 65%
172. Find the equation of the curve at every
point of which, the tangent line has a slope of 2x.
a. x
b. y=x2+c c. y=x1/2+c d. x=y2+c
173. csc 520˚ is equal to
a. cos 20˚ b. csc 20˚ c. tan 45˚ d. sin 20˚
174. A rotating wheel has a radius of 2 ft. and
6 in. A point on the circumference of the wheel moves 30 ft in 2 seconds. Find the angular velocity of the wheel.
a. 2 rad/sec b. 4 rad/sec c. 6 rad/sec d. 5 rad/sec
175. It is a series equal payments accruing at
equal intervals of the time where the first payment is made several periods after.
a. Deferred annuity b. Delayed annuity c. Progressive annuity d. Simple annuity
176. Exact angle of the dodecagon equal to
________ deg. a. 135 b. 150 c. 125 d. 105
177. A load of 100 lb. is hung from the
middle of a rope, which is stretched between wo rigid walls of 30 ft apart. Due to the load, the rope sags 4 ft in the middle. Determine the tension in the rope.
a. 165 lbs b. 173 lbs c. 194 lbs d. 149 lbs
178. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 seconds?
a. 185 mi b. 167 mi c. 200 mi d. 172 mi
179. A block weighing 500 kN rest on a ramp
inclined at 25˚ with horizontal. The force tending to move the block down the ramp is:
a. 100 kN b. 211 kN c. 255 kN d. 450 kN
180. What is the value of log25+log35?
a. 7.39 b. 3.79 c. 3.97 d. 9.37
181. The distance between the center of the
three circles which are mutually tangent to each other externally are 10, 12 and 14 units. The area of the largest circle is
a. 72 π b. 23 π c. 64 π d. 16 π
182. To maximize the horizontal range of the
projectile, which of the following applies? a. Maximize velocity b. Maximize the angle of elevation
and velocity c. Maximize the angle of elevation d. The tangent function of the
angle of trajectory must be equal to one
183. What is the lowest common factor of 10 and 32?
a. 320 b. 2
c. 180 d. 90
184. The distance that the top surface is displaced in the direction of the force divided by the thickness of the body is known as __________
a. Longitudinal strain b. Linear strain c. Shear strain d. Volume strain
185. It can be defined as the set of all points
on a plane whose sum of distances of any of which from two fixed points is constant.
a. Circle b. Hyperbola c. Parabola d. Ellipse
186. A statue 3m high is standing on a base
of 4m high. If an observer’s eye is 1.5m above the ground, how far should he stand from the base in order that the angle suspended bu the statue is maximum.
a. 3.41 m b. 3.51 m c. 3.71 m d. 4.41 m
187. A baseball is thrown from a horizontal
plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30˚ above the horizontal. How far from the throwing point well the ball attains its original level.
a. 882.2 m b. 8.828 m c. 288.8 m d. 82.88 m
188. A balloon is rising vertically over a point
A on the ground a rate of 15 ft/sec. A point B on the ground is level with and 30 ft from A. When the balloon is 40 ft from
A, at what rate is its distance from B changing?
a. 13 ft/sec b. 15 ft/sec c. 12 ft/sec d. 10 ft/sec
189. The diameter of a circle described by 9x2
+ 9y2 = 16 is ______ a. 4/3 b. 16/9 c. 8/3 d. 4
190. A man finds the angle of elevation of
the top of a tower to be 30 degrees. He walks 85 m nearer the tower and find its angle of elevation to be 60 degrees. What is the height of the tower?
a. 76.31 m b. 73.31 m c. 73.16 m d. 73. 61 m
191. Two electrons have speeds of 0.7c and x
respectively at an angle of 60.82 degrees between each other. If their relative velocity is 0.65c, find x.
a. 0.02c b. 0.12c c. 0.09c d. 0.25c
192. Arc tan{2 cos(arcsin
) )} is equal to:
a. π/3 b. π/4 c. π/6 d. π/2
193. Determine B such that 3x + 2y – 7 = 0 is
perpendicular to 2x – By + 2 = 0 a. 5 b. 4 c. 3 d. 2
194. Find the point in the parabola y2 = 4 at which the rate of change of the ordinate and abscissa are equal.
a. (1, 2) b. (-1, 4) c. (2, 1) d. (4, 4)
195. Find the equation of the axis of
symmetry of the function y= 2x2-7x+5 a. 7x+4=0 b. 4x+7=0 c. 4x-7=0 d. 7x-4=0
196. The major axis of the elliptical path in which the earth moves around the sum is approximately 186, 000, 000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth
a. 93 000 000 miles b. 91 450 000 miles c. 94 335 100 miles d. 94 550 000 miles
197. The angle of inclination of ascends of a
road having 8.25% grade is _____ degrees.
a. 4.72˚ b. 4.27˚ c. 5.12˚ d. 1.86˚
198. Find the sum of the first term of the
geometric progression 2,4,8,16,… a. 1 023 b. 2 046 c. 225 d. 1 596
199. Find the sum of the infinite geometric
progression 6, -2, 2/3
a. 9/2 b. 5/2 c. 11/2 d. 7/2
200. Evaluate (
)
a. Undefined b. 0 c. Infinity d. 1/7
201. What is the speed of asynchronous
earth’ satellite situated 4.5x107 m from the earth
a. 11 070.0 kph b. 12 000.0 kph c. 11 777.4 kph d. 12 070.2 kph
202. A semiconductor company will hire 7
men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position
a. 680 b. 540 c. 480 d. 840
203. The wheel of a car revolves n times while the car travels x km. The radius of the wheel in meter is:
a. 10 000x/π n b. 500 00x/ π n c. 500x/ π n d. 5 000x/ π n
204. The volume of a gas under standard
atmospheric pressure, 76 cm. Hg is 200 in3. What is the volume when the pressure is 80 cm. Hg, if the temperature is unchanged?
a. 190 in3 b. 110 in3 c. 90 in3 d. 30.4 in3
205. Find the 100th term of the sequence,
1.01, 1.00, 0.99, …. a. 0.05 b. 0.03 c. 0.04 d. 0.02
206. 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)
207. The roots of a quadratic equation are
1/3 and ¼. What is the equation? a. 12x2+7x+1=0 b. 122-7x+1=0 c. 12x2+7x-1=0 d. 12x2-7x-1=0
208. Covert θ=π/3 to Cartesian equation
a. x=31/2x b. 3y=31/2x c. y=x d. y=31/2x
209. A piece of wire is shaped to enclose a
square whose area is 169 sq cm. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is:
a. 165 m2 b. 170 m2 c. 175 m2 d. 156 m2
210. If (x+3) : 10=(3x-2): 8, find (2x-1).
a. 1 b. 4 c. 2 d. 3
211. In complex algebra, we use a diagram to represent a complex plane commonly called:
a. De Moivre’s diagram b. Argand diagram c. Funicular diagram d. Venn diagram
212. The quartile deviation is a measure of:
a. Division b. Certainty c. Central tendency d. Dispersion
213. The velocity of an automobile starting
from rest is given by
ft/sec.
determine its acceleration after an interval of 10 sec. (in ft/sec2)
a. 2.10 b. 1.71 c. 2.25 d. 2.75
214. An automobile accelerates at a constant
rate of 15 mi/hr to 45 mi/hr in 15 seconds, while traveling in a straight line. What is the average acceleration?
a. 2 ft/sec b. 2.12 ft/sec c. 2.39 ft/sec d. 2.93 ft/sec
215. A comfortable room temperature is
72˚F. What is the temperature, expressed in degrees Kelvin?
a. 290 b. 263 c. 275 d. 295
216. 15% when compounded semi-annually
will have effective rate of: a. 15.93% b. 16.02% c. 18.78% d. 15%
217. A non-square rectangle is inscribed in a
square so that each vertex of the rectangle is at the trisection point of the different sides of the square. Find the ratio of the area of the rectangle to the area of the square.
a. 4:9 b. 2:7 c. 5:9 d. 7:72
218. If the radius of the circle is decreased by
20%, by how much is its area decreased? a. 46% b. 36% c. 56% d. 26%
219. A flowerpot falls off the edge of a fifth-
floor window, just as it passes the third-floor window someone accidentally drops a glass of water from the window. Which of the following is true?
a. The flowerpot and the glass hit the ground at the same instant
b. The flowerpot hits the ground at the same time as the glass
c. The glass hits the ground before the flowerpot
d. The flowerpot hits the ground first with a higher speed than the glass
220. Is sinA=2.571x, cosA=3.06x, and sin2A=3.939, find the value of x.
a. 0.100 b. 0.150 c. 0.250 d. 0.350
221. How many terms of the sequence -9, -6,
-3 … must be taken so that the sum is 66? a. 12 b. 4 c. 11
d. 13
222. A man in a hot air balloon drops an apple at a height of 50 meters. If the balloon is rising at 15 m/s, find the highest point reached by the apple.
a. 141.45 m b. 171.55 m c. 151.57 m d. 161.47 m
223. If sin A=4/5 and A is in the second quadrant, sin B= 7/25 and B is in the first quadrant, find sin (A+B)
a. 3/5 b. 3/4 c. 2/5 d. 4/5
224. If cosθ=-15/17 and θ is in the third
quadrant, find cos θ/2.
a. -1/√
b. -8/√
c. 2/√
d. 3/√
225. What is the maximum moment of a 10 meter simply supported beam subjected to a concentrated load of 500kN at the mid-span?
a. 1250 kN-m b. 1520 kN-m c. 1050 kN-m d. 1510 kN-m
226. It represents the distance of a point
from the y-axis a. Ordinate b. Abscissa c. Coordinate d. Polar distance
227. The logarithm of a number to the base e (2.7182818….0 is called
a. Characteristic b. Mantissa c. Briggsian logarithm d. Napierian logarithm
228. Terms that a differ only in numeric
coefficients are known as: a. Unequal terms b. Like terms c. Unlike terms d. Equal terms
229. In Plain Geometry, two circular arcs that
together make up a full circle are called: a. Conjugate arcs b. Co-terminal arcs c. Half arcs d. Congruent arcs
230. For a particular experiment you need 5
liters of a 10% solution. You find 7% and 12% solution on the shelves. How much of the 7% solution should you mix with the appropriate amount of the 12% solution to get 4 liters of a 10% solution.
a. 1.43 b. 1.53 c. 1.63 d. 1.73
231. A mango falls from a branch 5 meters
above the ground. With what speed in meters per second does it strike the ground? Assume g=10m/s2.
a. 10 m/sec b. 14 m/sec c. 12 m/sec d. 8 m/sec
232. When two waves of the same frequency
speed and amplitude traveling in opposite directions are superimposed.
a. The phase difference is always zero
b. Distractive waves are produced c. Standing waves are produces d. Constructive interference always
results
233. The work done by all the forces except the gravitational force is always equal to the _____of the system
a. Total mechanical energy b. Total potential energy c. Total kinetic energy d. Total momentum
234. Ten less than four times a certain
number is 14. Determine the number a. 7 b. 5 c. 4 d. 6
235. Equal volumes of two different liquids
evaporate at different, but constant rates. If the first is totally evaporated in 6 weeks, and the second in 7 weeks, when will be the second be ½ the volume of the first.
a. 3.5 weeks b. 4 weeks c. 5/42 weeks d. 42/5 weeks
236. Find the fourth term of the progression ½ , 0.2, 0.125 …
a. 0.099 b. 1/11 c. 1/10 d. 0.102
237. The time required by an elevator to lift a
weight varies directly through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for a 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. 58 hp b. 48 hp c. 50 hp d. 56 hp
238. Find the dimensions of the right circular
cylinder of greatest volume that can be inscribed in a right circular cone of radius r and altitude h.
a. Radius=2/3r; altitude=2/3h b. Radius=1/3r; altitude=1/3h c. Radius=2/3r; altitude=1/3h d. Radius=1/3r; altitude=2/3h
239. An angular unit equivalent to 1/400 of
the circumference of a circle is called: a. Grad b. Mil c. Degree d. Radian
240. A condition where only few individuals
produce a certain product and that any action of one will lead to almost the same action of the others.
a. Monopoly b. Perfect competition c. Semi-monopoly d. Oligopoly
241. Ivory soaps floats in water because:
a. The specific gravity of ivory soap is less than that of water
b. The specific gravity of ivory soap is greater than that of water
c. The density of ivory soap is unity d. All matters has mass
242. On a certain test, the average passing score is 72 while the average for entire test is 62, what part of the group of students passed the test?
a. 5/9 b. 6/11 c. 7/13 d. 4/7
243. Ghost images are formed in a TV set
when the signal from the TV transmitter is received directly at the TV set and also indirectly after reflection from a building or other large metallic mass. In a certain 25 inch TV set, the ghost is about 1 cm, to the right of the principal image of the reflected signal arrives 1 microsecond after the principal signal. What is the difference in the path length of the reflected and principal signals in this case?
a. 100 meters b. 300 meters c. 200 meters d. 400 meters
244. A stone is dropped into a well, and the
sound of the splash was heard three seconds later. What was the depth of the well?
a. 37 meters b. 41 meters c. 53 meters d. 30 meters
245. Two thermometers, one calibrated in
Celsius and the other in Fahrenheit, are used o measure the same temperature, the numerical reading obtained on the Fahrenheit thermometer.
a. Is greater than that obtained on the Celsius thermometer
b. Is less than that obtained on the Celsius thermometer
c. May be greater or less than that obtained on the Celsius thermometer
d. Is proportional to that obtained on the Celsius thermometer
246. 1 atm of pressure is equal to _______. a. 101300 Pa b. 14.7 bars c. 1.013 psi d. 2117 psi
247. Find the least number of years
required to double a certain amount of money at 5% per annum compound interest to the nearest year
a. 14 years b. 12 years c. 18 years d. 20 years
248. The replacement of the original cost of an investment
a. Capital recovery b. Breakeven c. Payoff d. Return on investment
249. When comparing leasing against
outright purchase of equipment, which of the following is not correct?
a. Leasing frees needed working capital
b. Leasing reduces maintenance and administrative expenses
c. Leasing offers less flexibility with respect to technical obsolescence
d. Leasing offers certain tax advantages
250. Find the volume of the solid above the elliptic paraboloid 3x2+y2=z and below the cylinder x2+z=4
a. 2π cubic units
b. π/4 cubic units c. π cubic units d. 4 π cubic units
251. An oil well that yields 300 barrels of
cure oil a month will run dry in 3 years. If is estimated that t months from now, the
price of crude oil will be P(t)=18 + 0.3√ dollars per barrel. If the oil is sold as soon as it is extracted from the ground, what will be the total future revenue from the oil well?
a. $253,550 b. $207,612 c. $150,650 d. $190,324
252. A point on the graph of a differentianble
function where the concavity changes is called a point of ______
a. Inflection b. Mean value c. Local minimum value d. Deflection
253. Find the maximum and minimum values
of 3sinθ for 0˚ a. 3, 1/3 b. 1, 0 c. 2, -2 d. 1, -1
254. The spherical excess of a spherical triangle is the amount by which the sum of its angles exceed
a. 180˚ b. 90˚ c. 360˚ d. 270˚
255. the area of three adjacent surfaces of a rectangular block are 8 sq cm, 10 sq cm and 20 sq cm. the volume of the rectangular block is
a. 200 cu m b. 40 cu m c. 10 cu m d. 20 cu m
256. In the story about the crow who wanted
to drink water from a cylindrical can but could not reach the water, it is said that the crow dropped a pebble which was a perfect sphere 3 cm in radius into the can. If the can was 6 cm radius, what was the rise in water level inside the can after that pebble was dropped?
a. 2 cm b. 1 cm c. 3 cm d. 2.5 cm
257. When a line y=mx+b slopes downwards
from left to right, the slope m is a. Less than 0 b. Greater than 0 c. Equal to 0 d. Equal to 1
258. A line perpendicular to a plane
a. Is perpendicular to only two intersecting lines in the plane
b. Makes a right angle in the plane which passes through its foot
c. Is perpendicular to every line is the plane
d. Makes a right angle with every line is the plane
259. If the area of an equilateral triangle is
9√ sq cm then its perimeter is
a. 9√ cm b. 18 cm
c. 18√ cm d. 12 cm
260. A transport company has been contracted to transport a minimum of 600 factory workers from a gathering point in Makati to their working place in Canlubang daily. The transport company has nine 5-passenger cars, six 10-passenger mini buses and 12 drivers. The cars can make 14 trips a day while the mini busses can make 10 trips a day. How should the transport company use their cans and mini buses in order to carry the maximum number of passengers each day?
a. 9 cars and 3 mini buses b. 3 cars and 9 mini buses c. 6 cars and 6 mini buses d. 7 cars and 5 mini buses
261. When a certain polynomial p(x) is
divided by (x-1), remainder is 12. When the same polynomial is divided by (x-4), the remainder is 3. Find the remainder when the polynomial is divided by (x-1)(x-4)
a. x+5 b. -2x-8 c. -3x+15 d. 4x-1
262. The scalar product of A and B is equal to
the product of the magnitudes of A and B and the ______ of the angle between them
a. Sine b. Value in radians c. Tangent d. Cosine
263. If the surd (√ √ ) , then x is
equal to:
a. √
b. √
c. √ √
d.
√ √
264. A certain electronics company has 16
tons of raw materials, of which 10 tons are stored in warehouse in Quezon city, and 6 tons are stored in warehouse in Makati. The raw materials have to be transported to three production points in Dasmarinas Cavite, Canlubang Laguna and Batangas city in the amounts of 5, 7 and 4 tons respectively, the cost per ton for transporting the raw materials from the two warehouses to the three production points areas as follows
To/From
Damarinas
Canlubang
Batangas
Q.C P 700 P500 P800
Makati P 200 P300 P400
Find the minimum possible transportation cost. HINT let a=no of tons to be shopped from Q.C to Dasmarinas, b=no of tons to be shipped ftom Q.C to Canlubang, c=no of tons to be shipped from Q.C to Batangas, d= no of tons to be shopped from Makati to Dasmarinas, e= no of tons to be shopped from Makati to Canlubanga and f= no of tons to be shopped from Makati to Batangas.
a. 7 300.00 b. 8 300.00 c. 9 300.00 d. 10 300.00
265. Which of the following is a correct
relationship for any triangle whose sides are a, b, c and the respective sides are a, b, c and the respective opposite angles are A, B and C.
a. a2=b2+c2-bc cos A b. a2=b2+c2-2bc cos A
c. a2=b2+c2-2bc sin A d. a2=b2+c2-2bc cos B cos C
266. find the product MN of the following
matrices
M=|
| N=|
|
a. |
|
b. |
|
c. |
|
d. |
|
267. Arrange the following surds in
descending order: a=√ √ , b=3+√ ,
c=√ √ , d=√ √ a. c, d, a, b b. b, a, d, c c. c, d, b, a d. d, c, a, b
268. If
, which of the
following relationship is correct? a. x+z=y b. x=y+z c. x+y=z d. x-y=z
269. evaluate u= ( )
a. 2 b. 9 c. 6 d. 8
270. Evaluate: I= ∫ ∫
a. 88/3 b. 89 c. 3
d. 79/3
271. The probability for the ECE board examinees from a certain school to pass the subject in mathematics is 3/7 and for the subject of Communication is 5/7. If none of those examinees fail both subjects and there are four examinees who passed both subjects, find the number of examinees from that school who took the examinations
a. 21 b. 14 c. 28 d. 35
272. A number when divided by 6 leaves a
remainder of 5, when divided by 5 leaves a remainder of 4, by 4 leaves a remainder of 3, by 3 leaves a remainder of 2, and by 2 leaves a remainder of 1. Find the smallest possible value of the number.
a. 29 b. 39 c. 49 d. 59
273. _________ are irrational numbers
involving radical signs a. Radicals b. Surd c. Irrational number d. Transcendental number
274. When rounded off to two significant
figures, the number 4.371x10-10 becomes ______
a. 4.4x 10-10 b. 4x10-10 c. 4.3x10-10 d. 4.2x10-10
275. The __________ of a and b is the smallest positive integer that is a multiple of both a and b.
a. Least common multiple b. Least common denominator c. Least common factor d. Greatest common factor
276. If soldering lead contains 63% silver,
______ grams of soldering lead can be made from 520 grams of silver.
a. 852.4 b. 825.4 c. 845.2 d. 842.5
277. In the equation ÿ=mx+b”, m represents
the _______ a. Distance from a point b. Coordinate of the line c. Coefficients d. Slope of the line
278. In the equation “n x m=q”, the
multiplicand is _______ a. n b. m c. q d. none of the choices
279. The hypotenuse of an isosceles right
triangle whose perimeter is 24 inches is ____ inches.
a. 9.94 inches b. 7.94 inches c. 7.03 inches d. 6.94 inches
280. An arc equal to one-fourth of a circle is
called a ____ a. Quarter circular arc b. Quarter circle c. Conjugate circle d. Complimentary circle
281. If angle θ=2, then angle (180˚-θ)= __________
a. 1.1416 radian b. 1.1614 radian c. 1.6141 radian d. 1.4161 radian
282. The logarithm of a number to a given base is called the ______
a. Exponent b. Index c. Base d. Matrix
283. One is to fifty-two and one half as three
and one-third is to ______ a. 185 b. 175 c. 165 d. 155
284. Adjacent angles whose sum is 90
degrees are said to be _____ a. Complimentary b. Supplementary c. Explementary d. Reflex angles
285. If x >y and y>z, then x _____z.
a. Less than b. Greater than c. Equal to d. Less than or equal to
286. If any given triangle with sides a, b, and
c _______is equal to b(
)
a. sin A b. sin B c. b d. a
287. if a>b and c>d, then (a+c) is _______ of
(b+d)
a. less than b. greater than c. equal to d. less than or equal to
288. the following Fourier series equation
represents a periodic ____wave i(x)= i + i cos x + i2 cos 2x+ i3 cos 3x +…+i sin x + i2 sin 2x+ i3 sin 3x+…
a. cosine b. tangent c. cotangent d. sine
289. a percentage is a fraction whose denominator is ____
a. 1000 b. 100 c. 10 d. 10000
290. A swimming pool is constructed in the
shape of two partially overlapping identical circle. Each of the circles has a radius of 9 meters, and each circle passes through the center of the other. Find the area of the swimming pool.
a. 409.44 sq m b. 309.44 sq m c. 509.44 sq m d. 209.44 sq m
291. The dartboard has nine numbered
blocks. Each block measuring 20cm x 20 cm. The number on each block is the score earned when a dart hits that block. A dart, which hits the unnumbered portion of the dartboard, gets a score of zero. Assuming all the darts hit the dartboard and with two darts, what is the probability of getting a total score of 11?
a. 0.0128 b. 0.0328
c. 0.228 d. 0.0168
292. The dartboard has nine numbered
blocks. Each block measuring 20cm x 20 cm. The number on each block is the score earned when a dart hits that block. A dart, which hits the unnumbered portion of the dartboard, gets a score of zero. Assuming all the darts hit the dartboard, what is the probability of getting a score of zero with one dart?
a. 0.64 b. 0.04 c. 0.44 d. 0.54
293. The dartboard has nine numbered
blocks. Each block measuring 20cm x 20 cm. The number on each block is the score earned when a dart hits that block. A dart, which hits the unnumbered portion of the dartboard, gets a score of zero. Assuming all the darts hit the dartboard, what is the probability of getting a score of seven with one dart?
a. 0.04 b. 0.10 c. 0.07 d. 0.70
294. A rectangular metal sheet measures 22 ft long and 2R ft wide. From this rectangular metal sheet, three identical circles were cut, each circle measuring R/3 ft. radius. If the area of the remaining metal sheet is 66 sq ft, find R.
a. 1.56 ft b. 40.47 ft c. 2.56 ft d. 13.56 ft
295. If a and y are complimentary, find the value of P if: P= cos (540˚+x) sin(540˚+y) +cos(90˚+x)sin (90+y)
a. sin 2x b. cos 2x c. –cos 2x d. –cos 2y
296. Given: ,
,
. Find a, n, and m. a. 2, 16, 4 b. 16, 2, 4 c. 4, 16, 2 d. 2, 4, 16
297. Given: P= A sin t + B cos t, Q= A cos t – B
sin t. From the given equations, derive another equation showing the relationship between P, Q, A, and B not involving any of the trigonometric functions of angle t.
a. P2-Q2=A2+B2 b. P2+Q2=A2-B2 c. P2-Q2=A2-B2 d. P2+Q2=A2+B2
298. In a certain electronic factory, the ratio
of the number of male to female workers is 2:3. If 100 new female workers are hired, the number of female workers will increase to 65% of the total number of workers. Find the original number of workers in the factory.
a. 420 b. 450 c. 480 d. 490
299. During installation, a section of an
antenna was lifted to a height of 5 meters with a force of 400 kg moving by the use of a pulley mounted on a frame. If the efficiency of the input multiplied by 100%, what is the efficiency of the pulley? The tower section weighs 1000 kg
a. 62.5%
b. 52.5% c. 72.5% d. 82.5%
300. An elevator can lift a load of 5000
Newtons from ground level to a height of 20.0 meters in 10 seconds. What horsepower, hp can the elevator develop?
a. 12.4 hp b. 13.4 hp c. 14.4 hp d. 15.4 hp
301. What is the force in Newtons, required
to move a car with 1000 kg mass with an acceleration of 12.0 meters/sec2?
a. 12 000N b. 10 000N c. 8 000N d. 6 000N
302. If the same car in problem 301, with
1000 kg mass is driven around a curve with radius of 10.0 meters at a speed of 20 meters per second, find the centrifugal force in Newtons.
a. 40000N b. 30000N c. 20000N d. 10000N
303. Crew 1 can finish the installation of an
antenna tower in 200 hours while crew 2 can finish the same job in 300 hours. How long will it take both crews to finish the same job working together?
a. 180 hours b. 160 hours c. 140 hours d. 120 hours
304. Evaluate the limit of x2+3x-4 as x
approaches the value of 4 a. 24 b. 42
c. 35 d. 12
305. log Mn is equal to
a. log nM b. log Mn c. n log M d. M log n
306. The volume of a cube is reduces to
______ if all the sides are halved a. 1/2 b. 1/4 c. 1/8 d. 1/16
307. Evaluate the value of the determinant
|
|
a. -101 b. 011 c. -001 d. 111
308. Give the factors of a2-x2
a. 2a-2x b. (a+x)(a-x) c. 2x-2a d. (a+x)(x-a)
309. Give the area of a triangle in square
meters when the base is equal to 24.6cm and the height is equal to 50.8 cm. One of the sides is equal to 56.53 cm
a. 0.062484 b. 0.1252 c. 2877.44 d. 1252.1
310. The cost of running an electronic shop is
made up of the following: Office rental=40% Labor=35% Materials=20% Miscellaneous=5%. If the office rental is increased by 24%, labor increased by 15%, cost of materials increased by 20%, and the miscellaneous costs are
unchanged, find the percentage increase in the cost of running the shop.
a. 18.85% b. 28.85% c. 16.85% d. 10.85%
311. The selling price of a TV set is double
that of its net cost. If the TV set is sold to a customer at a profit of 255 of the net cost, how much discount was given to the customer?
a. 27.5% b. 47.5% c. 37.5% d. 30.5%
312. Find the sum of the interior angles of a
pentagram a. 180 degrees b. 360 degrees c. 540 degrees d. 720 degrees
313. Find the value of P if it I equal to sin2 1˚ + sin22˚ + sin23˚ + .. + sin2 90˚
a. Infinity b. 0 c. 44.5 d. Indeterminate
314. Find the value of P if it is equal to
a. 0 b. 1 c. 2 d. 4
315.
√
= ?
a. 0.3
b. 0.4 c. 0.5 d. 0.6
316. Find the value of
a. 4 b. 2 c. 0 d. 1
317. Find the value of √ √ √
a. 3/2 b. 2 c. 3 d. 1/2
318. Find the value of
(
)
a. 25/48 b. 125/48 c. 125/16 d. 125/8
319. Find the value of a. 2 b. 4 c. 8 d. 16
320. Simplify (
)
a. 2 b. 4 c. 8 d. 16
321.
= ?
a. tan B b. sec B c. cot B d. csc B
322. Simplify the following:
a. 0 b. 1 c. 2 d. cot (A+B)
323. Solve for the following:
a. -7a b. +7a c. -7-a d. +7-a
324. Simplify {
[
]
}
a.
b.
c.
d.
325. Simplify ( )
( )
a.
b.
c.
d.
326. If A was originally a range of numbers
with four significant figures which, when
rounded off to three significant figures yielded a value of 3.10, what was the original range of values of A?
a. 3.10 to 3.105 b. 3.101 to 3.105 c. 3.101 to 3.109 d. 3.101 to 3.104
327. Round off: 6785768.342 to the nearest
one tenth a. 6785768.34 b. 6785768.3 c. 7000000.0 d. 6785770.00
328. Round off: 2.371x10-8 to two significant
figures a. 2.3x10-8 b. 2.4x10-8 c. 2.0x10-8 d. 2.5x10-8
329. Round off: 0.003086 to two significant
figures a. 0.00308 b. 0.00310 c. 0.00300 d. 0.00311
330. Round off: 0.00386 to three significant
figures a. 0.00308 b. 0.00309 c. 0.003 d. 0.00310
331. Round off: 34.2814 to four significant
figures a. 34.2814 b. 34.2800 c. 35.0000 d. 34.2000
332. Round off: 30 562 to three significant figures
a. 30 500 b. 30 600
c. 30 400 d. 30 300
333. Round off: 149.691 to one decimal place
a. 149.6 b. 149.7 c. 148.5 d. 148.4
334. Round off: 149.691 to the nearest
integer a. 149 b. 148 c. 147 d. 150
335. Round off: 149.691 to two decimal
places a. 149.69 b. 149.70 c. 148.69 d. 148.70
336. Which of the following is equivalent to
the expression:
a. sin b. cos c. sec d. csc
337. A stone is thrown outward, at an angle
of 30 with the horizontal, into the river from a cliff, which is 120 meters above the water level at a velocity of 36 km/hr. At what height above the water level will the stone start to fall?
a. 121.274 m b. 131.274 m c. 141.274 m d. 161.274 m
338. A stone is thrown outward, at an angle
of 30 with the horizontal, into the river from a cliff, which is 120 meters above the water level at a velocity of 36 km/hr.
how far from the cliff will the stone strike the water?
a. 57.46 meters b. 47.46 meters c. 67.46 meters d. 77.46 meters
339. The speed of light is closest to:
a. 30x108 m/sec b. 300x108 m/sec c. 3000x108 m/sec d. 3x108 m/sec
340. When a ray of light is incident from a
medium, such as air, to a denser medium, like water, the refracted ray lie _____ to the perpendicular than does the incident ray.
a. Closer b. Farther c. Parallel d. Perpendicular
341. In nuclear energy, the splitting apart of
the heavy nuclei of uranium is called a. Fusion b. Fission c. Neutron d. Diffusion
342. A parabola which opens upward and
whose vertex is at the origin is defined by what equation?
a. b. c. d.
343. The curve traced by a point moving in a
plane is shown as the _____ of that point. a. Parameter b. Pattern c. Locus d. Formula
344. (a-b)3 is equivalent to which of the following?
a. b. c. d.
345. Payment for the use of borrowed
money is called a. Loan b. Maturity value c. Interest d. Rate
346. Area of a triangle is given by the formula a. 1/2bh b. bh c. 1/4bh d. 3/4bh
347. Evaluate ∫
dx
a. 37.6 b. 47.6 c. 27.6 d. 57.6
348. In the Cartesian coordinate, the
coordinates if the vertices of a square are (1, 1), (0, 8), (4, 5), and (-3, 4). What is the area of the square?
a. 25 sq units b. 16 sq units c. 32 sq units d. 50 sq units
349. Given log2=0.30 and log3=0,477. Find
the value of log 48 a. 1.681 b. 1.683 c. 1.685 d. 1.687
350. sinAcosB + sinBcosA= ?
a. sin(A+B) b. sin(A-B) c. cos(A+B) d. cos(A-B)
351. sinh2x+tanh2 x= ?
a. cosh2x-sech2x b. cosh2x+sech2x c. sech2x-cosh2x d. sech2x+cosh2x
352. If the freezing point of water is zero deg
Celsius or 32 Fahrenheit, and its boiling point is 100 deg Celsius or 212 Fahrenheit, which relationship is correct?
a. F=9/5C+32 b. F=5/9C+32 c. C=9/5F+32 d. C=5/9F+32
353. What is the probability of obtaining either four or five heads if a fair coin is tossed 10 times?
a. 231/512 b. 233/512 c. 221/512 d. 235/512
354. Find the volume generated by revolving
the ellipse whose equation is
about the x-axis a. 4/3πab2 b. 2/3 πab2 c. 4/3 πba2 d. 2/3 πa2b
355. A telephone pole 3ft high is to be guyed
from its middle section with a guy wire making an angle of 45 degrees with the ground. Find the total length of the guy wire if an additional three feet is to be provided for splicing. Solve by using trigonometric functions.
a. 24.21 ft b. 34.21 ft
c. 44.21 ft d. 25.21 ft
356. A rubber ball is made to fall from a
height of 50 feet 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. 200 m b. 225 m c. 250 m d. 300 m
357. The slope of a family of curves at any
point (x, y) is equal to 3x4-x2. Find the equation of the curve that is passing through point (1, 1).
a. (
)
(
)
b. (
)
(
)
c. (
)
(
)
d. (
)
(
)
358. The slope of a family of curves at any point (x, y) is equal to (x+1)(x+2). Find the equation of the curve that is passing through the point (-3, -3/2)
a.
b.
c.
d.
359. Reduce the following complex fraction
into simple functions
a.
b.
c.
d.
360. Reduce the following complex fraction
into simple fractions
a. –
b. +
c. –
d. +
361. A missile with a mass of 2200 kilograms
was fired the rocket burns for a short period of time causing a constant force of 100 000 N to be exerted on the missile for 10 seconds. After the 10 second period, what is the final velocity, v in m/sec of the missile?
a. 365.45 m/sec b. 352.45 m/sec c. 356.45 m/sec d. 256.45 m/sec
362. A missile with a mass of 2200 kilograms
was fired the rocket burns for a short period of time causing a constant force of 100 000 N to be exerted on the missile for 10 seconds. After the 10 second period, what is the acceleration of the missile in m/s2?
a. 35.64 b. 33.64 c. 30.64 d. 39.64
363. A consortium of international telecommunication companies contracted for the purchase and
installation of a fiber optic cable linking two major Asian cities at a total cost of US$ 960M. This amount includes freight and installation charges that are estimated at 10% of the above total price, if the cable shall be depreciated over a period of 15 years with zero salvage value, what is the depreciation charge during the 8th year using the sum of the year’s digit method?
a. $64 M b. $74 M c. $84 M d. $54 M
364. A consortium of international
telecommunication companies contracted for the purchase and installation of a fiber optic cable linking two major Asian cities at a total cost of US$ 960M. This amount includes freight and installation charges that are estimated at 10% of the above total price, if the cable shall be depreciated over a period of 15 years with zero salvage value. Given the sinking fund deposit factor of 0.0430 at 6% interest where n=15, what is the annual depreciation charge?
a. $43.28M b. $42.28M c. $44.28M d. $41.28M
365. Find the derivative of y with respect to x
in the following equations
a.
( )
b.
c.
d.
366. Find the value of y’ at x=1 of the
equation
a. 21 b. -21 c. 12 d. -12
367. An equipment can be purchased by
paying P100 000 down payment and 24 equal monthly installments of P10 000 with 6% interest compounded monthly? Find the cash value of the equipment given the following: present value of an annuity where n=24 at 0.5% interest, PV factor=22.563
a. P235630 b. P352630 c. P325630 d. P253630
368. Simplify the following expression:
a.
b.
c.
d.
369. Solve for the values of a in the equation
a8-17a4+16=0 a. b. c. d. All of the choices
370. Log(MN) is equal to
a. logM-N b. log M+N c. nlogM d. logM+logN e. NMlog10
371. Snell’s law on light incidence and
refraction gives us the following equation: n1sinθ1=n2sinθ2 where n1 and n2 denote the indexes on refraction θ1 and θ2 are the angle of incidence and refraction, respectively through the first
and second medium. If light beamed at an angle of 30 degrees with the vertical is made pass from air to a transparent glass with an index of refraction equal to 1.25, what is the angle of refraction in the glass?
a. θ=33.6˚ b. θ=43.6˚ c. θ=53.6˚ d. θ=23.6˚
372. If
, y’=?
a.
b.
c. -
d.
373. Sin215˚+sin275˚
a. 1 b. 2 c. 3 d. 4
374. In the ECE board examinations, the
probability that an examinee pass in each subject is 0.8. What is the probability that he will pass in at least 2 subjects?
a. 0.896 b. 0.986 c. 0.689 d. 0.869
375. A Morse code transmitter at station A
sending out either a dot or dash signal. The signal is received at station B, from where it is retransmitted to station C. The probability that the signal being sent from A is receives correctly at B is 0.98, while the probability that the signal being received correctly at C is 0.965. What is the probability that when a dot signal is transmitted from A, a dot signal is also received at C?(Express your answer up o four decimal places)
a. 0.9557 b. 0.9457 c. 0.4957 d. 0.5947
376. In the figure shown, ABCD is a square
and BEC is an equilateral triangle. Find angle AED.
a. 75˚ b. 150˚ c. 120˚ d. 140˚
D eeeee
B
B C
377. Solve for the radius of the circle shown. Large circle r=4m, small circle r=radius=?
a. 0.686 m b. 0.688 m c. 0.866 m d. 0.868 m
378. Differentiate the equation
a.
b.
c.
E
A D
4-r
4+r
45˚
d. 1
379. Give the slope of the curve at
point (1, 1)
a. 1/4 b. -1/4 c. 4 d. -1/3
380. Evaluate b in the following
equation logb 1024=5/2 a. 2560 b. 2 c. 4 d. 16
381. Obtain the differential equation of the family of straight lines with slope and -intercept equal.
a. b. c. d.
382. Obtain the differential equation of
all straight lines with algebraic sum of the intercepts fixed as .
a. b. c. d.
383. Obtain the differential equation of
all straight lines at a fixed distance from the origin.
a. [ ]
b. [ ] c. . [ ] d. [ ]
384. Determine the differential equation
of the family of lines passing through the origin.
a. b. c.
d.
385. Obtain the differential equation of all circles with center on line and passing through the origin.
a.
b.
c.
d. ( )
( )
386. Obtain the differential equation of
all parabolas with axis parallel to the -axis.
a. b. c. d.
387. What is the differential equation of
the family of parabolas having their vertices at the origin and their foci on the -axis.
a. b. c. d.
388. Obtain the particular solution of
/ when , .
a.
b.
c.
d.
389. Obtain the general solution of the
differential equation
a. b. c. d.
390. Obtain the general solution of
.
a. ( )
b. c.
d.
391. Solve the equation .
a.
b. c. d.
392. Obtain the particular solution of ; when , .
a. b. c. d.
393. Solve the equation
. a. b. c. d.
394. Solve the equation
.
a. b. c. d.
395. Solve the equation
.
a. b. c. d.
396. Solve
.
a.
b.
c.
d.
397. Solve the equation
.
a. b. c. d.
398. Solve the equation
. a. | | b. | | c. | | d. | |
399. Solve the equation
.
a. b. c. d.
400. Solve the equation .
a. b. c. d.
MULTIPLE CHOICE QUESTIONS IN
<MATHEMATICS>
<DIEGO INOCENCIO TAPANG GILLESANIA>
ENCODED BY: BORBON, MARK ADRIAN C.
401. Evaluate
.
A. 0
B. 1
C. 2
D. 3
402. Simplify the expression:
.
A. 1
B. 8
C. 0
D. 16
403. Evaluate the following limit,
.
A. 2/5
B. infinity
C. 0
D. 5/2
404. Evaluate the limit / (
.
A. 0
B. undefined
C. 1/7
D. infinity
405. Evaluate the limit / as x
approaches positive infinity.
A. 1
B. 0
C. e
D. infinity
406. Evaluate the limit:
.
A. 1
B. indefinite
C. 0
D. 2
407. Evaluate:
.
A. 0
B. ½
C. 2
D. -1/2
408. Evaluate the following:
.
A. infinity
B.
C. 0
D.
409. Find / if .
A.
B.
C.
D.
410. Find / if √ .
A. √ / √
B. √ /√
C. / √
D. √ √
411. Find / if and
.
A.
B.
C.
D.
412. Evaluate the first derivative of the
implicit function: .
A.
B. -
C.
D. -
413. Find the derivative of /
with respect to x.
A.
/
B.
/
C. /
D.
/
414. If is a simple constant, what is the
derivative of ?
A.
B.
C.
D.
415. Find the derivative of the function
with respect to x.
A.
B.
C.
D.
416. What is the first derivative / of the
expression ?
A. - /
B. 0
C. - /
D. /
417. Find the derivative of / .
A.
B.
C.
D.
418. Given the equation: , find
.
A.
B. /
C.
D.
419. Find the derivatives with respect to x of
the function √ .
A. - /√
B. - /√
C. - /√
D. - /√
420. Differentiate to the ½ power.
A. -
B.
C.
D.
421. Find / if √ .
A. √ /
B. x/
C. 1/2x
D. 2/x
422. Evaluate the differential of .
A.
B.
C.
D.
423. If , what is / ?
A.
B. -
C.
D. -
424. Find / : .
A.
B. /x
C.
D. /
425. The derivative of is:
A.
B. -
C. -
D.
426. A function is given below, what x value
maximizes ?
A. 2.23
B. -1
C. 5
D. 1
427. The number of newspaper copies
distributed is given by
, where is in years. Find
the minimum number of copies
distributed from 1995 to 2002.
A. 9850
B. 9800
C. 10200
D. 7500
428. Given the following profit-versus-
production function for a certain
commodity:
(
)
Where P is the profit and x is the unit of
production. Determine the maximum
profit.
A. 190000
B. 200000
C. 250000
D. 550000
429. The cost C of a product is a function of
the quantity of the product given by the
relation: .
Find the quantity for which the cost is a
minimum.
A. 3000
B. 2000
C. 1000
D. 1500
430. If to the 3rd power - . Find the
maximum value of .
A. 0
B. -1
C. 1
D. 2
431. Divide 120 into two parts so that the
product of one and the square of the
other is maximum. Find the numbers.
A. 60 & 60
B. 100 & 120
C. 70 & 50
D. 80 & 40
432. If the sum of two numbers is , find the
minimum value of the sum of their
squares.
A. ⁄
B. ⁄
C. ⁄
D. ⁄
433. A certain travel agency offered a tour
that will cost each person P 1500.00 if
not more than 150 persons will join,
however the cost per person will be
reduced by P 5.00 per person in excess
of 150. How many persons will make
the profit a maximum?
A. 75
B. 150
C. 225
D. 250
434. Two cities and are 8 km and 12 km,
respectively, north of a river which runs
due east. City being 15 km east of .
A pumping station is to be constructed
(along the river) to supply water for the
two cities. Where should the station be
located so that the amount of pipe is a
minimum?
A. 3 km east of
B. 4 km east of
C. 9 km east of
D. 6 km east of
435. A boatman is at , which is 4.5 km from
the nearest point on a straight shore
. He wishes to reach, in minimum
time, a point situated on the shore 9
km from . How far from should he
land if he can row at the rate of 6 kph
and walk at the rate of 7.5 kph?
A. 1 km
B. 3 km
C. 5 km
D. 8 km
436. The shortest distance from the point
(5,10) to the curve is:
A. 4.331
B. 3.474
C. 5.127
D. 6.445
437. A statue 3 m high is standing on a base 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. 3.51 m
C. 3.71 m
D. 4.41 m
438. An iron bar 20 m long is bent to form a
closed plane area. What is the largest
area possible?
A. 21.56 square meter
B. 25.68 square meter
C. 28.56 square meter
D. 31.83 square meter
439. A Norman window is in the shape of a
rectangle surmounted by 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?
A. 1
B. 2/3
C. 1/3
D. ½
440. A rectangular field is to be fenced into
four equal parts. What is the size of the
largest field that can be fenced this way
with a fencing length of 1500 feet if the
division is to be parallel to one side?
A. 65,200
B. 62,500
C. 64,500
D. 63,500
441. Three sides of a trapezoid are each 8 cm
long. How long is the 4th side, when the
area of the trapezoid has the greatest
value?
A. 16 cm
B. 15 cm
C. 12 cm
D. 10 cm
442. An open top rectangular tank with
square bases is to have a volume of 10
cubic meters. The material for its
bottom cost P150.00 per square meter,
and that for the sides is P60.00 per
square meter. The most economical
height is:
A. 2 meters
B. 2.5 meters
C. 3 meters
D. 3.5 meters
443. A rectangular box having a square base
and open top is to have a capacity of
16823cc. Find the height of the box to
use the least amount of material.
A. 16.14 cm
B. 32.28 cm
C. 18.41 cm
D. 28.74 cm
444. The altitude of a cylinder of maximum
volume that can be inscribed in a right
circular cone of radius and height is:
A. ⁄
B. ⁄
C. ⁄
D. ⁄
445. What is the least amount of tin in sheet,
in sq. inches, that can be made into a
closed cylindrical can having a volume of
108 cu. inches?
A. 125 square meter
B. 137 square meter
C. 150 square meter
D. 120 square meter
446. The volume of the closed cylindrical
tank is 11.3 cubic meter. If the total
surface area is a minimum, what is its
base radius, in m?
A. 1.44
B. 1.88
C. 1.22
D. 1.66
447. A cylindrical steam boiler is to be
constructed having a capacity of 1000
cu. m. The material for the sides cost P
2000.00 per square meter and for the
ends P 3000.00 per square meter. Find
the radius so that the cost is least.
A. 3.52 m
B. 4.12 m
C. 4.73 m
D. 5.25 m
448. A box is to be constructed from a piece
of zinc 20 inches square by cutting equal
squares 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. 599.95 cubic inches
B. 579.50 cubic inches
C. 592.59 cubic inches
D. 622.49 cubic inches
449. A load of 40kN is to be raised by means
of a lever weighing 250N/m, which is
supported at one end. If the load is
placed 1 m from the support, how long
should the lever be so that the force
required be a minimum?
A. 13.43 m
B. 20.19 m
C. 18.56 m
D. 17.89 m
450. As increases uniformly at the rate of
0.002 feet per second, at what rate is
the expression (1+ ) to the 3rd power
increasing when becomes 8 feet?
A. 430 cfs
B. 0.300 cfs
C. 0.486 cfs
D. 0.346 cfs
451. Integrate:
A.
B.
C.
D.
452. Evaluate ∫
A.
B.
C.
D.
453. Evaluate the integral of .
A.
B.
C.
D.
454. What is the integral of ?
A. -
B.
C.
D. -
455. The integral of with respect to ;
∫ is:
A.
B.
C.
D. -
456. Integrate .
A. ⁄
B.
C. ⁄
D. ⁄
457. Evaluate ∫
.
A.
B.
C. ½
D.
458. Evaluate ∫ .
A.
B.
C.
D. √
459. Evaluate ∫ .
A.
B.
C. ½
D. ½
460. Evaluate ∫
.
A. ½
B.
C. ½
D. arctan
461. Evaluate ∫
√ .
A. arcsec
B.
[ ]
C. √
D. arcsin
462. Evaluate ∫
.
A.
B.
C.
D.
463. Evaluate ∫
.
A. ½
B.
C.
D.
464. Evaluate ∫
.
A.
B.
C.
D.
465. Evaluate the integral of .
A. -
B. -
C.
D. -
466. Evaluate ∫ .
A.
B. -
C. -
D.
467. Evaluate ∫ .
A. √
B.
C. √
D.
468. Integrate the square root of
.
A. √
B. - √
C. -
D. - √
469. Evaluate the integral of with
limits from 0 to .
A. 0.143
B. 0.258
C. 0.114
D. 0.186
470. Evaluate the integral of
with limits from 5 to 6.
A. 81/182
B. 82/182
C. 83/182
D. 84/182
471. Evaluate the integral of
if it has an
upper limit of 1 and a lower limit of 0.
A. 0.022
B. 0.056
C. 0.043
D. 0.031
472. Find the integral of
if lower limit = 0 and upper limit = .
A. 0.2
B. 0.8
C. 0.6
D. 0.4
473. Using lower limit = 0 and upper limit =
, what is the integral of ?
A. 6.783
B. 6.857
C. 6.648
D. 6.539
474. Evaluate the integral of
using lower limit of 0 and upper limit = .
A. 2.0
B. 1.7
C. 1.4
D. 2.3
475. Evaluate the integral of
using lower limit = 0 and
upper limit = .
A. 0.5046
B. 0.3068
C. 0.6107
D. 0.4105
476. Find the area under the curve
and the x-axis between
and .
A. 28 sq. units
B. 46 sq. units
C. 36 sq. units
D. 54 sq. units
477. Find the area bounded by
, the lines and , and
the X-axis.
A. 19.456 sq. units
B. 20.567 sq. units
C. 22.567 sq. units
D. 21.478 sq. units
478. Find the area of the region bounded by
the curves
, the -axis, , and
.
A.
B.
C.
D.
479. Find the area bounded by the -axis and
.
A. 25.6
B. 28.1
C. 12.8
D. 56.2
480. Find the area of the region bounded by
one loop of the curve .
A. sq. units
B. sq. units
C. sq. units
D. sq. units
481. Find the area bounded by the curve
A.
B.
C.
D.
482. What is the area within the curve
?
A. 26
B. 28
C. 30
D. 32
483. Find the area enclosed by
A.
B.
C.
D.
484. Find the curved surface (area) of the
solid generated by revolving the part of
the curve from to √
about the -axis.
A. 62 sq. units
B. 62 /3 sq. units
C. 62 /5 sq. units
D. 5/62 sq. units
485. Find the volume generated by rotating
the region bounded by , ,
and , about the -axis.
A.
B.
C.
D.
486. The area bounded by the curve
and the line is revolved
about the line . What is the
volume generated?
A. 186
B. 179
C. 181
D. 184
487. Given is the area in the first quadrant
bounded by , the line and
the -axis. What is the volume
generated by revolving this area about
the y-axis?
A. 50.26
B. 52.26
C. 53.26
D. 51.26
488. Given is the area in the first quadrant
bounded by , the line
and the -axis. What is the volume
generated when this area is resolved
about the line ?
A. 28.41
B. 26.81
C. 27.32
D. 25.83
489. Find the length of the arc of
from - to - , in the second
quadrant.
A. 2.24
B. 2.61
C. 2.75
D. 2.07
490. How far from the -axis is the centroid
of the area bounded by the curve
, the line , and the -axis.
A. 1.2
B. 1.4
C. 1.6
D. 1.8
491. The area in the first quardrant, bounded
by the curve , the -axis and
the line is revolved about the
line . Find the centroid of the solid
formed.
A. (2.2,6)
B. (1.6,6)
C. (1.8,6)
D. (2.0,6)
492. A solid is formed by revolving about the
-axis, the area bounded by the curve
, the -axis, and the line .
Find its centroid.
A. (0,9.6)
B. (0,12.4)
C. (0,8.3)
D. (0,12.8)
493. A solid is formed by revolving about the
-axis, the area bounded by the curve
, the -axis, and the line .
Find its centroid.
A. (0,4.75)
B. (0,4.5)
C. (0,5.25)
D. (0,5)
494. Find the moment of inertia of the area
bounded by the parabola , -
axis and the line , with respect to
the -axis.
A. 1.067
B. 1.244
C. 0.968
D. 0.878
495. Find the work done in stretching a
spring of natural length 8 cm from 10
cm to 13 cm. Assume a force of 6 N is
needed to hold it at a length of 11 cm.
A. 21 N-m
B. 2.1 N-m
C. 0.21 N-m
D. 0.021 N-m
496. A conical tank that is 5 meters high has
a radius of 2 meters, and is filled with a
liquid that weighs 800 kg per cubic
meter. How much work is done in
discharging all the liquid at a point 3
meters above the top of the tank?
A. 21,256 kg-m
B. 21,896 kg-m
C. 23,457 kg-m
D. 22,667 kg-m
497. How much work is required to pump all
the water from a right circular
cylindrical tank, that is 8 feet in
diameter and 9 feet tall, if it is emptied
at a point 1 foot above the top of the
tank?
A. 49,421 ft-lb
B. 52,316 ft-lb
C. 54,448 ft-lb
D. 56,305 ft-lb
498. A 60-m cable that weighs 4 kg/m has a
500-kg weight attached at the end. How
much work is done in winding up the
last 20m of the cable?
A. 9,866 kg-m
B. 10,800 kg-m
C. 12,500 kg-m
D. 15,456 kg-m
499. A uniform chain that weighs 0.50 kg per
meter has a leaky 15-liter bucket
attached to it. If the bucket is full of
liquid when 30 meters of chain is out
and half-full when no chain is out, how
much work is done in winding the
chain? Assume that the liquid leaks out
at a uniform rate and weighs 1 kg per
liter.
A. 356.2 kg-m
B. 458.2 kg-m
C. 562.5 kg-m
D. 689.3 kg-m
500. The velocity of a body is given by
, where the velocity is
given in meters per second and is
given in seconds. The distance covered
in meters between and
second is close to:
A. 2
B. -5
C. 5
D. -2
501. If equals are added to equals, the sum is
equal.
A. theorem
B. postulate
C. axiom
D. corollary
502. Any number multiplied by ________
equally unity.
A. infinity
B. itself
C. its reciprocal
D. zero
503. If every element of a column (or row) of
a square matrix is multiplied by m, the
determinant of the matrix will be:
A. unchanged
B. multiplied by m
C. it depends
D. none of these
504. In probability theory, the set of possible
outcomes of an experiment is termed
as:
A. a sample space
B. a set of random events
C. a set of random variables
D. a fuzzy set
505. Which of the following is not a property
of probability:
A. If events and are mutually
exclusive, then the probability that both
events can happen is zero.
B. The probability that an event can
happen is always positive and is less
than one or equal to one.
C. If is an event which cannot occur
in the sample space, the probability of
is zero.
D. If events & are mutually
exclusive, then
506. An angle greater that a straight angle
and less than two straight angles is
called:
A. right angle
B. obtuse angle
C. reflex angle
D. acute angle
507. A line segment joining two point in a
circle is called:
A. arc
B. tangent
C. sector
D. chord
508. All circles having the same center but
with unequal radii are called:
A. encircle
B. tangent circles
C. concyclic
D. concentric circles
509. A triangle having three sides equal is
called:
A. equilateral triangle
B. scalene triangle
C. isosceles triangle
510. In a regular polygon, the perpendicular
line drawn from the center of the
inscribed circle to any of the sides is
called:
A. radius
B. altitude
C. median
D. apothem
511. A quadrilateral with two and only two
sides of which are parallel, is called:
A. parallelogram
B. trapezoid
C. quadrilateral
D. rhombus
512. A polygon with fifteen sides is called:
A. dodecagon
B. decagon
C. pentedecagon
D. nonagon
513. A rectangle with equal sides is called:
A. rhombus
B. trapezoid
C. square
D. parallelogram
514. The sum of the sides of a polygon is
termed as:
A. circumference
B. altitude
C. apothem
D. perimeter
515. A line that meets a plane but not
perpendicular to it, in relation to the
plane, is:
A. parallel
B. collinear
C. coplanar
D. oblique
516. A quadrilateral whose opposite sides
are equal is generally termed as:
A. a square
B. a rectangle
C. a rhombus
D. a parallelogram
517. A part of a line included between two
points on the line is called:
A. a tangent
B. a secant
C. a sector
D. a segment
518. The section of the sphere cut by a plane
through its center is termed as:
A. small circle
B. incircle
C. big circle
D. great circle
519. Line that pass through a common point
are called:
A. collinear
B. coplanar
C. concurrent
D. congruent
520. Point which lie on the same plane, are
called:
A. collinear
B. coplanar
C. concurrent
D. congruent
521. In two intersecting lines, the angles
opposite to each other are termed as:
A. opposite angles
B. vertical angles
C. horizontal angle
D. inscribed angle
522. A normal to a given plane is:
A. perpendicular to the plane
B. lying on the plane
C. parallel to the plane
D. oblique to the plane
523. The chord passing through the focus of
the parabola and perpendicular to its
axis is termed as:
A. directrix
B. translated axis
C. latus rectum
D. axis
524. The locus of the point which move so
the sum of its distances between two
fixed points is known as:
A. a parabola
B. a circle
C. an ellipse
D. a hyperbola
525. A tangent to a conic is a line
A. which is parallel to the normal
B. which touches the conic at only one
point
C. which passes inside the conic
D. all of the above
526. The locus of a point that move so that
its distance from a fixed point and a
fixed line is always equal, is known as:
A. a parabola
B. a circle
C. an ellipse
D. a hyperbola
527. The locus of a point, which moves so
that it is always equidistant from a fixed
point, is known as:
A. a parabola
B. a circle
C. an ellipse
D. a hyperbola
528. In polar coordinate system, the polar
angle is positive when:
A. measured clockwise
B. measured counterclockwise
C. measured at the terminal side of
D. none of these
529. The plane rectangular coordinate
system is divided into four parts which
are known as:
A. coordinates
B. octants
C. quadrants
D. axis
530. The rectangular coordinate system in
space is divided into eight
compartments, which are known as:
A. quadrants
B. octants
C. axis
D. coordinates
531. A conic section whose eccentricity is less
than one (1) is known as;
A. a parabola
B. a circle
C. an ellipse
D. a hyperbola
532. A conic section whose eccentricity is
equal to one (1) is known as:
A. a parabola
B. a circle
C. an ellipse
D. a hyperbola
533. In polar coordinate system, the distance
from a point to the pole is known as:
A. polar angle
B. -coordinate
C. radius vector
D. -coorcinate
534. The curve represented by the equation
is:
A. a parabola
B. a line
C. an ellipse
D. a circle
535. When two lines are perpendicular, the
slope of one is:
A. equal to the other
B. equal to the negative of the other
C. equal to the reciprocal of the other
D. equal to the negative reciprocal of
the other
536. The axis of the hyperbola, which is
parallel to its directrices, is known as:
A. conjugate axis
B. transverse axis
C. major axis
D. minor axis
537. The axis of the hyperbola through the
foci is known as:
A. conjugate axis
B. transverse axis
C. major axis
D. minor axis
538. A polygon is _____ if no side, when
extended, will pass through the interior
of the polygon.
A. convex
B. equilateral
C. isopometric
D. congruent
539. Which of the following statements is
correct?
A. all equilateral triangles are similar
B. all right-angled triangles are similar
C. all isosceles triangle are similar
D. all rectangles are similar
540. The volume of any solid of revolution is
equal to the generating area times the
circumference of the circle described by
the centroid of the area. This is
commonly known as:
A. First proposition of Pappus
B. Second proposition of Pappus
C. Cavalier’s Principle
D. Simpson’s Rule
541. If the product of the slopes of any two
straight lines is negative 1, one of these
lines are said to be:
A. parallel
B. skew
C. perpendicular
D. non-intersecting
542. When two planes intersect with each
other, the amount of divergence
between the two planes is expressed to
be measuring the:
A. dihedral angle
B. plane angle
C. polyhedral angle
D. reflex angle
543. The angle which the line of sight to the
object, makes with the horizontal,
which is above the eye of the observer
is called:
A. angle of depression
B. angle of elevation
C. acute angle
D. bearing
544. The median of a triangle is the line
connecting a vertex and the midpoint of
the opposite side. For a given triangle,
these medians intersect at a point which
is called the:
A. orthocenter
B. incenter
C. circumcenter
D. centroid
545. The altitudes of the side of a triangle
intersect at the point known as:
A. orthocenter
B. circumcenter
C. centroid
D. incenter
546. The angular bisector of the sides of a
triangle intersects at the point which is
known as:
A. orthocenter
B. circumcenter
C. centroid
D. incenter
547. The arc length equal to the radius of the
circle is called:
A. 1 radian
B. 1 quarter circle
C. radian
D. 1 grad
548. A five pointed star is also known as:
A. pentagon
B. pentatron
C. pentagram
D. quintagon
549. The area bounded by two concentric
circles is called:
A. ring
B. disk
C. annulus
D. sector
550. The line passing through the focus and
perpendicular to the directrix of a
parabola is called:
A. latus rectum
B. axis of parabola
C. tangent line
D. secant line
551. The altitudes of the sides of a triangle
intersect at the point known as:
A. orthocenter
B. circumcenter
C. centroid
D. incenter
552. The length of time during which the
property may be operated at a profit is
called:
A. life
B. length of time
C. physical life
D. economic life
553. What is the graph of the equation
?
A. circle
B. ellipse
C. parabola
D. hyperbola
554. Prisms are classified according to their
_____.
A. diagonals
B. sides
C. vertices
D. bases
555. It is a polyhedron of which two faces are
equal polygons in parallel planes and
the other faces are parallelograms
A. tetrahedron
B. prism
C. frustum
D. prismatoid
556. In Plain Geometry, two circular arcs that
together make up a full circle are called:
A. coterminal arcs
B. conjugate arcs
C. half arcs
D. congruent arcs
557. It represents the distance of a point
from the -axis.
A. ordinate
B. coordinate
C. abscissa
D. polar distance
558. Polygons are classified according to the
number of:
A. vertices
B. sides
C. diagonals
D. angles
559. In a conic section, if the eccentricity >
1, the locus is;
A. an ellipse
B. a hyperbola
C. a parabola
D. a circle
560. The family of curves which intersect a
given family of curves at an angle less
than 90° are called:
A. orthogonal trajectories
B. intersecting curves
C. isogonal trajectories
D. acute angle
561. A line perpendicular to the -axis has a
slope of:
A. zero
B. unity
C. infinity
D. none of these
562. The locus of points generated when a
circle is made to roll externally along the
circumference of another circle.
A. Cissoid of circles
B. Folium of Descartes
C. Epicycloid
D. Cardioid
563. It is the surface generated by moving a
straight line (called the generator)
which is always parallel to a fixed line
and which always intersect a fixed plane
curve (called the directrix) is:
A. cylindrical surface
B. locus of a point
C. spherical surface
D. paraboloid
564. How many faces have an icosahedron?
A. 16
B. 18
C. 20
D. 22
565. Each of the faces of a regular
hexahedron is a:
A. square
B. triangle
C. hexagon
D. circle
566. An arc length, which is equal to the
radius of the circle, is called:
A. 1 degree
B. 2 radians
C. 1 radian
D. 1 radians
567. Polygons with all interior angles less
than 180° are called:
A. concave polygon
B. convex polygon
C. acute polygon
D. supplemental polygon
568. To cut a right circular cone in order to
reveal a parabola, it must be cut
A. perpendicular to the axis of
symmetry
B. at any acute angle to the axis of
symmetry
C. parallel to an element of a cone and
intersecting the axis of symmetry
D. parallel to the axis of symmetry
569. To find the angles of a triangle, given
only the lengths of the sides, one would
use
A. the law of cosines
B. the law of tangents
C. the law of sines
D. the inverse square law
570. In finding the distance between two
points and , the
most direct procedure is to use:
A. the law of cosines
B. the slope of the line
C. the translation of axes
D. the Pythagorean Theorem
571. In finding the distance between two
points and , the
most direct procedure is to use:
A. the law of cosines
B. the slope of the line
C. the translation of axes
D. the Pythagorean Theorem
572. The area of a region bounded by two
concentric circles is called:
A. washer
B. ring
C. annulus
D. circular disk
573. It can be defined as the set of all points
in the plane the sum of whose distance
from two fixed points is a constant.
A. circle
B. ellipse
C. hyperbola
D. parabola
574. If the equation is unchanged by the
substitution of – for , its curve is
symmetric with respect to the:
A. -axis
B. -axis
C. origin
D. line 45° with the axis
575. A line which is perpendicular to the -
axis has a slope equal to:
A. zero
B. either
C. one
D. infinity
576. In an ellipse, a chord which contains a
focus and is in a line perpendicular to
the major axis is a:
A. latus rectum
B. minor
C. focal width
D. conjugate axis
577. In general triangles the expression
/ / / is called:
A. Euler’s formula
B. law of cosines
C. law of sines
D. Pythagorean theorem
578. What type of curve is generated by a
point which moves in uniform circular
motion about an axis, while travelling at
a constant speed, , parallel to the axis?
A. helix
B. spiral of Archimedes
C. hypocycloid
D. cycloid
579. An angle more than radian but less
than radians is:
A. straight angle
B. obtuse angle
C. related angle
D. reflex angle
580. The sum of the sides of a polygon:
A. perimeter
B. square
C. hexagon
D. circumference
581. A plane closed curve, all points of which
are the same distance from a point
within, called the center:
A. arc
B. circle
C. radius
D. chord
582. One-fourth of a great circle:
A. cone
B. quadrant
C. circle
D. sphere
583. Points that lie in the same plane:
A. coplanar
B. oblique
C. collinear
D. parallel
584. The study of the property of figures of
three dimensions;
A. physics
B. plane geometry
C. solid geometry
D. trigonometry
585. The volume of a circular cylinder is
equal to the product of its base and
altitude.
A. postulate
B. theorem
C. corollary
D. axiom
586. A point on the curve where the second
derivative of a function is equal to zero is called:
A. maxima
B. minima
C. point of inflection
D. point of intersection
587. The point on the curve where the first
derivative of a function is zero and the
second derivative is positive is called:
A. maxima
B. minima
C. point of inflection
D. point of intersection
588. At the minimum point, the slope of the
tangent line is:
A. negative
B. infinity
C. positive
D. zero
589. At the point of inflection where ,
A. is not equal to zero
B.
C.
D.
590. Point of the derivatives, which do not exist (
and so equals zero) is called:
A. stationary point
B. maximum points
C. maximum and minimum point
D. minimum point
591. If the second derivative of the equation of a
curve is equal to the negative of the
equation of that same curve, the curve is:
A. a cissoid
B. a paraboloid
C. a sinusoid
D. an exponential
MULTIPLE CHOICE QUESTIONS IN
<PHYSICS>
<DIEGO INOCENCIO TAPANG GILLESANIA>
592. It is defined as the motion of a rigid
body in which a straight line passing
through any two of its particles always
remains parallel to its initial position.
A. translation
B. rotation
C. plane motion
D. kinetics
593. Which of the following is not a vector
quantity?
A. mass
B. torque
C. displacement
D. velocity
594. The product of force and the time
during which it acts is known as:
A. impulse
B. momentum
C. work
D. impact
595. The property of the body which
measures its resistance to changes in
motion.
A. acceleration
B. weight
C. mass
D. rigidity
596. The study of motion without reference
to the forces which causes motion is
known as:
A. kinetics
B. dynamics
C. statics
D. kinematics
597. A branch of physical science that deals
with state of rest or motion of bodies
under the action of forces is known as:
A. mechanics
B. kinetics
C. kinematics
D. statics
598. In physics, work is defined in terms of
the force acting through a distance. The
rate at which the work is done is called:
A. force
B. energy
C. power
D. momentum
599. The point through which the resultant
of the disturbed gravity force passes
regardless of the orientation of the
body in space is called:
A. center of inertia
B. center of gravity
C. center of attraction
D. moment of inertia
600. The specific gravity of the substance is
the ratio of the density of the substance
to the density of water. Another term
for specific gravity is:
A. specific weight
B. unit weight
C. relative density
D. density
601. The momentum of a moving object is
the product of its mass ( ) and velocity
( ). Newton’s Second Law of Motion
says that the rate of change of
momentum with respect to time is:
A. power
B. energy
C. momentum
D. force
602. The acceleration due to gravity in the
English System or ft/s2 is:
A. 20.2
B. 32.2
C. 15.2
D. 62.4
603. Ivory soap floats in water because:
A. all matter has mass
B. the density of ivory soap is unity
C. the specific gravity of ivory soap is
greater than that of water
D. the specific gravity of ivory soap is
less than that of water
604. One (1) gram of ice at 0°C is placed on a
container containing 2,000,000 cu. m. of
water at 0°C. Assuming no heat loss,
what will happen?
A. ice will become water
B. some part of the ice will not change
C. the volume of the ice will not change
D. all of the above
605. When two waves of the same
frequency, speed and amplitude
travelling in opposite directions
superimposed,
A. destructive interference always
results
B. constructive interference always
results
C. standing waves are produced
D. the phase difference is always zero
606. Any two points along a steamline in an
ideal fluid in steady flow, the sum of the
pressure, the potential energy per unit
volume, and the kinetic energy per unit
volume has the same value. This
concept is known as the:
A. Pascal’s theorem
B. Bernoulli’s energy theorem
C. Fluid theory
D. Hydraulic theorem
607. Whenever a net force acts on a body, it
produces an acceleration in the
direction of the resultant force, an
acceleration which is directly
proportional to the resultant force and
inversely proportional to the mass of
the body. This theory is popularly
known as:
A. Newton’s first law of motion
B. Newton’s second law of motion
C. Faraday’s law of forces
D. Hooke’s law of equilibrium
608. Kinematic viscosity in SI derived unit is
described as:
A. watt per meter Kelvin
B. sq. m. per second
C. Pascal-second
D. Newton per meter
609. In a cantilever beam with a
concentrated load at the free end, the
moment is:
A. constant along the beam
B. maximum at the wall
C. ¼ maximum halfway out on the beam
D. maximum at the free end
610. What is the name of the vector that
represents the sum of two vectors?
A. scalar
B. tangent
C. tensor
D. resultant
611. The loss of weight of a body submerged
in a fluid is:
A. proportional to the weight of the
body
B. proportional to the depth of
submergence
C. equal to the weight of the fluid
displaced
D. independent of the volume of the
body
612. A leak from a faucet comes out in
separate drops. Which of the following
is the main cause of this phenomenon?
A. gravity
B. air resistance
C. viscosity of the fluid
D. surface tension
613. Inelastic collision in which the total
kinetic energy after collision is _____
before collision.
A. equal to zero
B. equal
C. less than
D. greater than
614. The property by virtue of which a body
tends to return to its original size or
shape after a deformation and when the
deforming forces have been removed.
A. elasticity
B. malleability
C. ductility
D. plasticity
615. A flowerpot falls off the edge of a fifth-
floor window. Just as it passes the third-
floor window someone accidentally
drops a glass of water from the window.
Which of the following is true?
A. The flowerpot hits the ground at the
same time as the glass.
B. The glass hits the ground before the
flowerpot.
C. The flowerpot hits the ground first
and with a higher speed than the glass.
D. The flowerpot and the glass hit the
ground at the same instant.
616. One Joule of work is done by a force of
one Newton acting through a distance
of:
A. one centimeter
B. one inch
C. one meter
D. one foot
617. Kinetic energy equals:
A. ½ velocity
B. mass velocity
C. mass acceleration
D. ½ mass velocity2
618. In an ideal gas where = pressure, =
volume, and = absolute temperature
in degrees Kelvin, which of the following
is constant?
A.
B.
C.
D.
619. The path of the projectile is:
A. a parabola
B. an ellipse
C. a part of a circle
D. a hyperbola
620. One mole of gas at standard
temperature and pressure (STP)
conditions occupies a volume equal to:
A. 22.4 liters
B. 9.81 liters
C. 332 liters
D. 2274.5 liters
621. “Equal volume of all gases under the
same conditions of temperature and
pressure contain the same number of
molecules”. This hypothesis is popularly
known as:
A. Dalton’s hypothesis
B. Avogadro’s hypothesis
C. Debye-Sear’s hypothesis
D. Compton’s hypothesis
622. The ratio of the uniform triaxial stresses,
to the change in volume at equal stress
in all directions is:
A. modulus of flexure
B. modulus of rapture
C. bulk modulus of elasticity
D. coefficient of restitution
623. According to the laws of Johannes
Kepler, “The orbit of satellite is an
ellipse, the radius vector sweeps equal
areas in equal intervals of time and the
square of the periods of revolution with
respect to both the satellite and planet
is proportional to the cubes of their
mean distance from each other.” The
shape of the ellipse depends upon its:
A. eccentricity
B. lengths of latera recta
C. apogee and perigee
D. ascending and descending nodes
624. This implies the resistance to shock or
difficulty of breaking and express the
work per unit volume required to
fracture a material.
A. toughness
B. malleability
C. hardness
D. ductility
625. The reciprocal of bulk modulus of
elasticity of any fluid is called:
A. compressibility
B. volume strain
C. volume stress
D. shape factor
626. “The resultant of the external force
applied to an object composed of a
system of particles, is equal to the
vector summation of the effective
forces acting on all particles”. This
principle is known as:
A. Archimedes’s principle
B. Bernoulli’s principle
C. D’Alembert’s principle
D. Gauss-Jordan principle
627. Calorie is the amount of heat required
to increase the temperature of _____ of
water by one degree centigrade.
A. 1 kg
B. 1 lb
C. 1 mg
D. 1 gram
628. It describes the luminous flux incidence
per unit area and is expressed in lumens
per square meter.
A. luminous intensity
B. illuminance
C. radiance
D. luminance
629. The moment of inertia of a plane figure:
A. is zero at the centroidal axis
B. increase as the distance of the axis
moves farther from the centroid
C. decrease as the distance of the axis
moves farther from the centroid
D. is maximum at the centroidal axis
630. The distance that the top surface is
displaced in the direction of the force
divided by the thickness of the body is
known as:
A. longitudinal strain
B. shear strain
C. volume strain
D. linear strain
631. To maximize the horizontal range of the
projectile, which of the following
applies?
A. maximize the angle of elevation
B. maximize velocity
C. maximize the angle of elevation and
velocity
D. the tangent function of the angle of
trajectory must be equal to one
632. According to this law, “The force
between two charges varies directly as
the magnitude of each charge and
inversely as the square of the distance
between them.
A. law of universal gravitation
B. Newton’s law
C. Coulomb’s law
D. inverse square law
633. Formation of bubbles in a low-pressure
area in a centrifugal pump and later
their sudden collapse, is called:
A. compression
B. corrosion
C. explosion
D. cavitation
644. The hardness of steel may be increased
by heating to approximatelyv1500°F and
quenching in oil or water if
A. the carbon content is above 3.0%
B. the carbon content is from 0.2% to
2.0%
C. the carbon content is below 0.2%
D. the steel has been hot rolled instead
of cast
645. Galvanized iron is a term referring to
iron coated with:
A. magnesium
B. aluminum
C. zinc
D. tin
646. A process of welding metals in molten
or in vaporous state without application
of mechanical pressure or blow. Such
welding may be accomplished by the
oxyacetylene or by hydrogen flame or
by electric arc. It is called:
A. fusion welding
B. TIG welding
C. MIG welding
D. cold welding
647. A chemical method of feed water
treatment wherein water is passed
through a bed of sodium zeolite
Nesub2Z which reacts with calcium and
magnesium salts:
A. demineralization process
B. ion exchange treatment
C. lime soda treatment
D. thermal treatment
648. Used as a guide to selecting the most
efficient centrifugal pump:
A. specific speed
B. impeller type
C. Bernoulli’s equation
D. overall efficiency
649. The impulse and momentum principle is
mostly useful for problems involving;
A. velocity, acceleration, and time
B. force, acceleration, and time
C. force, velocity, and time
D. force, velocity, and acceleration
650. Which of the following is not true
regarding the Blasius boundary layer
solution/
A. It permits one to calculate the skin
friction on a flat plate
B. It is valid for laminar flow
C. It is an approximate solution
D. It is valid only for potential flow
651. The greatest unit pressure the soil can
continuously withstand:
A. point of raptue
B. bearing strength
C. ultimate strength
D. yield point
652. Heat transmission carried by the
movement of heated fluids away from a
hot body, as in the heating of water by a
hot surface:
A. radiation
B. convection
C. conduction
D. absorption
653. The type of cooler extensively used for
medium and large size diesel engines:
A. radiation cooler
B. shell and tube cooler
C. disk cooler
D. plate cooler
654. A closed vessel intended for use in
heating water or for application of heat
to generate steam or other vapor to be
used externally to itself is called:
A. unfired pressure vessel
B. steam generator
C. boiler or steam generator
D. boiler
655. The sum of the three types of energy at
any point in the system is called:
A. Bernoulli’s theorem
B. enthalpy
C. internal energy
D. pressure heads
656. In energy transformation process in
which the resultant condition lacks the
driving potential needed to reverse the
process, the measure of this loss is
expressed as:
A. enthalpy increase of the system
B. specific bent ratio of the moment
C. entropy increase of the system
D. entropy decrease of the system
657. The system is safe to be in
thermodynamics equilibrium:
A. if it has no tendency to undergo
further chemical reaction
B. when there is no tendency towards
spontaneous change
C. when the system is not accelerating
D. when all its parts are at the same
temperature
658. An instrument used for measuring high
temperature gas
A. plenometer
B. manometer
C. anemometer
D. pyrometer
659. The power output of the engine is
increased through:
A. turbo-charging
B. scavenging
C. all of these
D. super-charging
660. The equilibrium temperature that a
regular thermometer measures if
exposed to atmospheric air is:
A. dry bulb temperature
B. °C
C. wet bulb temperature
D. dew point
661. On the hoist or load block or some
equality visible space of every hoist
designed to lift its load vertically shall be
legibly marked:
A. its electrical voltage
B. its brand and model
C. its rated load capacity
D. its motor hp or kW
662. The hardness of water is given in ppm
(parts per million, i.e., pounds per
million pounds of water). This hardness
is
A. the total number of pounds of
dissolved solids in the water per million
pounds of water
B. the total number of pounds of
calcium and magnesium bicarbonate in
the water.
C. the total number of pounds of
sodium bicarbonate in the water per
million pounds of water.
D. the total number of pounds of salt
(sodium chloride) in the water per
million pounds of water
663. Momentum = Force _____
A. time
B. velocity
C. velocity2
D. ½ velocity
664. An instrument used for measuring
specific gravity of fluids:
A. hygrometer
B. flowmeter
C. psycrometer
D. hydrometer
MULTIPLE CHOICE QUESTIONS IN
<MECHANICS>
<DIEGO INOCENCIO TAPANG GILLESANIA>
ENCODED BY: BORBON, MARK ADRIAN C.
665. A 10-lbm object is acted upon by a 4-lb
force. What is the acceleration in ft/min2?
A. 8.0 10 to the 4th power ft/min2
B. 9.2 10 to the 4th power ft/min2
C. 7.8 10 to the 4th power ft/min2
D. 4.637 10 to the 4th power ft/min2
666. What horizontal force P can be applied
to a 100-kg block in a level surface with
coefficient of friction of 0.2, that will
cause an acceleration of 2.50m/s2?
A. 343.5 N
B. 224.5 N
C. 53.8 N
D. 446.2 N
667. A skier wishes to build a rope tow to
pull herself up a ski hill that is inclined at
15° with the horizontal. Calculate the
tension needed to give the skier’s 54-kg
body an acceleration of 1.2 m/s2.
Neglect friction.
A. 202 N
B. 403 N
C. 106 N
D. 304 N
668. A pick-up truck is travelling forward at
25 m/s. The truck bed is located with
boxes, whose coefficient of friction with
the bed is 0.4. What is the shortest time
that the truck can be brought to a stop
such that the boxes do not shift?
A. 4.75 sec
B. 2.35 sec
C. 5.45 sec
D. 6.37 sec
669. A 40-kg block is resting on an inclined
plane making an angle 20° from the
horizontal. If the coefficient of friction is
0.60, determine the force parallel to the
incline that must be applied to cause
impending motion down the plane.
A. 77
B. 82
C. 72
D. 87
670. A 50-kilogram block of wood rest on top
of the smooth plane whose length is 3
m, and whose altitude is 0.8 m. How
long will it take for the block to slide to
the bottom of the plane when released?
A. 1.51 seconds
B. 2.41 seconds
C. 2.51 seconds
D. 2.14 seconds
671. A body weighing 40 lbs. starts from rest
and slides down a plane at an angle of
30° with the horizontal for which the
coefficient of friction µ=0.3. How far will
it move during the third second?
A. 19.99 ft
B. 39.63 ft
C. 18.33 ft
D. 34.81 ft
672. A car and its load weighs 27 kN and the
center of gravity is 600 mm from the
ground and midway between the front
and rear wheel which are 3 m apart. The
car is brought to rest from a speed of 54
kph in 5 seconds by means of the
brakes. Compute the normal force on
each of the front wheels of the car.
A. 7.576 kN
B. 9.541 kN
C. 5.478 kN
D. 6 kN
673. An elevator weighing 2,000 lb attains an
upward velocity of 16 fps in 4 sec with
uniform acceleration. What is the
tension in the supporting cables?
A. 1,950 lb
B. 2,150 lb
C. 2,495 lb
D. 2,250 lb
674. A block weighing 200 N rests on a plane
inclined upwards to the right at a slope
of 4 vertical to 3 horizontal. The block is
connected to a cable initially parallel to
the plane, passing through the pulley
and connected to another block
weighing 100 N moving vertically
downward. The coefficient of kinetic
friction between the 200 N block and
the inclined plane is 0.10. Which of the
following most nearly gives the
acceleration of the system?
A.
B.
C.
D.
675. A car travels on the horizontal
unbanked circular track of radius .
Coefficient of friction between the tires
and track is 0.3. If the car’s velocity is 10
m/s, what is the smallest radius it may
travel without skidding?
A. 50 m
B. 60 m
C. 15 m
D. 34 m
676. If a car travels at 15 m/s and the track is
banked 5°, what is the smallest radius it
can travel so that the friction will not be
necessary to resist skidding?
A. 262.16 m
B. 651.23 m
C. 278.14 m
D. 214.74 m
677. A vertical bar of length with a mass of
40 kg is rotated vertically about one end
at 40 rpm. Find the length of the bar if it
makes an angle 45° with the vertical?
A. 1.58 m
B. 2.38 m
C. 3.26 m
D. 1.86 m
678. The seats of a carousel are attached to a
vertical rotating shaft by a flexible cable
8 m long. The seats have a mass of 75
kg. What is the maximum angle of tilt
for the seats if the carousel operates at
12 rpm?
A. 30°
B. 35°
C. 45°
D. 39°
679. A highway curve is superelevated at 7°.
Find the radius at the end of the cable
that will break if there is no lateral
pressure on the wheels of a car at a
speed of 40 mph.
A. 247.4 m
B. 265.6 m
C. 229.6 m
D. 285.3 m
680. A 2-N weight is swung in a vertical circle
of 1-m radius at the end of a cable that
will break if the tension exceeds 500 N.
Find the angular velocity of the weight
when the cable breaks.
A. 49.4 rad/s
B. 37.2 rad/s
C. 24.9 rad/s
D. 58.3 rad/s
681. Traffic travels at 65 mi/hr around a
banked highway curve with a radius of
3000 ft. What banking angle is
necessary such that friction will not be
required to resist the centrifugal force?
A. 5.4°
B. 18°
C. 3.2°
D. 2.5°
682. A concrete highway curve with a radius
of 500 feet is banked to give a lateral
pressure equivalent to . For
what coefficient of friction will skidding
impend for a speed of 60 mph?
A. < 0.360
B. < 0.310
C. > 0.310
D. > 0.360
683. A 3500 lbf car is towing a 500 lbf trailer.
The coefficient of friction between all
tires and the road is 0.80. How fast can
the car and the trailer travel around an
unbanked curve of radius 0.12 mile
without either the car or trailer
skidding?
A. 87 mph
B. 72 mph
C. 26 mph
D. 55 mph
684. A cast-iron governor ball 3 inches in
diameter has its center 18 inches from
the point of support. Neglecting the
weight of the arm itself, find the tension
in the arm if the angle with the vertical
axis is 60°.
A. 7.63 lb
B. 6.36 lb
C. 7.56 lb
D. 7.36 lb
685. An object is placed 3 feet from the
center of a horizontally rotating
platform. The coefficient of friction is
0.3. The object will begin to slide off
when the platform speed is nearest to:
A. 17 rpm
B. 12 rpm
C. 22 rpm
D. 26 rpm
686. A force of 200 lbf acts on a block at an
angle of 28° with respect to the
horizontal. The block is pushed 2 feet
horizontally. What is the work done by
this force?
A. 320 J
B. 540 J
C. 480 J
D. 215 J
687. A 10-kg block is raised vertically 3
meters. What is the change in potential
energy. Answer in SI units closest to:
A. 350N-m
B. 294 J
C. 350 kg-m2/s2
D. 320 J
688. At her highest point, a girl on the swing
is 7 feet above the ground, and at her
lowest point, she is 3 feet above the
ground. What is her maximum velocity?
A. 10 fps
B. 12 fps
C. 14 fps
D. 16 fps
689. An automobile has a power output of 1
hp. When it pulls a cart with a force of
300 N, what is the cart’s velocity?
A. 249 m/s
B. 24.9 m/s
C. 2.49 m/s
D. 0.249 m/s
690. The weight of a mass of 10 kilograms at
a location where g=9.77m/s2 is:
A. 79.7 N
B. 77.9 N
C. 97.7 N
D. 977 N
691. What is the resultant velocity of a point
of -component , and -
component at time ?
A. 63.1326
B. 62.1326
C. 64.1326
D. 74.1326
692. A boat has a speed of 8 mph in still
water attempts to go directly across a
river with a current of 3 mph. What is
the effective speed of the boat?
A. 8.35 mph
B. 8.54 mph
C. 7.42 mph
D. 6.33 mph
693. A ship moving North at 10 mph. A
passenger walks Southeast across the
deck at 5 mph. In what direction and
how fast is the man moving, relative to
the earth’s surface.
A. N 28°40’W; 7.37 mph
B. N 61°20’E; 7.37 mph
C. N 61°20’W; 7.37 mph
D. N 28°40’E; 7.37 mph
694. A man wishes to cross due west on a
river which is flowing due north at the
rate of 3 mph. if he can row 12 mph in
still water, what direction should he
take to cross the river?
A. S 14.47°W
B. S 75.52°W
C. S 81.36°W
D. S 84.36°W
695. A plane is headed due east with air
speed of 240 kph. If a wind of 40kph is
blowing from the north, find the ground
speed of the plane.
A. 243 kph
B. 423 kph
C. 200 kph
D. 240 kph
696. Three forces 20N, 30N, and 40N are in
equilibrium. Find the angle between the
30-N and 40-N forces.
A. 30°15’25’’
B. 28.96°
C. 40°
D. 25.97°
697. A 10-kg weight is suspended by a rope
from a ceiling. If a horizontal force of
5.80 kg is applied to the weight, the
rope will make an angle with the vertical
equal to:
A. 60°
B. 30°
C. 45°
D. 75°
698. A 100kN block slides down a plane
inclined at an angle of 30° with the
horizontal. Neglecting friction, find the
force that causes the block to slide.
A. 86.6 kN
B. 80 kN
C. 20 kN
D. 50 kN
699. What tension must be applied at the
ends of a flexible wire cable supporting
a load of 0.5 kg per horizontal meter in
a span of 100 m if the sag is to be
limited to 1.25 m?
A. 423.42 kg
B. 584.23 kg
C. 500.62 kg
D. 623.24 kg
700. The allowable spacing of towers to carry
an aluminum cable weighing 0.03 kg per
horizontal meter if the maximum
tension at the lowest point is not to
exceed 1150 kg at sag of 0.50 m is:
A. 248 m
B. 390 m
C. 408 m
D. 422 m
701. A wooden plank meters long has one
end leaning on top of a vertical wall 1.5
m high and the other end resting on a
horizontal ground. Neglecting friction,
find if a force (parallel to the plank) of
100 N is needed to pull a 400 N block up
the plank.
A. 6 m
B. 5 m
C. 4 m
D. 3 m
702. A block of wood is resting on a level
surface. If the coefficient of friction
between the block and the surface is
0.30, how much can the plane be
inclined without causing the block to
slide down?
A. 16.7°
B. 30.2°
C. 21.2°
D. 33.3°
703. A 500-kg block is resting on a 30°
inclined plane with a µ=0.3 Find the
required force acting horizontally that
will prevent the block from sliding.
A. 1020 N
B. 1160 N
C. 4236 N
D. 5205 N
704. A 500-kg block is resting on a 30°
inclined plane with a µ=0.3 Find the
required force acting horizontally that
will start the block to block up the
plane.
A. 4236 N
B. 1160 N
C. 5205 N
D. 2570 N
705. What is the acceleration of the body
that increases in velocity from 20 m/s to
40 m/s in 3 seconds? Answer in S.I.
units.
A. 8 m/s2
B. 6.67 m/s2
C. 5 m/s2
D. 7 m/s2
706. From a speed of 75 kph, a car
decelerates at the rate of 500 m/min2
along a straight path. Howw far in
meters, will it travel in 45 sec?
A. 795
B. 791
C. 797
D. 793
707. With a starting speed of 30 kph at a
point , a car accelerates uniformly.
After 18 minutes, it reaches point , 21
km from . Find the acceleration of the
car in m/s2.
A. 0.126 m/s2
B. 0.0562 m/s2
C. 0.0206 m/s2
D. 3.42 m/s2
708. A train upon passing point at a speed
of 72 kph accelerates at 0.75 m/s2 for
one minute along a straight path then
decelerates at 1.0 m/s2. How far in
kilometers from point will it be in 2
minutes after passing point .
A. 4.95
B. 4.75
C. 4.85
D. 4.65
709. A car starting from rest moves with a
constant acceleration of 10 km/hr2 for 1
hour, then decelerates at a constant -5
km/hr2 until it comes to a stop. How far
has it travelled?
A. 10 km
B. 20 km
C. 12 km
D. 15 km
710. The velocity of an automobile starting
from rest is given by /
/ ft./sec.
Determine its acceleration after an
interval of 10 seconds (in ft/sec2).
A. 2.10
B. 1.71
C. 2.25
D. 2.75
711. A train running at 60 kph decelerated at
8 m/min2 for 14 minutes. Find the
distance traveled, in kilometers within
this period.
A. 12.2
B. 13.2
C. 13.8
D. 12.8
712. An automobile accelerates at a constant
rate of 15 mi/hr to 45 mi/hr in 15
seconds, while travelling in a straight
line. What is the average acceleration?
A. 2 ft/s2
B. 2.39 ft/s2
C. 2.12 ft/s2
D. 2.93 ft/s2
713. A car was travelling at a speed of 50
mph. The driver saw a road block 80 m
ahead and stepped on the brake causing
the car to decelerate uniformly at 10
m/s2. Find the distance from the
roadblock to the point where the car
stopped. Assume perception reaction
time is 2 seconds.
A. 12.48 m
B. 6.25 m
C. 10.28 m
D. 8.63 m
714. A man driving his car at 45 mph
suddenly sees an object in the road 60
feet ahead. What constant deceleration
is required to stop the car in this
distance?
A. -36.3 ft/s2
B. -45.2 ft/s2
C. -33.4 ft/s2
D. -42.3 ft/s2
715. Determine the outside diameter of
hallow steel tube that will carry a tensile
load of 500 kN at a stress of 140 MPa.
Assume the wall thickness to be one-
tenth of the outside diameter.
A. 123 mm
B. 113 mm
C. 103 mm
D. 93 mm
716. A force of 10 Newtons is applied to one
end of a 10 inches diameter circular rod.
Calculate the stress.
A. 0.20 kPa
B. 0.05 kPa
C. 0.10 kPa
D. 0.15 kPa
717. What force is required to punch a 20-
mm diameter hole through a 10-mm
thick plate. The ultimate strength of the
plate material is 450 MPa.
A. 241 kN
B. 283 kN
C. 386 kN
D. 252 kN
718. A steel pipe 1.5m in diameter is
required to carry am internal pressure
of 750 kPa. If the allowable tensile
stress of steel is 140 MPa, determine
the required thickness of the pipe in
mm.
A. 4.56
B. 5.12
C. 4.25
D. 4.01
719. A spherical pressure vessel 400-mm in
diameter has a uniform thickness of 6
mm. The vessel contains gas under a
pressure of 8,000 kPa. If the ultimate
tensile stress of the material is 420 MPa,
what is the factor of safety with respect
to the tensile failure?
A. 3.15
B. 3.55
C. 2.15
D. 2.55
720. A metal specimen 36-mm in diameter
has a length of 360 mm. A force of 300
kN elongates the length by 1.20 mm.
What is the modulus of elasticity?
A. 88.419 GPa
B. 92.564 GPa
C. 92.658 GPa
D. 95.635 GPa
721. A steel wire 5-m long hanging vertically
supports a weight of 1200 N. Determine
the required wire diameter if the stress
is limited to 140 MPa and the total
elongation must not exceed 4mm.
Neglect the weight of the wire and
assume GPa.
A. 3.09 mm
B. 3.56 mm
C. 3.33 mm
D. 2.89 mm
722. During a stress-strin test, the unit
deformation at a stress of 35 MPa was
observed to be m/m and at
a stress of 140 MPa it was
m/m. If the proportional limit was
200 MPa, what is the modulus of
elasticity. What is the strain
corresponding to the stress of 80 MPa?
A. MPa;
m/m
B. MPa;
m/m
C. MPa;
m/m
D. MPa;
m/m
723. An axial load of 100 kN is applied to a
flat bar 20 mm thick, tapering in width
from 120 mm to 40 mm in a length of 10
m. Assuming GPa, determine
the total elongation of the bar.
A. 3.43 mm
B. 2.125 mm
C. 4.33 mm
D. 1.985 mm
724. Steel bar having a rectangular cross-
section 15 mm 20 mm and 150 m
long is suspended vertically from one
end. The steel has a unit mass of 7850
kg/m3 and a modulus of elasticity of
200 GPa. If a loaf of 20 kN is suspended
at the other end of the rod, determine
the total elongation of the rod.
A. 43.5 mm
B. 54.3 mm
C. 35.4 mm
D. 45.3 mm
725. A steel bar 50 mm in diameter and 2 m
long is surrounded by a shell of cast iron
5 mm thick. Compute the load that will
compress the bar a total of 1 mm in the
length of 2 m. Use GPa
and GPa.
A. 200 kN
B. 240 kN
C. 280 kN
D. 320 kN
726. A 20-mm diameter steel rod, 250 mm
long is subjected to a tensile force of 75
kN. If the Poisson’s ratio µ is 0.30,
determine the lateral strain of the rod.
Use GPa.
A. mm/mm
B. mm/mm
C. mm/mm
D. mm/mm
727. A solid aluminum shaft of 100-mm
diameter fits concentrically in a hollow
steel tube, determine the minimum
internal diameter of the steel tube so
that no contact pressure exists when
the aluminum shaft carries an axial
compressive load of 600 kN. Assume
Poisson’s ratio µ=1/3 and the modulus
of elasticity of aluminum be 70 GPa.
A. 100.0364 mm
B. 100.0312 mm
C. 100.0303 mm
D. 100.0414 mm
728. The maximum allowable torque, in kN-
m, for a 50-mm diameter steel shaft
when the allowable shearing stress is
81.5 MPa is:
A. 3.0
B. 1.0
C. 4.0
D. 2.0
729. The rotation of twist in degrees of a
shaft, 800 mm long subjected to a
torque of 80 N-m, 20 mm in diameter
and shear modulus of 80,000 MPa is:
A. 3.03
B. 4.04
C. 2.92
D. 1.81
730. Compute the value the shear modulus
of steel whose modulus of elasticity is
200 GPa and Poisson’s ratio µ is 0.30.
A. 72,456 MPa
B. 76,923 MPa
C. 79,698 MPa
D. 82,400 MPa
731. Determine the length of the shortest 2-
mm diameter bronze wire, which can be
twisted through two complete turns
without exceeding a stress of 70 MPa.
Use GPa.
A. 6.28 m
B. 5.23 m
C. 6.89 m
D. 8.56 m
732. A hollow steel shaft 2540 mm long must
transmit torque of 35 kN-m. The total
angle of twist must not exceed 3
degrees. The maximum shearing stress
must not exceed 110 MPa. Find the
inside diameter and the outside
diameter of the shaft that meets these
conditions.
A. mm; mm
B. mm; mm
C. mm; mm
D. mm; mm
733. Determine the maximum shearing stress
in a helical steel spring composed of 20
turns of 20-mm diameter wire on a
mean radius of 80 mm when the spring
is supporting a load of 2 kN.
A. 110.6 MPa
B. 101.1 MPa
C. 120.6 MPa
D. 136.5 MPa
734. A load is supported by two springs
arranged in series. The upper spring has
20 turns of 29-mm diameter wire on a
mean diameter of 150 mm. The lower
spring consist of 15 turns of 10-mm
diameter wire on a mean diameter of
130 mm. Determine the value of that
will cause a total deflection of 80 mm.
Assume GPa for both springs.
A. 223.3 N
B. 228.8 N
C. 214.8 N
D. 278.4 N
735. A 10-meter long simply supported beam
carries a uniform load of 8 kN/m for 6
meters from the left support and a
concentrated load of 15 kN 2 meters
from the right support. Determine the
maximum shear and moment.
A. kN; kN-
m
B. kN; kN-
m
C. kN;
kN-m
D. kN; kN-
m
736. A simple beam, 10 m long carries a
concentrated load of 500 kN at the
midspan. What is the maximum
moment of the beam?
A. 1250 kN-m
B. 1050 kN-m
C. 1520 kN-m
D. 1510 kN-m
737. A small square 5 cm by 5 cm is cut out
of one corner of a rectangular
cardboard 20 cm by 30 cm long. How
far, in cm from the uncut longer side, is
the centroid of the remaining area?
A. 9.56
B. 9.35
C. 9.48
D. 9.67
738. What is the inertia of a bowling ball
(mass = 0.5 kg) of radius 15 cm rotating
at an angular speed of 10 rpm for 6
seconds?
A. 0.0045 kg-m2
B. 0.001 kg-m2
C. 0.005 kg-m2
D. 0.002 kg-m2
739. What is the moment of inertia of a
cylinder of radius 5 m and a mass of 5
kg?
A. 62.5 kg-m2
B. 80 kg-m2
C. 72.5 kg-m2
D. 120 kg-m2
740. The mass of air in a room which is 3m
5m 20m is known to be 350 kg. Find its
density.
A. 1.167 kg/m3
B. 1.176 kg/m3
C. 1.617 kg/m3
D. 1.716 kg/m3
741. One hundred (100) grams of water are
mixed with 150 grams of alcohol
( kg/ cu m). What is the specific
gravity of the resulting mixtures,
assuming that the two fluids mix
completely?
A. 0.96
B. 0.82
C. 0.63
D. 0.86
742. 100 g of water are mixed with 150 g of
alcohol ( kg/ cu m). What is the
specific volume of the resulting
mixtures, assuming that the two fluids
mix completely?
A. 0.88 cu cm/g
B. 1.20 cu cm/g
C. 0.82 cu cm/g
D. 0.63 cu cm/g
743. The pressure 34 meters below the
ocean is nearest to:
A. 204 kPa
B. 222 kPa
C. 344 kPa
D. 362 kPa
744. What is the atmospheric pressure on a
planet where the absolute pressure is
100kPa and the gage pressure is 10 kPa?
A. 90 kPa
B. 80 kPa
C. 100 kPa
D. 10 kPa
745. If the pressure at a point in the ocean is
60 kPa, what is the pressure 27 meters
below this point?
A. 256.3 kPa
B. 521.3 kPa
C. 332.8 kPa
D. 185.4 kPa
746. A pressure gage 6 m above the bottom
of the tank containing a liquid reads 90
kPa; another gage height 4 m reads 103
kPa. Determine the specific weight of
the liquid.
A. 6.5 kN/m3
B. 5.1 kN/m3
C. 3.2 kN/m3
D. 8.5 kN/m3
747. The weight density of a mud is given by
, where is in kN/m3
and is in meters. Determine the
pressure, in kPa, at a depth of 5m.
A. 89.36 kPa
B. 56.25 kPa
C. 62.5 kPa
D. 78.54 kPa
748. What is the resulting pressure when one
pound of air at 15 psia and 200°F is
heated at constant volume to 800°F?
A. 28.6 psia
B. 52.1 psia
C. 36.4 psia
D. 15 psia
749. The volume of a gas under standard
atmospheric pressure 76 cm Hg is 200
in3. What is the volume when the
pressure is 80 cm Hg, if the temperature
is unchanged?
A. 190 in3
B. 90 in3
C. 110 in3
D. 30.4 in3
750. A two-meter square plane surface is
immersed vertically below the water
surface. The immersion is such that the
two edges of the square are horizontal.
If the top of the square is 1 meter below
the water surface, what is the total
water pressure exerted on the plane
surface?
A. 43.93 kN
B. 52.46 kN
C. 64.76 kN
D. 78.48 kN
751. Find the total water pressure on a
vertical circular gate, 2 meters in
diameter, with its top 3.5 meters below
the water surface.
A. 138.7 kN
B. 107.9 kN
C. 169.5 kN
D. 186.5 kN
752. An iceberg having specific gravity of
0.92 is floating on salt water of sp. gr.
1.03. If the volume of ice above the
water surface is 1000 cu. m., what is the
total volume of the ice?
A. 8523 m3
B. 7862 m3
C. 9364 m3
D. 6325 m3
753. A block of wood requires a force of 40 N
to keep it immersed in water and a
force of 100 N to keep it immersed in
glycerin (sp. gr. = 1.3). Find the weight
and sp. gr. Of the wood.
A. 0.7
B. 0.6
C. 0.9
D. 0.8
754. Reynolds number may be calculated
from:
A. diameter, density, and absolute
viscosity
B. diameter, velocity, and surface
tension
C. diameter, velocity, and absolute
viscosity
D. characteristic length, mass flow rate
per unit area, and absolute viscosity
755. The sum of the pressure head, elevation
head, and the velocity head remains
constant, this is known as:
A. Bernoulli’s Theorem
B. Boyle’s Law
C. Archimedes’ Principle
D. Torrecelli’s Theorem
756. What is the expected head loss per mile
of closed circular pipe (17-in inside
diameter, friction factor of 0.03) when
3300 gal/min of water flow under
pressure?
A. 38 ft
B. 0.007 ft
C. 3580 ft
D. 64 ft
757. What is the rate of flow of water
passing through a pipe with a diameter
of 20 mm and speed of 0.5 m/sec?
A. m3/s
B. m3/s
C. m3/s
D. m3/s
758. An orifice has a coefficient of discharge
of 0.62 and a coefficient of contraction
of 0.63. Determine the coefficient of
velocity for the orifice.
A. 0.98
B. 0.99
C. 0.97
D. 0.96
759. The theoretical velocity of flow through
an orifice 3 m below the surface of
water in a tall tank is:
A. 8.63 m/s
B. 9.85 m/s
C. 5.21 m/s
D. 7.67 m/s
760. Water having kinematic viscosity
m2/s flows in a 100-mm
diameter pipe at a velocity of 4.5 m/s.
the Reynolds number is:
A. 346,150
B. 258,250
C. 387,450
D. 298,750
761. Oil having specific gravity of 0.869 and
dynamic viscosity of 0.0814 Pa-s flows
through a cast iron pipe at a velocity of
1 m/s. The pipe is 50 m long and 150
mm in diameter. Find the head lost due
to friction.
A. 0.73 m
B. 0.45 m
C. 0.68 m
D. 1.25 m
762. What commercial size of new cast iron
pipe shall be used to carry 4490 gpm
with a lost of head of 10.56 feet per
mile? Assume .
A. 625 mm
B. 576 mm
C. 479 mm
D. 352 mm
763. Assume that 57 liters per second of oil
( kg/m3) is pumped through a
300 mm diameter pipeline of cast iron.
If each pump produces 685 kPa, how far
apart can they be placed? (Assume
)
A. 23.7 m
B. 32.2 m
C. 12.6 m
D. 19.8 m
764. A 20-mm diameter commercial steel
pipe, 30 m long is used to drain an oil
tank. Determine the discharge when the
oil level in the tank is 3 m above the exit
of the pipe. Neglect minor losses and
assume .
A. 0.000256 m3/s
B. 0.000179 m3/s
C. 0.000113 m3/s
D. 0.000869 m3/s
MULTIPLE CHOICE QUESTIONS IN
<ENGINEERING ECONOMICS>
<DIEGO INOCENCIO TAPANG GILLESANIA>
ENCODED BY: BORBON, MARK ADRIAN C.
765. The recorded current value of an asset
is known as:
A. scrap value
B. book value
C. salvage value
D. present worth
766. The ratio of the interest payment to the
principal for a given unit of time and is
usually expressed as a percentage of the
principal is known as:
A. investment
B. nominal interest
C. interest
D. interest rate
767. A method of depreciation whereby the
amount to recover is spread over the
estimated life of the asset in terms of
the periods or units of output is called:
A. SOYD method
B. declining balance method
C. straight line method
D. sinking fund method
768. The interest rate at which the present
worth of cash flow on a project is zero,
or the interest earned by an investment.
A. rate of return
B. effective rate
C. nominal rate
D. yield
769. The lessening of the value of an asset
due to the decrease in the quantity
available. This refers to the natural
resources such as coal, oil, and timber in
the forest.
A. depreciation
B. depletion
C. inflation
D. incremental cost
770. The method of depreciation where a
fixed sum of money is regularly
deposited at compound interest in a
real or imaginary fund in order to
accumulate an amount equal to the
total depreciation of an asset at the end
of the asset’s estimated life is known as:
A. straight line method
B. SYD method
C. declining balance method
D. sinking fund method
771. The term used to express the series of
uniform payments occurring at equal
interval of time is:
A. compound interest
B. annuity
C. perpetuity
D. depreciation
772. The profit derived from a project or
business enterprise without
consideration of obligations to financial
contributors and claims of others based
on profit is known as:
A. yield
B. earning value
C. economic return
D. expected yield
773. As applied to capitalized asset, the
distribution of the initial cost by periodic
changes to operation as in depreciation
or the reduction of the depth by either
periodic or irregular prearranged
program is called:
A. amortization
B. annuity
C. depreciation
D. capital recovery
774. Those funds that are required to make
the enterprise or project a going
concern.
A. banking
B. accumulated amount
C. working capital
D. principal or present worth
775. These are product or services that are
desired by humans and will be
purchased if money is available after the
required necessities have been
obtained.
A. utilities
B. necessities
C. luxuries
D. producer goods and services
776. These are product or services that are
required to support human life and
activities, that will be purchased in
somewhat the same quantity even
though the price varies considerably.
A. utilities
B. necessities
C. luxuries
D. producer goods and services
777. A condition where only few individuals
produce a certain product and that any
action of one will lead to almost the
same action of the others.
A. oligopoly
B. semi-oligopoly
C. monopoly
D. perfect competition
778. This occurs in a situation where a
commodity or service is supplied by a
number of vendors and there is nothing
to prevent additional vendors entering
the market.
A. perfect competition
B. monopoly
C. oligopoly
D. elastic demand
779. It is the amount that a willing buyer will
pay to a willing seller for a property
where each has equal advantage and is
under no compulsion to buy or sell.
A. fair value
B. use value
C. market value
D. book value
780. It is defined to be the capacity of a
commodity to satisfy human want.
A. discount
B. luxuries
C. utility
D. necessity
781. A form of summary of assets, liabilities,
and net worth:
A. balance method
B. break-even point
C. balance sheet
D. production
782. The worth of a property, which is equal
to the original cost less depreciation, is
known as:
A. earning value
B. scrap value
C. book value
D. face value
783. When using net present worth
calculations to compare two projects,
which of the following could invalidate
the calculations?
A. mutually exclusive projects
B. evaluation over different periods
C. non-conventional cash flows
D. difference in the magnitude of the
projects
784. Which of the following is a form of
business/company ownership?
A. partnership
B. corporation
C. single proprietorship
D. all of these
785. What must two investments with the
same present worth and unequal lives have?
A. identical salvage value
B. different salvage values
C. identical equivalent uniform annual
cash flows
D. different equivalent annual cash
flows
786. Find the interest on P6800.00 for 3 years at
11% simple interest.
A. P1,875.00
B. P1,987.00
C. P2,144.00
D. P2,244.00
787. A man borrowed P10,000.00 from his friend
and agrees to pay at the end of 90 days
under 8% simple interest rate. What is the
required amount?
A. P10,200.00
B. P11,500.00
C. P9,500.00
D. P10,700.00
788. Annie buys a television set from a merchant
who offers P25,000.00 at the end of 60
days. Annie wishes to pay immediately and
the merchant offers to compute the
required amount on the assumption that
the money is worth 14% simple interest.
What is the required amount?
A. P20,234,87
B. P19,222.67
C. P24,429.97
D. P28,456.23
789. What is the principal amount if the amount
of interest at the end of 2½ year is P4500
for a simple interest of 6% per annum?
A. P35,000.00
B. P30,000.00
C. P40,000.00
D. P45,000.00
790. How long must a P40,000 note bearing 4%
simple interest to run to amount to
P41,350.00?
A. 340 days
B. 403 days
C. 304 days
D. 430 days
791. If P16,000 earns P480 in 9 months, what is
the annual rate of interest?
A. 1%
B. 2%
C. 3%
D. 4%
792. A man lends P6000 at 6% simple interest for
4 years. At the end of this time he invests
the entire amount (principal plus
investment) at 5% compounded annually
for 12 years. How much will he have at the
end of the 16-year period?
A. P13,361.20
B. P13,633.20
C. P13,333.20
D. P16,323.20
793. A time deposit of P110,000 for 31 days
earns P890.39 on maturity date after
deducting the 20% withholding tax on
interest income. Find the rate of interest
per annum.
A. 12.5%
B. 11.95%
C. 12.25%
D. 11.75%
794. A bank charges 12% simple interest on a
P300.00 loan. How much will be repaid if
the load is paid back in one lump sum after
three years?
A. P408.00
B. P551.00
C. P415.00
D. P450.00
795. The tag price of a certain commodity is for
100 days. If paid in 31 days, there is a 3%
discount. What is the simple interest paid?
A. 12.15%
B. 6.25%
C. 22.32%
D. 16.14%
796. Accumulate P5,000.00 for 10 years at 8%
compounded quarterly.
A. P12,456.20
B. P13,876.50
C. P10,345.80
D. P11,040.20
797. Accumulate P5,000.00 for 10 years at 8%
compounded semi-annually.
A. P10,955.61
B. P10,233.67
C. P9,455.67
D. P11,876.34
798. Accumulate P5,000.00 for 10 years at 8%
compounded monthly.
A. P15,456.75
B. P11,102.61
C. P14,768.34
D. P12,867.34
799. Accumulate P5,000.00 for 10 years at 8%
compounded annually.
A. P10,794.62
B. P8,567.98
C. P10,987.90
D. P7,876.87
800. How long will it take P1,000 to amount to
P1,346 if invested at 6% compounded
quarterly?
A. 3 years
B. 4 years
C. 5 years
D. 6 years
801. How long will it take for an investment to
double its amount if invested at an interest
rate of 6% compounded bi-monthly?
A. 10 years
B. 12 years
C. 13 years
D. 14 years
802. If the compound interest on P3,000.00 in 2
years is P500.00, then the compound
interest on P3,000.00 in 4 years is:
A. P956.00
B. P1,083.00
C. P1,125.00
D. P1,526.00
803. The salary of Mr. Cruz is increased by 30%
every 2 years beginning January 1,1982.
Counting from that date, at what year will
his salary just exceed twice his original
salary?
A. 1988
B. 1989
C. 1990
D. 1991
804. If you borrowed P10,000 from a bank with
18% interest per annum, what is the total
amount to be repaid at the end of one
year?
A. P11,800.00
B. P19,000.00
C. P28,000.00
D. P10,180.00
805. What is the effective rate for an interest
rate of 12% compounded continuously?
A. 12.01%
B. 12.89%
C. 12.42%
D. 12.75%
806. How long will it take for an investment to
fivefold its amount if money is worth 14%
compounded semiannually?
A. 11
B. 12
C. 13
D. 14
807. An interest rate of 8% compounded
semiannually is how many percent if
compounded quarterly?
A. 7.81%
B. 7.85%
C. 7.92%
D. 8.01%
809. A man is expecting to receive P450,000.00
at the end of 7 years. If money is worth 14%
compounded quarterly, how much is it
worth at present?
A. P125,458.36
B. P147,456.36
C. P162,455.63
D. P171,744.44
810. A man has a will of P650,000.00 from his
father, If his father deposited an amount of
P450,000.00 in a trust fund earning 8%
compounded annually, after how many
years will the man receive his will?
A. 4.55 years
B. 4.77 years
C. 5.11 years
D. 5.33 years
811. Mr. Adam deposited P120,000.00 in a bank
who offers 8% interest compounded
quarterly. If the interest is subject to a 14%
tax, how much will he receive after 5 years?
A. P178,313.69
B. P153.349.77
C. P170,149.77
D. P175,343.77
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