VIP NO.

5 - MESL
1. If vector A is 10 units and vector B, which B. Negative D. Undefined
makes 60° with vector A, is 20 units. What is 16. An isosceles triangle has a 10cm base and a
the difference of vectors A and B? 10 cm altitude. Calculate the moment of
A. 18.76 units C. 15.34 units inertia of the triangular area relative to a
B. 17.32 units D. 13.45 units line parallel to the base and through the
2. How many HP are there in one KW upper vertex, in cm^4.
A. 746 C. 1.34 A. 2450 C. 3025
B. 0.8 D. 0.746 B. 2550 D. 2500
3. Piping color for communication: 17. Determine the outside diameter of a hollow
A. Silver-grey C. White steel tube that will carry a tensile load of
B. Yellow D. Black 500 kN at a stress of 140 Mpa. Assume the
4. 100 g of pure water are mixed with 150 g of wall thickness to be one—tenth of the outside
denatured alcohol (sg = 790 kg/cu.m). What is diameter.
the specific volume of the resulting A. 93 mm C. 103 mm
mixtures, assuming that the fluids mix B. 113 mm D. 123 mm
completely? 18. Which of the following number has three
A. 1.20 cu cm/g C. 0.63 cu cm/g significant digits?
B. 0.82 cu cm/g D. 0.88 cu cm/g A. 1.1111 C. 0.0011
5. What is the last term of the series 2, 4, 8, B. 0.0111 D. 0.01111
16,...... to the 15th term? 19. Another name for derivative is _______.
A. 32,678 C. 23,867 A. Differential form
B. 23,786 D. 32,768 B. Partial derivative
6. How much money should a man invest in a fund C. Differential coefficient
paying 8 percent annual interest compound D. Differential manifold
continuously if he wants to use the money to 20. An engine operates between temperature limits
buy a Php 20,000 equipment in 4 years? of 900K and T2, and another between T2 and
A. 11,237.45 C. 14,522.98 400K. If both are to be equally efficient,
B. 15,346.76 D. 12,457.45 solve the value of T2?
7. What is an annuity? A. 600K C. 650K
A. An annual repayment of a loan B. 630K D. 750K
B. The future worth of a present amount 21. An electric motor has a cash price of P8000.
C. A series of uniform amounts over a period It can also be bought on installment basis
of time with down payment of P2000 and with periodic
D. The present worth of a future amount equal payments at the end of every 6 months
8. The pressure, dry bulb temperature and for 5 years if interest rate is fixed at 8%
relative humidity of air in a room are 1 bar, compounded semi-annually, how much is each
301/2 C and 70% respectively. Calculate the periodic payment?
specific humidity of the room air in kg water A. 439.56 C. 874.32
vapor per kg of dry air if the saturated steam B. 739.75 D. 122.56
pressure at 301/2 C is 4.25 kPa. 22. Determine the equation of the line whose
A. 0.0322 C. 0.0191 slope is -3 and the x-intercept is 5.
B. 0.0079 D. 0.0124 A. 3x+y=15 C. y=15x-3
9. Change the equation y = x from rectangular to B. y=3x-15 D. 3x-y=5
polar coordinates. 23. The arc length equal to the radius of the
A. π/3 C. π circle is called _________.
B. π/2 D. π/4 A. π radian C. 1 radian
10. An MRT travels between two terminals 1 km B. 1 quarter circle D. 1 grad
apart at a minimum time of 1 minute. If the 24. The proportions of blood phenotypes A, B, AB
MRT cart accelerates and decelerates at 3.4 and O in the population of all Caucasians in
per sec², starting from rest at the first the US are reported as 0.41, 0.10, 0.04 and
terminal and coming to stop at the second 0.45, respectively. If a Caucasian is chosen
terminal. Determine the minimum speed. randomly from the population, what is the
A. 40 kph C. 20 kph probability that he or she will either type
B. 66 kph D. 55 kph A or type AB blood?
11. Which one of the following statements A. 0.10 C. 0.15
regarding organic substances is NOT TRUE? B. 0.45 D. 0.35
A. Organic substances generally do not 25. An Electrical Engineer obtained a loan of
dissolve in water. 50,000.00 at the rate of 6% compounded
B. All organic matter contains carbon annually in order to repair his mistress
C. Organic substances generally dissolve in house. How much must the Electrical Engineer
high-concentration acids pay monthly to amortize the loan within a
D. Organic matter is generally stable at very period of ten years?
high temperatures. A. P605.20 C. P508.90
12. If the density of a gas is 0.003 slug/ft^3, B. P550.90 D. P505.90
find the specific weight of the gas. 26. What is the power factor of a 2HP 240 V 15
A. 76.3 N/m^3 C. 9.04 N/m^3 Amps electric motor with 85% motor
B. 15.2 N/m^3 D. 98.2 N/m^3 efficiency?
13. What is the polar equation of the circle with A. 0.687 C. 0.487
center at the pole containing the given point B. 0.987 D. 0.497
( 1, 1 ) , rectangular coordinates? 27. Which of the following compounds and elements
A. r = sq. rt of 2 C. r = 1/2 is unstable in its pure form?
B. r = 2 D. r = 1 A. Helium C. Sodium
14. Factor the said expression (x raised to (4) B. Carbon dioxide D. Hydrochloric acid
– y raised to (4)) as completely. 28. Determine the equation of the line that is
A. (x+y) (x²+2xy+y²) perpendicular to the line segment (-4,2) and
B. (1x-x²) (1+y) (1+y²) (1,-7) and passes through the point x = 4 and
C. (x²+y²) (x+y) (x-y) y = -3
D. (x²+y²) (x²-y²) A. 5x – 9y – 47 = 0 C. 2x + 3y + 12 = 0
15. If the columns (on rows) of a determinant are B. 9x – 5y + 40 = 0 D. x + 5y – 10 = 0
identical, the value of the determinant is 29. What is the amount that must be deposited
______. every quarterly in a fund paying 12%
A. zero C. Positive
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compounded quarterly in order to have P25,000 43. ______________ is the length of time at which
in 8 years? the original cost of capital used to purchase
A. P674.71 C. P476.17 a unit has already been recovered.
B. P700.00 D. P746.71 A. Salvage value C. Physical life
30. Find the maximum area of a rectangle B. Economic life D. Write off period
inscribed in a semi-circle of radius 5 inches 44. What is the maximum area of the rectangle
if its base lies along the diameter of the whose base is on the x-axis and whose upper
semi-circle? two vertices line on the parabola y = 12 -
A. 100 C. 25 x»?
B. 5 D. 35 A. 20 C. 32
31. A wet pipe sprinkler system includes an alarm B. 54 D. 16
check valve. The alarm check valve is 45. What is the absolute pressure in the
equipped with a retard chamber. The main condenser the vacuum gage reads 710 mm Hg
purpose of the retard chamber is to minimize when the barometer is at 755mm Hg?
_____________. A. 5.6 kPa C. 6.1 kPa
A. cavitation B. 5.9 kPa D. 5.8 kPa
B. damage to the piping from pressure 46. The moment of inertia of a section 2 inches
transients wide and 2 feet high about an axis 1 foot
C. noise and vibrations from water hammer above the bottom edge of the section, in
D. the number of spurious alarms inches raised to 4 is:
32. Factor the said expression (1-a to the 8th A. 1834 C. 9214
power) as completely. B. 384 D. 2304
A. (1+a to the 4th power)(1+a>>)(1-a>>) 47. What do you think is the output or sales at
B. (1+a to the 4th power)(1-a to the 4th which income is insufficient to equal
power) operating cost?
C. (1+a to the 4th power)(1+a>>)(1+a)(1-a) A. Break even point C. Investment
D. (1+a>>)(1-a>>)(1-a to the 4th power) B. Depreciation D. Cash flow
33. From a plastic box containing 8 red balls, 10 48. A vessel with a volume of 1 cu.m. contains
white balls and 12 blue balls. If one ball is liquid water and water vapor in equilibrium
drawn at random, what is the probability that at 87.05 psi. The liquid water has a mass of
is not blue? 2.205 lb. Compute the approximate mass of the
A. 0.45 C. 0.35 water vapor.
B. 0.50 D. 0.60 Note: from steam tables at 600 kPa. Vf =
34. If John can do the job in X days and James in 0.001101 m3/kg, Vg = 0.3157 m3/kg
Y days, how long will they finish the job A. 7.0 lb C. 3.2 lb
working together? B. 2.3 lb D. 5.4 lb
A. (x+y)/xy days C. (xy)/(x+y) days 49. A spherical snow ball melting in such a way
B. (x+y)/2 days D. x+y days that its surface area decreases at the rate
35. What is the process called, the more solute of 1 cu.cm/min. How fast is its radius
is added to an already saturated solution shrinking when it is 3 cm?
which will cause the excess solute to settle A. -1/48π C. -1/20π
to the bottom of the container? B. -1/24π D. -1/12π
A. Precipitation C. Hydration 50. What is the maximum shearing stress in a
B. Saturation D. Dehydration helical mild steel spring composed of 16
36. What is the polar equation of the circle with turns of 18-mm diameter wire on a mean radius
the given radius a = 3/2, and with center in if 75 mm when the spring is supporting a load
polar coordinates, (3/2, Ð)? of 4 kN.
A. R = 5cos Õ C. R = -3cos Õ A. 308 MPa C. 136.5 Mpa
B. R = 2sin Õ D. R = 3sin Õ B. 120.6 MPa D. 110.6 Mpa
37. Starting from rest, an airplane acquires a 51. Find the value of the first derivative at x=1
take-off velocity of 150 mph on a 2-mile if the given function of f(x) = x to the 3rd
runway. The acceleration is assumed to be power is -12x+1.
uniform. Calculate the time required to reach A. 12 C. 9
take-off speed. B. -9 D. 3
A. 80 sec C. 116 sec 52. Any line segment joining a vertex of a
B. 96 sec D. 132 sec triangle to a point on the opposite side is
38. A 10-kg block is raised vertically 3 meters. called as:
What is the change in potential energy? A. Newton line C. Cevian
A. 350.3 N-m C. 294.3 J B. Secant D. Euclidian line
B. 320.3 J D. 350.3 kg-m²/s² 53. Annie buys a television set from a merchant
39. A five-point star is also termed as: who offers P25,000.00 at the end of 60 days.
A. Pentatron C. Pentagon Annie wishes to pay immediately and the
B. Pentagram D. Quintagon merchant offers to compute the required
40. The force F of attraction between two amount on the assumption that money is worth
electric charges varies inversely as the 14% interest. What is the required amount?
square of the distance D between them. If the A. P24,429.97 C. P28,456.23
force is 20.0 grams when they are 15.0 cm B. P19,222.67 D. P20,234.87
apart, find the force when they are 7.5 cm 54. If five coins are tossed simultaneously, find
apart. the probability of getting at least four
A. 60 grams C. 45 grams tails.
B. 30 grams D. 80 grams A. ¼ C. 3/16
41. A father, Max is 24 years older than his son B. 4/5 D. 6/31
Joey. In 8 years he will be twice as old as 55. A kite 100 feet above the ground, moving in
his son Joey. What is the present age? a strictly horizontal direction at a rate of
A. 35 C. 40 10 ft/s. How fast is the angle between the
B. 50 D. 45 string and the horizontal changing when there
42. Use the slope-intercept equation of a line y= is 300 ft of string out?
mx+b with the slope of 2/3 and y-intercept of A. – 1/90 C. – 1/70
2. B. – 5/70 D. – 3/20
A. y = 2x + 3/2 C. y = 2/3x +2 56. Who can be responsible charge of preparation
B. y = 3/2x +2 D. y = 3x/2 +3/2 of plans and design of mechanical plant?
A. Licensed ME
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B. CPM 69. A square with side S has a perimeter equal to
C. Professional Mechanical Engineer the circumference of a circle with radius R.
D. all of the above Which of the following is true?
57. If the daily wage of a Mechanical Engineer A. 2S = ÐR C. S = 2ÐR
and CPM are in the ratio 2:1. In a day, a B. 4S = ÐR D. S = ÐR
Mechanical Engineer has to work 8 hrs but the 70. It is the type of bond where the corporation’s
CPM only 6 hrs. Determine the ratio of their owner name is recorded and the interest is
hour wages. paid periodically to the owners.
A. 8:3 C. 5:3 A. Bail bond
B. 3:2 D. 4:3 B. Preferred bond
58. Determine the accumulated value of P2,000.00 C. Registered bond
in 5 years it is invested at 11% compounded D. Incorporator’s bond
quarterly. 71. The amount of P2,825.00 in 8 years at 5%
A. P4,304.00 C. P3,044.00 compounded continuously is:
B. P3,404.00 D. P3,440.00 A. P4,214.40 C. P4,188.56
59. A projectile launched at 2000 ft/sec from B. P4,166.77 D. P4,397.86
Tower A at an angle of 30 deg with the 72. Second law limitations on the maximum
horizontal, impacts at the same elevation at horsepower output from any power unit burning
Tower B. Assume no in-flight propulsion and 1,000,000 BTU/hr of fuel with high and low
no aerodynamic drag. Horizontal distance in temperature extremes of 1540 deg F and 40 deg
miles between Tower A and Tower B is nearest F is ________.
to _______. A. 3830 C. 295
A. 20.3 C. 15.9 B. 98 D. 1140
B. 7.9 D. 10.2 73. From a point 2 cm distance from a circle, a
60. If the outside diameter of a locomotive wheel tangent line is drawn 3 cm long. Find the
minus its steel tire is 62.378 in and the radius of the circle.
inside diameter of the steel tire at 65F is A. 1.75 cm C. 1.5 cm
62.263 inches, to what temperature in B. 2.5 cm D. 1.25 cm
Fahrenheit mus the tire be heated to just fit 74. Maximum plant capacity in kW which a licensed
the wheel? (k for steel = 0.0000065 in per ME is allowed to operate, tend or maintain:
in-degF). A. 300 kW C. 2000 kW
A. 325 C. 349 B. 1000 kW D. 6000 kW
B. 249 D. 225 75. An aluminum is to be measured with a steel
61. What is the unit of pressure in the SI System? gage when the room temperature is 35½C. The
A. in Hg C. in H2O aluminum has a coefficient of linear
B. Pascal D. PSI expansion 24.7 micro mm/mm-degC and the steel
62. Find the radius of curvature 3y = x raised to gage 10.8 micro mm/mm-degC. If the reference
3 at (1, 1/3) temperature is 20½C, with the specified
A. 1 C. Sqrt of 3 length of aluminum equal to 20.021 mm, what
B. Sqrt of 2 D. 3 is the change in measured length due to the
63. Japanese firm specializes the shipment of given temperature?
pressurized gaseous materials. An order is A. 0.002 mm C. 0.005 mm
received for 500 liters of a particular gas B. 0.003 mm D. 0.004 mm
at (32 °F and 1 atm). What minimum volume of 76. How much of a 40% solution of denatured
tank is necessary to transport the gas at 90 alcohol should be mixed to an 80% solution to
°F and a maximum pressure of 10 atm? give 150 liters of a 50% solution?
A. 141 liters C. 152 liters A. 122.5 liters C. 127.5 liters
B. 56 liters D. 60 liters B. 112.5 liters D. 37.5 liters
64. Which of the following are the solutions to 77. A 5-meter extension ladder leans against the
the following wall; the bottom is 3m from the wall. If the
y’’’ - 3y’’ + 3y’ – y = 0? bottom stays at the same place, how much
should the ladder be extended so that the top
I. e raised to x would lean against the wall 1 meter higher.
II. x (e raised to x) A. 0.83095 m C. 1.2 m
III. e raised to –x B. 0.5 m D. 1.5 m
A. II only C. III only 78. Which of the following events will cause the
B. I only D. I and II only optimal lot size, given by the classic EOQ
65. The geometric mean of numbers 3 and 12 is: model with no shortages, to increase?
A. 15 C. 6 A. An increase in demand
B. 7.5 D. 18 B. A decrease in inventory carrying cost and
66. Jen borrowed P200,000 from a local bank and an increase in demand
agreed to pay the loan at the end of one year. C. decrease in inventory carrying cost
The local bank discounted the loan and gave D. A decrease in demand
her P100,950.00 in cash. Find the rate of 79. A company can manufacture a product with off-
discount. the-shelf hand tools. Fixed cost will be Php
A. 2.5% C. 3.75% 50,000.00 for the tools and Php 75.00
B. 1.3% D. 3.12% manufacturing cost per unit. As an
67. Find the length of the latus rectum of the alternative, an automated syste will cost Php
curve x² = -12y? 750,000.00 with a Php 25.00 manufacturing
A. -12 C. 3 cost unit. With annual anticipated volume of
B. 12 D. -3 5,000 units, how many years to break-even?
68. From the top of Tektite Tower A, the angle of A. 2.8 C. 15.0
elevation of the top of the Tektite Tower B B. 2.0 D. 3.6
is 461/2. From the foot of Tektite Tower B, 80. Justine was told to get the 20 cans of milk
the angle of elevation of the top of the in a store. Justine can carry only three cans
Tektite Tower A is 28o. Both towers are on a at a time. How many trips would Justine have
level ground. If the height of Tektite Tower to make?
B is 120m, how high is Tektite Tower A? A. 6.7 trips C. 7 trips
A. 38.6 m C. 42.3 m B. 6 trips D. 7.6 trips
B. 44.1 m D. 40.7 m 81. Each year, a machine loses 20% of the value
it has at the beginning of the year. What is
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the original value of the machine if its value 97. Estimate the median of the following set of
at the end of sixth year is 120,000 pesos? number: 18, 24, 27, 30, 35, 42, 50
A. Php 572,205 C. Php 457,764 A. 29.96 C. 31.82
B. Php 715,256 D. Php 366,211 B. 32.29 D. 30
82. What is the minimum point of y=x+1/x2 =0? 98. A pendulum with a concentrated mass (m) is
A. (1, 1.5) C. (1.5, 2) suspended vertically inside a stationary
B. (1, 2) D. (2, 1) railroad freight car by means of a rigid
83. What occurs when unique product available weightless connecting rod. If the connecting
only from one supplier? rod is pivoted where it attaches to the box
A. duopoly C. competition car, compute the angle that the rod makes
B. monopoly D. oligopoly with the vertical as a result of a constant
84. Justine’s average in 5 subjects is 89. horizontal acceleration of 2 ft/sec^2 of the
Disregarding the lowest grade his average is box car.
90. What is Justine’s lowest grade? A. 3.55 deg C. 6.33 deg
A. 85 C. 87 B. 4.66 deg D. 7.55 deg
B. 86 D. 89 99. A highway curve radius 40 meters is designed
85. Find the factor given in this expression: 6- for a maximum car speed of 72 kph. If the
3m²-8m+4m³ coefficient of friction between tires and the
A. (3+4m) (2+m²) C. (3-4m) (2+m²) road is 0.50, what is the angle from the
B. (3+4m) (2-m²) D. (3-4m) (2-m²) horizontal that the road should be banked?
86. Points (5,4) is at the center of the circle A. 11 deg C. 19 deg
that is tangent to the y-axis. Determine the B. 15 deg D. 23 deg
point of tangency? 100. A refill bullet weighing 4 grams was fired
A. (5,0) C. (0,5) from a 0.45-caliber gun with the barrel
B. (4,0) D. (0,4) measuring 12 cm long. If the bullet was fired
87. A ball is dropped from a height of 60 meters with a speed of 380 m/s, calculate the energy
above ground. How long does it take to hit of the bullet in Joules.
the ground? A. 258 C. 345
A. 4.5 seconds C. 3.5 seconds B. 289 D. 189
B. 2.5 seconds D. 1.5 seconds
88. Which of the following is part of the valence
electrons? ***END***
A. Electrons with positive charge
B. The K-quantum shell electrons NOTE: Please answer and try to resolve EXTRA
C. The outer-shell electrons
D. The electrons of complete quantum shells COACHING posted on our APP.
89. A particles position (in inches) along the x-
axis after t seconds of travel is given by Location: Powerpoint Lectures > EXTRA COACHING
the equation x = 24t>> - 3t raised to 3 + 10.
What is the particle’s average velocity in
in/sec during the first 3 seconds? (For EXTRA COACHING, NO PRINTABLE materials
A. 70 C. 45 will be available)
B. 48 D. 63
90. The sum of P15,000.00 was deposited in an
account earning 4% per annum compounded
quarterly and will become P18,302.85. What is
the effective rate of interest per annum?
A. 4.06 % C. 3.06 %
B. 6.06 % D. 5.06 %
91. China made lathe machine was purchased under
these terms: P30,000.00 down and 5,000.00
each month for 5 years. If money is worth 12%
compounded monthly, determine the cash price
of the machine?
A. P542, 775.91 C. P144, 775.19
B. P254, 775.19 D. P245, 775.19
92. What can you say about the present worth of
all depreciation over the economic life of
the item?
A. Maintenance
B. Annuity
C. Capital recovery
D. Depreciation recovery
93. What is the banking angle if the radius of
the turn of a cyclist leaning towards the
center is 30 ft and the velocity is 15 fps?
A. 14.1 degrees C. 12.9 degrees
B. 13.1 degrees D. 13.6 degrees
94. Find the partial derivative with respect to
x of the function: 150x^2 y-10xy+3y+5
A. 300xy-10y C. 150x2-10x
B. 150y-10y D. 300xy-10x+3
95. The height (in feet) at any time t (in
seconds) of a projectile thrown vertically is
h(t) = - 16t^2 + 256t. When does the
projectile reach the ground?
A. 12 s C. 16 s
B. 18 s D. 10 s
96. The normal boiling point of liquid oxygen is
90 deg K. What is this temperature in deg R?
A. 162 C. 168
B. - 183 D. – 330