Me Preboard -Mar 2011 Set a Math Prc Format

Republic of the Philippines PROFESSIONAL REGULATION COMMISSION Manila BOARD OF MECHANICAL ENGINEERING

Registered Mechanical Engineer Licensure Examination Saturday, January 29, 2011 07:30 a.m. – 12:30 p.m. --------------------------------------------------------------- MATHEMATICS,E  MATHEMATICS,ENG’G NG’G ECONOMIC ECONOMICS S & ENG’G ENG’G SCIENCES SCIENCES

SET A

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by marking the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil No.2 only. MULTIPLE CHOICE 1. A type of bond where the corporation pledges securities which it owns (I,e, stocks, bonds of its subsidiaries). A. Mortgage C. Coupon bond B. Registered bond D. Collateral trust bond * 2. The place where buyers and sellers come together. A. Market * C. Recreation center B. Business D. Buy and sell section 3. An evil wrong committed by a person damaged another person’s property or reputation is A. tort * C. negligence B. material breach D. fraud 4. What is the probability of not getting a red ball from a bag containing 3 white balls, 5 blue balls , and 4 red balls? A. 2/3 * C. 1/3 B. 5/12 D. 1/4 5. In how many ways can 7 persons be seated on a round table if a certain couple is in the group and must be seated together? A. 240 * C. 120 B. 360 D. 720 6. A 100 liter mixture with 85% alcohol is placed in a container. How much water should be added to produce a mixture with 65% alcohol? A. 25.6 C. 30.8 * B. 20.6 D. 35.8 7. What is the highest position in the corporation? A. President C. Chairman of the Board * B. Board of Directors D. Stockholders

8. An association of two or more individuals for the purpose of operating a business as co-owners for profit. A. Sole proprietorship C. Partnership * B. Company D. Corporation 9. Liquid assets such as cash and other assets that can be converted quickly into cash, such as accounts receivable and merchandise are called A. total assets C. current assets * B. fixed assets D. none of the above 10. The length of time which the property may be operated at a profit. A. Physical life C. Operating life B. Economic life * D. All of the above 11. The provision in the contract that indicates the possible adjustment of material cost and labor cost. A. Secondary clause C. Contingency clause B. Escalatory clause * D. Main clause 12. Gross profit, sales less cost of good sold, as a percentage of a sales is called A. profit margin C. net income B. gross margin * D. rate of return 13. Those funds that are required to make the project a going concern. A. Initial investment C. Working capital * B. Current accounts D. Subscribed capital

enterprise

or

14. The payment for the use of borrowed money is called A. loan C. interest * B. maturity value C. principal 15. Sometimes called second hand value. A. Scrap value C. Book value B. Salvage value * D. Going value 16. If John gives $5 to Allen and Allen gives $2 to Eduard, and they have the same money thereafter, how much is Johns money higher than Allen? A. $7 C. $8 * B. $5 D. $3 17. Transform the polar equation r2cos(theta)sin(theta)= rectangular coordinates. A. xy = 4 * C. x + y = 4 2 B. x y = 4 D. x2 + y2 = 4 18. Given of f(x) A. 0, B. 0, 19.

4

to

f(x)= (x –  1)/(x3 – 3x2  + 2x), find x when the value is undefined. -1 and -2 C. 0 and 2 1 and 2 * D. 1 and 2

Given f(x)= 3x – 5, g(f(x))= x , find g(x). A. (2x + 5)/3 C. (x + 5)/3 * B. (3x – 5)/4 D. (x – 5)/3

20. The value which has a disinterested third party, different from the buyer and seller, will determine in order to establish a price acceptable to both parties. A. Market value C. Fair value * B. Goodwill value D. Franchise value 21. It is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods, after the beginning of the payment. A. Deferred annuity * C. Progressive annuity B. Delayed annuity D. Simple annuity 22. A method of computing depreciation in which the annual charge is a fixed percentage of the depreciation book value at the beginning of the year to which the depreciation applies. A. Straight lime method C. SYD method B. Sinking fund method D. Declining balance method * 23. A 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. A. Straight line method C. Declining balance method B. Sinking fund method * D. SYD method 24. The lessening of the value of an asset due to the decrease in the quantity available (referring to the natural resources, coal, oil, etc.) A. Depreciation C. inflation B. depletion * D. incremental cost 25. An association of two or more persons engaging in a profitable business. A. Sole proprietorship C. Partnership * B. Enterprise D. Corporation

for

a

purpose

of

26. A distinct legal entity which can practically transact any business transaction which a real person could do. A. Sole of proprietorship C. Partnership B. Enterprise D. Corporation * 27. A type of bind where the corporation pledges securities which it owns (I,e, stocks, bonds of its subsidiaries). A. Mortgage C. Coupon bond B. Registered bond D. Collateral trust bond * 28. A type of bond which does not have security except a promise to pay by the issuing corporation. A. Mortgage bond C. Collateral trust bond B. Registered bond D. Debenture bond * 29. The residual value of a company’s assets after all outside liabilities (shareholders excluded) has been allowed for. A. Dividend C. Return B. Equity * D. Per value

30. The quantity of a certain commodity that certain price at a given time and place. A. Demand * C. Market B. Supply D. Utility

is

bought

at

a

31. Solve for N if log of 3 top the base 6 equals N. A. 0.613 * C. 0.316 B. 0.218 D. 0.816 32. A man bought a $20 book and wishes to sell it. At what price should he mark it if he wishes to give a 40 percent discount and make 50 percent profit on the cost? A. $40 C. $ 50 * B. $55 D. $30 33. A steel plate 6 cm square is to be formed into an open box by cutting equal squares out of the corners and bending up the edges to form a box. What is the side of the square removed so that the box formed will have a maximum volume? A. 1.0 cm * C. 0.5 cm B. 1.5 cm D. 2.0 cm 34. The greatest unit pressure the soil can continuously stand is called A. bearing strength * C. ultimate strength B. yield strength D. fatigue strength 35. Refers to the highest ordinate on the diagram. A. Rapture strength C. Yield strength B. Ultimate strength * D. Allowable strength

stress-strain

36. A kind of stress that is caused by forces acting along or parallel to the area resisting the force. A. Tensile stress C. Shearing stress * B. Bearing stress D. Tangential stress 37. The ratio of the unit deformation or strains in a transverse direction is constant for stresses within the proportional limit. This is known as A. Hooke’s Law C. Poisson ratio * B. Mohr’s circle D. Slenderness ratio 38. What is the constant term in the expansion of (2x2 + 1/x)9 ? A. 672 * C. 748 B. 724 D. 860 29. Solve for x: 23x = 64 A. 4 B. 6

C. D.

2 * 1

39. Find x in the expression log 3 to the base 6 equals x times log 3 to the base 2. A. 1/3 * C. 2/3 B. 1/2 D. 3/4

40. If ln x = 3 and ln y = 5, find ln(x2 /y1/2) A. 1.5 C. 3.5 * B. 2.5 D. 4.5 41. A river is 580 ft wide. The bridge constructed across the river is banked 1/7 of its length in the east and 1/6 in the west. What is the length of the bridge? A. 840 ft * C. 910 ft B. 760 ft D. 1000 ft 42. What is the probability of getting two faces in a deck of cards if drawing of cards is to be done twice? A. 0.02 C. 0.04 B. 0.05 * D. 0.03 43. A plane with a velocity of 300 mph din still air, is travelling against the wind and travels a distance of 900 miles in 4 hours. Find the headwind velocity. A. 75 mph * C. 150 mph B. 100 mph D. 200 mph 44. A, B and C are points on a circle. AC bisects the circle and AB = BC. The area of triangle ABC is most clearly what percent of the circles area? A. 44 C. 32 * B. 36 D. 24 45. Find the value of x for which f(x) is minimum given f(x) = x2 + 5x + 2 = 0 A. 0 C. -2 B. -5/2 * D. -3/2 46. Solve for x: x – 3 = 3(1 – x) A. 0.67 C. B. 0.33 D.

1.50 * 1.67

47. Find the equation of the family of lines in which the slope and the y- intercept are equal. A. y’ = x/y C. y’ = y/x B. y’ = y/(x + 1) * D. y’ = x + y 48. Find the radius of the circle circumscribing pentagon with area 560 square units. A. 15.347 * C. 11.254 B. 16.879 D. 10.543

a

regular

49. Find the equation of the circle circumscribing a triangle with vertices (-1,-3), (-2, 4), (2, 1). A. x2 + 3x + y2 – 7y – 10 = 0 B. x2 + 3x + y2 + 7y – 10 = 0 C. x2 + 3x + y2 – y – 10 = 0 * D. x2 + 3x + y2 – 7y + 10 = 0 50. The upper and lower bases of a trapezoid measures 12 in and 16 in respectively. If the base angles are 55 deg and 65 deg. What is the length of the shorter leg? A. 3.78 * C. 5.24 B. 2.18 D. 4.29

51. What is the maximum area of the ellipse having an equation of 4x2 + A. 4 * C. B. 12 D.

rectangle inscribed in an 16y2 = 16. 8 6

52. When a right circular cone is cut by a plane parallel to the axis of the cone the conic section formed is a/an A. parabola C. circle B. ellipse D. hyperbola * 53. 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. paraboloid C. tangent B. exponential D. sinusoidal * 54. The act of charging two or more buyers or sellers different prices for the same product where the elasticity of supply or demand at each price level differs among market is known as A. price manipulation C. price discrimination * B. price optimization D. price war 55. A situation in which rival firms drive prices down through attempts to undercut each others prices is called A. price war * C. price leadership B. price discrimination D. price manipulation 56. Maximum plant capacity operate, tend or maintain A. 200 kW B. 220 kW

in

which C. D.

a

CPM

is

allowed

to

224 kW 242 kW *

57. The state of a thermodynamic system is defined by its A. temperature C. process B. pressure and temperature D. properties * 58. The partial pressure of a gas is the pressure that the gas will exert if it alone occupies the volume occupied by the mixture at the same temperature of the mixture. A. Dalton’s law * C. Amagat’s law B. Avogadro’s law D. Pascal’s law 59. An accounting book where the original record transaction is ordinarily recorded. A. journal * C. ledger B. balance sheet D. balance sheet 60. Given f(x)= 2x + 4, g(x) = 1/x, find f(g(f(x))) A. 1/(2x + 4) * C. 2x + 4 B. 1/2x D. 2x + 4 61. Simplify : (a-2)2 / (b-2)3 A. b6/a4 * B. a6/b4 62.

C. D.

b4/a6 a4/b6

Find the roots of the equation x3 – 16x = 0. A. 0,4 C. 0,-4 B. 0,-4,-4 D. 0,-4,4 *

of

all

63.

Solve for x in the equations: 2(x A. 4.55 C. B. 4.25 D.

64.

What is the value of x in the proportion (x + 1):4 = 15:44. A. 6 C. 5 B. 4 * D. 3

65. Determine sides. A. 60 B. 80

the

number

of

+ y)

=100 and 4(x 4.75 4.15 *

diagonals C. D.

of

a

+ y)

=10.

polygon

with

15

120 90 *

66. What is the area of the rhombus with diagonals of 10 m and 24 m ? A. 150 C. 120 * B. 240 D. 180 67.

Evaluate the limit of xx as x approaches to zero. A. 0 C. 1 * B. 1/2 D. indeterminate

68. Three circles are externally tangent to each other and having the distances of their centers of 20 in., 23 in., and 25 in. What is the radius of the largest circle? A. 10 C. 12 B. 14 * D. 16 69. Tom earned $200 for working 40 hours, if he works overtime he will be paid 1.5 times his regular income. If tom received a total of $230, how many hours did he worked? A. 4 C. 5 B. 44 * D. 55 70. The point on the curve where the second derivative of the function is zero. A. maxima C. point of inflection * B. minima D. point of deflection 71. What is the trigonometric substitution used for a function involving a2 – x2 ? A. x = asin(theta)* C. x = atan(theta) B. x = acos(theta) D. x = asec(theta) 72.

The first derivative of cosine x is A. sin x C. –sin x * B. –cosx D. sec x

73. The sum of three numbers is 19. What is the smallest number in the group if their geometric mean is 6. A. 2 C. 8 B. 6 D. 4 * 74. Which of the following numbers will difference when subtracted by its cube? A. 0.707 C. 0.500 B. 0.533 D. 0.577 *

give

a

maximum

75. Decrease in the value passage of time. A. depreciation * B. inflation

of

physical C. D.

property

due

to

the

recession depletion

76. A situation whereby payment is made for work not done. The term also applies to the case where more workers are used than are reasonable requirement for efficient operation. A. feather bedding * C. check-in pay B. downtime pay D. moon lighting 77. The minimum grade of mechanical engineer operation of 500 kW Diesel Power Plant. A. RME * C. PME B. CPM D. MPE 78.

required

in

the

The ratio of average load to plant capacity. A. capacity factor * C. demand factor B. use factor D. load factor

79. Two cylinders each weighing 100 kN and 200 kN with radii of 100 mm and 200 mm respectively, are placed with the heavier weight above the lighter weight and placed in a container with a width of 500 mm. Assume the lengths of the cylinders and container are the same. What is the reaction between the cylinders? A. 268.28 * C. 200.00 B. 300.00 D. 293.25 80. A man is standing on a cliff 897 meters. He struck a tree with his axe and the sound 5.2 seconds after. Assuming constant temperature, what is the velocity of sound on that day? A. 340 m/s C. 345 m/s * B. 342 m/s D. 453 m/s 81. A 4 inches diameter sphere is floating on water with its hemisphere submerged. Solve for the density of the sphere. A. 31.2 lb/ft3 * C. 62.4 lb/ft3 B. 1000 lb/ft3 D. 64.2 lb/ft3 82. A block of wood is floating in seawater with submerged height of 30 cm. If placed in a pool of mineral oil with specific gravity of 0.80, what will be the submerged height of the wood? A. 30 cm C. 43 cm B. 39 cm * D. 29 cm 83. Find the velocity of the liquid 10 meters below the surface. A. 14 m/s * C. B. 20 m/s D. 84. The cause of a fluid to contract. A. adhesion C. B. surface tension * D.

in the tank at the bottom 16 m/s 10 m/s capillary cohesion

85.

Entropy is a measure of A. randomness or disorder B. the change of enthalpy C. the heat capacity of a D. the internal energy of

* of a system substance a gas

86.

What is the most efficient thermodynamic cycle? A. Rankine C. Diesel B. Otto D. Carnot *

87.

What is the pressure at 4000 ft above sea level? A. 29.92 in Hg C. 26 in Hg * B. 24.00 in Hg D. 22 in Hg

88. At what temperature are the degrees Fahrenheit and degrees Celsius equal? A. 40 C. -40 * B. 60 D. -60 89. A pendulum has a certain frequency in London. What is the effect of this frequency if it is measured with respect to the equator? A. increase C. remains the same B. decrease * D. none of these 90. An interest earning fund in which equal deposits are made at equal intervals of time for the purpose of gradually accumulating a specific sum of money required at some future date. A. sinking fund * C. amortization B. annuity D. capitalized cost 91. Find the minimum force P required to turn a 350 lb wheel with diameter of 10 inches over a block with a height of 2 inches. A. 240 N * C. 120 N B. 340 N D. 170 N 92. Find the nominal rate which if converted semi-annually could be used instead of 11.55% compounded quarterly? A. 11.06% C. 11.72% * B. 11.39% D. 12.72% 93. A company purchased an asset for P10,000 and plans to keep it for 10 years. The salvage value after 10 years is P2000. Find the book value after 3 years. A. P6700 C. P7600 * B. P7100 D. P8000 94. A formal organization of producers with an industry forming a perfect collision purposely formed to increase profit and block new comers from the industry: A. monopoly C. cartel * B. corporation D. competitors

95. A pile of logs contains 75 logs so that the top layer contains 3 logs and each lower layer has one more log than the layer above. How many logs are there in the bottom layer? A. 10 C. 12 * B. 14 D. 16 96.

If f(x, y) = (x2 - 2xy + y2)/(x2 – y2), f(-x , -y)is equal to A. 1/(-x + y) C. (-x + y)/(x + y) B. (x + y)/(y – x) D. (x – y)/(x + y) *

97.

Kinematic viscosity is an SI derivative unit described as A. watt per meter Kelvin C. Pascal second B. sq. meters per second * D. Newton per meter

98. The length of the operated at a profit: A. life B. length of time

time

during

which

property

may

be

C. physical life D. economic life *

99. In a cantilever beam with a concentrated load at the free end, the moment is: A. constant along the beam C. ¼ maximum half way out on the beam B. maximum at the wall * D. maximum at the free end 100. The logarithm of 1 to any base is: A. indeterminate C. infinity B. zero * D. one

SUBMIT THIS TEST QUESTION SET TOGETHER WITH THE ANSWER SHEET TO YOUR WATCHERS. BRINGING THE TEST QUESTION SET OUT OF THE ROOM  WILL BE A GROUND FOR DISCIPLINARY ACTION.