Mechanical Engineering Review Online

1. Find the remainder when (x¹² + 3) is divided by (x – 60.5).

a. 46,659

b. 46,872

c. 46,320

d. 46,775

2. A marksman hits 70% of all his targets. What is the probability of hitting exactly 5 of his next 12 shots?

a. 0.09713

b. 0.04561

c. 0.02911

d. 0.05211

3. The perimeter of a rectangle is 90 cm while its diagonal is 35 cm. Its area is ___.

a. 320 cm²

b. 400 cm²

c. 410 cm²

d. 0.360 cm²

4. The _____ between planes is measured by an angle formed by two lines, one in each plane, perpendicular to the edge.

a. Congruent angle

b. Dihedral angle

c. Interior angle

d. Exterior angle

5. The _____ is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10¹² hertz, and that has a radiant intensity in that direction of 1/683 watt per steradian.

a. Mole

b. Ampere

c. Lumen

d. Candela

6. The collision between two bodies, where relatively large forces result over a comparatively short interval of time, is called:

a. Moment

b. Impulse

c. Balancing

d. Collision

7. a + b = b + a, where ab = ba is an example of ____.

a. Inverse law

b. Identity law

c. Commutative law

d. Associative law

8. It is any limited position of space, bounded by surface.

a. Liquid

b. Gas

c. Plasma

d. Solid

9. A parallelogram all of whose sides are congruent

a. Rhombus

b. Prism

c. Trapezoid

d. Square

10. The arithmetic mean of 3a and 4b is ____.

a. (a+2b)/2

b. (2a+3b)/2

c. (3a+4b)/2

d. (3a-4b)/2

11. Find the value of A in the partial fraction: (3x²-32x -50)/(x-1)(x-2)(x+3)=A/x-1 + B/x-2+C/x+3.

a. 70/4

b. 73/4

c. 79/4

d. 77/4

12. A ball has a radius of 1.50-in and a weight of 0.8 lbs. Find the mass moment of inertia about the center of gravity.

a. 2.65x10^-4 ft-lb-sec²

b. 1.55x10^-4 ft-lb-sec²

c. 3.26x10^-4 ft-lb-sec²

d. 4.66x10^-4 ft-lb-sec²

13. X can do a job in 5 days, Y can do the job in 7 days and Z can do the job in 9 days. How long will it take to do the job if X and Y work for 2 days then Y and Z finish the job?

a. 1.23 days

b. 4.26 days

c. 2.66 days

d. 3.24 days

14. Find the integral of 12sin7xcos7xdx with limits from 0 to π/2.

a. 0.0429

b. 0.0562

c. 0.0332

d. 0.0762

15. Determine the equation describing the locus of point P(x,y), such that the sum of the distances between P and (-6, 0) and between P and (6, 0) is constant at 25 units.

a. (x/12.5) 2+(y/10.97)2=1 

b. (x/12.5) 2+(y/15.30)2=1

c. (x/10.3) 2+(y/9.97)2=1

d. (x/16.1) 2+(y/14.33)2=1

16. The semi-major axis of an ellipse is 5 and its semi-minor axis is 4. The distance from the center to the directrix is ____.

a. 9.24

b. 5.72

c. 8.33

d. 6.62

17. At constant temperature, the pressure is inversely proportional to the volume

a. Boyle’s law

b. General gas law

c. Charles’ law

d. Gay Lussac’s law

18. It is a force acting outward on a body as it transverses a curvilinear path.

a. Centripetal force

b. Centrifugal force

c. Compression

d. Tangential force

19. It is a geometric figure having identical shape and size

a. Common multiple

b. Transitive

c. Conjunction

d. Congruent

20. The major axis of the elliptical path in which the earth moves around the sun is approximately 185,000,000 miles and the eccentricity of the ellipse is 1/70. Determine the apogee of the earth.

a. 176,029,012 mi

b. 186,321,428 mi

c. 166,912,981

d. 198,241,222

21. What value of F satisfies the equation (9F + 1) = cot (18) where all the angles are in degrees?

a. 7.89 deg

b. 6.32 deg

c. 8.22 deg

d. 5.75 deg

22. A fencing material has a limited length of 90 ft. What is the largest triangular area that can be fenced in?

a. 389.7 ft²

b. 354.5 ft²

c. 333.0 ft²

d. 327.6 ft²

23. With a throw of 3 dice, what is the probability of getting a 9 or an 11?

a. 0.5611

b. 0.2407

c. 0.3291

d. 0.4201

24. A drawer contains 11 white and 7 black balls. What is the probability of randomly drawing a white and a black ball?

a. 0.4521

b. 0.6710

c. 0.5033

d. 0.8215

25. A concrete highway curve with a radius of 600 ft is banked to give a lateral pressure equivalent of f=0.18. For what coefficient will sliding impend for a speed of 70 mph?

a. 0.3330

b. 0.5621

c. 0.4511

d. 0.6530

26. Three circles are externally tangent to each other. The distances between centers are 55 cm between circles A and B, 51 cm between circles B and C, and 45 cm between circles C and A. Find the diameters, in cm of each circle A, B and C, respectively.

a. 50,62,42

b. 48,60,42

c. 52,62,40

d. 49,61,41

27. The sum of two positive numbers is 8. Find one of the two numbers such that the sum of the cube of one number and the square of the other number is a minimum.

a. x=3,y=2

b. x=2,y=6

c. x=2,y=7

d. x=3,y=9

28. A British unit area which is equal to 4840 square yards.

a. Hectare

b. Bushel

c. Cable

d. Acre

29. ____ is represented by a dot, or by the intersection of two line

a. Ray

b. Line

c. Point

d. Midpoint

30. ____ is a point at which a function has a first derivative of infinity, thus having slope which is vertical

a. Critical point

b. Upper yield part

c. Lower yield part

d. Ultimate strength

31. It is an expression that is assigned a certain set of values

a. Numerals

b. Variables

c. Digits

d. Equation

32. Are issued promissory notes on goods or services received from the business

a. Notes receivables

b. Notes payable

c. Bad debt

d. Barter

33. Includes coins, checks, money orders, treasury warrant and other cash items which are received and in the position of cashier or treasurer of the company.

a. Debit

b. Cash

c. Notes payable

d. Notes receivable

34. It present oral promises made by third party to pay at future date

a. Account payable

b. Account Receivable

c. A and B

d. All of these

35. Amount spent for transport of merchandise bought

a. Debt

b. Contra-asset

c. Freight-in

d. Purchase

36. A rectangular field is to be fenced into 4 equal parts. What is the size of the largest field that can be fenced this way with a fencing length of 1800 ft. If the division is to be parallel to one side?

a. 81000 sqf

b. 82000 sqf

c. 80000 sqf

d. 84000 sqf

37. In a box are 100 balls each numbered from 1 to 100. If one ball is drawn, find the probability that the number on it is even or above 70.

a. 0.88

b. 0.65

c. 0.76

d. 0.58

38. In how many ways can we set 7 people at a round table with certain 3 people not in consecutive order?

a. 556

b. 576

c. 533

d. 541

39. Two men running at constant speeds along a circular track 1450-m circumference. Running in opposite directions, they meet each other every 4 minutes. Running in the same direction, they come abreast every 32 minutes. Determine the speed of the faster man, in kph.

a. 12.2 kph

b. 13.2 kph

c. 10.1 kph

d. 14.7 kph

40. In 20 kilos of gold losses 1 kilo and 12 kilos of silver losses 1 kilo when weighed in water, find the weight of gold in a bar of gold and silver weighing 105 kilos in air and 99 kilos in water?

a. 80.2 kg

b. 86.5 kg

c. 88.3 kg

d. 82.5 kg

41. Compute the sum of all the coefficients in the expansion of (x + 3y – z)³.

a. 27

b. 29

c. 25

d. 22

42. A 298.3 cm³ of vapor at 100 deg C and 120 kPa has a mass of 0.852 gr. What is the molecular weight of the vapor?

a. 73.81

b. 75.98

c. 77.44

d. 79.32

43. Are deductions on the price of merchandise sold due to payment in cash or payment of account with in the specific period.

a. Gross discount

b. Sales allowance

c. Cost of sales

d. Sales discount

44. ______ is the study of the nature and behavior of light its passage through different transparent media, and its behavior

a. Electricity and Magnetism

b. Optics

c. Wave motion

d. Mechanics

45. An SI units of electric current

a. Coulombs

b. Ampere

c. Volts

d. Ohms

46. A unit of force in the cgs metric system and is equivalent to 1 gram-cm/s².

a. Newton

b. Grain

c. Pounds

d. Dyne

47. It is an arrangement of a set of objects in a particular order.

a. Mean

b. Class mark

c. Population

d. Permutation

48. If the circumference of a circle increases from 1 inch to 2 inches, what changes occurs in the area?

a. It doubles

b. It remains the same

c. It quadruples

d. It is halved

49. A two triangles are congruent if they have the same size and

a. Are proportional

b. Length

c. Shape

d. Are similar

50. Two angles whose sum is 90 degrees

a. Complementary angles

b. Adjacent angles

c. Vertical angles

d. Supplementary angles

51. A portion of the surface of a sphere included between two parallel planes

a. Base

b. Altitude

c. Diameter

d. Zone

52. A financial security issued by the government through the discount market as a means of borrowing for short period of time

a. Treasury bills or t-bills

b. Trust

c. Common stock

d. Coupon bond

53. A generous payment made to an employee who is dismissed prior to the expiry of his contract

a. Golden money

b. Golden handshake

c. Golden goodbye

d. Golden hello

54. Bullions are

a. Money which forms part of the country’s international reserve 

b. Bars of gold

c. Scientific discoveries

d. Sophisticated weapons

55. How much water overflows when a Pyrex vessel is filled to the brim with 1.5 L of water at 23 deg C is heated to 90 deg C? The coefficient of linear expansion of Pyrex and water can be considered as 3 x 10-⁶/^oC and 72 x 10^-6/^oC, respectively.

a. 28.31cm³

b. 32.11cm³

c. 24.21cm³

d. 20.20cm³

56. A 60 HP motor (70% efficient) drives a 950 rpm pump (85% efficient) that moves 6.0 cubic feet/sec of gasoline (SG=0.738). What is the specific speed?

a. 2030.1 rpm

b. 2015.9 rpm

c. 2045.6 rpm

d. 2080.1 rpm

57. Eight men can excavate 16 m³ of drainage open canal in 8 hours. Three men can backfill 12 m³ in 5 hours. How long will it take 10 men to excavate and backfill 25 m³ in the project?

a. 12.76 hrs

b. 18.21 hrs

c. 13.13 hrs

d. 14.28 hrs

58. Estimate the ownership in terms of present worth for a machine based on the following date: Cost of machine = P130,000, resale in 8 years = P25,000, maintenance etc. = P2,400 per year and increased by P600 each year. Rate of interest is 17%.

a. P146,905.08

b. P132,721.10

c. P160,877.20

d. P172,453.11

59. Find the shortest distance from the point (1, 3) to the point on the circumference of the circle x² + y² + 12x + 8y + 30 = 0.

a. 5.21 units

b. 6.35 units

c. 4.33 units

d. 7.02 units

60. The probability of drawing a black king and an ace in a deck of cards in succession is ___.

a. 0.002959

b. 0.003219

c. 0.005822

d. 0.006729

61. The kilowatt that can be transmitted safely by a shaft varies directly as the number of revolution it makes per minute and the cube of its diameter. If a shaft is 4 cm in diameter making 250 rpm can safely transmit 65 kW, what kW can be safely transmitted by a 3 cm shaft making 350 rpm?

a. 38.39 kW

b. 42.01 kW

c. 35.29 kW

d. 40.43 kW

62. A motorcycle cost P45,000 and has an expected life of ten years. The salvage value is estimated to be P2,500 and annual operating costs are estimated at P1,000. What is the approximate return on investment if the annual revenue is P15,000?

a. 32.1%

b. 20.2%

c. 25.8%

d. 28.8%

63. The exchange of goods and services without the use of money

a. Voluntary

b. Sale

c. Barter

d. None of these

64. The selling of goods and products and services by competitive bidding

a. Wash sale

b. Promo

c. Auction

d. Marketing discount

65. The probation of the export and import of a particular types of product or a complete ban on trade with a particular country as an adjunct to the political policies pursued by the government

a. Tariff

b. Trade

c. Embargo

d. None of these

66. The money that is inactive and does not contribute to productive effort in an economy is known as

a. Idle money

b. Frozen money

c. Hard money

d. All of these

67. A measure of precision of a numerical value of some quantity is ____

a. Constant

b. Variable

c. Variance

d. Average

68. It is a fixed line opposite the focus of a conic section which the eccentricity of the conic section is defined

a. Focal

b. Catenoid

c. Directrix

d. Coordinate

69. The speed of light is equal to _____.

a. 0.9997x10³ kW/min

b. 1.66054x10^-27 mile/hr

c. 2.99792x10³ m/s

d. 13.5950x10³ km/s

70. In an expression x – y, x is the ____

a. Minuend

b. Addend

c. Multiplier

d. Subtrahend

71. The installed cost of air conditioning unit is P300,000. It has a salvage value of P35,000 after an economic life of 10 years. Using straight-line depreciation method, calculate the book value at the end of 5 years.

a. P167,500

b. P189,000

c. P154,621

d. P133,092

72. A contractor wishes to set up a special fund by making uniform semi-annual end of period deposits for 20 years. The fund is to provide P12,000 at the end of the last 6 years of the 20 year period. If interest is 8% compounded semi-annually, the required semi-annual deposit is closest to ____.

a. P930.14

b. P880.12

c. P782.19

d. P652.11

73. A woman wishes to accumulate a total of P15,000 in a savings account at the end of 10 years. If the bank pays 5% compounded quarterly, the sum that should be deposited now is closest to ____.

a. P8,021.2

b. P9,126.2

c. P7,090.1

d. P6,091.4

74. How much money would be needed to be deposited in a bank now at 6% to provide P1800 per year for the next 50 years? The amount is closest to ____.

a. P32,928

b. P20,651

c. P25,817

d. P28,371

75. A trust fund is to be established to pay P120,000 per year operating cost of a laboratory and in addition to provide of P80,000 of replacement equipment every 4 years, beginning 4 years from now at an 9% interest the amount of money now required in the perpetual trust is nearest to ___.

a. P1,527,705

b. P1,662,097

c. P1,880,982

d. P1,421,000

76. Annual maintenance costs for a particular section of highway pavement are P2,200. The placement of a new a surface would reduce the annual maintenance cost to P600 per year for the first five years and to P1000 per year for the next five years. The annual maintenance after ten years would again be P2,200. If maintenance costs are the only saving, what maximum investment can be justified for the new surface? Assume the interest at 5%.

a. P4,029

b. P5,591

c. P5,989

d. P6,271

77. You deposit P2000 into a 10% account today. At the end of two years, you will deposit another P4000. In five years, you plan a P5,000 purchase. How much is left in the account one year after the purchase.

a. P3,921

b. P4,485

c. P5,661

d. P7,012

78. A person invests P480 to be collected in eight years. Given that the interest rate on the investment is 15% per year, compounded annually, what sum, in pesos, will be collected eight years hence?

a. P1,468.3

b. P1,821.0

c. P1,700 .3

d. P1,545.0

79. What is referred to an individual who organizes factors of production to undertake a venture with a view to profit

a. Salesman

b. Commissioner

c. Agent

d. Entrepreneur

80. A government bond which has an infinite life rather than specific maturity

a. Contract

b. Coupon

c. Bond

d. Consol

81. Any number which cannot be expressed as a quotient of two integers

a. Rational numbers

b. Natural numbers

c. Irrational numbers

d. Imaginary numbers

82. Roman numeral for 500

a. D

b. L

c. I

d. M

83. A machine is under consideration for investment, the cost of the machine is P28,000. Each year it operates, the machine will generate a savings of P16,000. Given an effective annual interest rate of 19%, what is the discounted payback period, in years, on the investment in the machine?

a. 3.27 yrs

b. 2.32 yrs

c. 4.82 yrs

d. 1.65 yrs

84. The capitalized cost of a piece of equipment was found to be P150,000. The rate of interest used in the computations was 13%, with a salvage value of P8,000 at the end of a service life of 10 years. Assuming that the cost of perpetual replacement remains constant, determine the original cost of the equipment.

a. P182,176

b. P165,029

c. P108,168

d. P179,092

85. A loan association lends money at the rate of 15% compounded monthly. A man borrows P45,000 payable in 60 equal monthly installments, the first payment due at the end of 1 year reckoned from the date of the loan. How much is each of the monthly installments?

a. P1,227.3

b. P1,321.2

c. P1,562.9

d. 1,880.5

86. The most frequently appearing score or group of scores appearing in the distribution

a. Mode

b. Median

c. Percentile

d. Mean

87. A polygon of 5 sides

a. Pentagon

b. Octagon

c. Heptagon

d. Nonagon

88. A part of a circle bounded by an arc and a chord

a. Diameter

b. Segment

c. Secant

d. Tangent

89. It is a number represented by using power-of-ten notation used to describe a very large numbers

a. Measurements

b. Significant figures

c. Scientific notation

d. Factorial

90. The portion of a sphere lying between two semi-circles of great circle is called ____.

a. Spherical segment

b. Spherical sector

c. Zone

d. Line

91. An angle whose vertex is a point on the circle and whose sides are chords

a. Vertical angle

b. Inscribe angle

c. Bisector of an angle

d. Adjacent angle

92. How much money would you have to deposit for five consecutive years starting one year from now if you want to be able to withdraw P55,000 ten years from now? Assume the interest to be 12% compounded annually.

a. P3,291.6

b. P7,918.1

c. P5,545.5

d. P4,912.5

93. A man borrows P12,000 from a loan firm. The rate of simple interest is 15%, but the interest is to be deducted from the loan at the time the money is borrowed. At the end of one year he has to pay back P12,000. What is the actual rate of interest?

a. 16.16%

b. 15.26%

c. 14.21%

d. 17.65%

94. A piece of property is purchased for P15,000 and yields a P800 yearly profit. If the property is sold after five years, what is the minimum price to break-even, with interest at 8%?

a. P17,612.8

b. P17,050.1

c. P17,346.6

d. P17,980.1

95. P1500 is borrowed for one year at an interest rate of 1.2% per month. If this sum of money is borrowed for the same period at an interest rate of 13% per annum, the saving in interest charges would be ____.

a. P35.84

b. P38.91

c. P30.21

d. P42.77

96. _____ is the angle formed by the prolongation of one side and the adjacent side of the polygon

a. Interior angle

b. Exterior angle

c. Vertical angle

d. Supplementary angle

97. It is a geometric figures not having the same center

a. Vertex

b. Eccentric

c. Plane

d. Curve

98. To draw a geometric figure inside another geometric figure in such way that the two figures having common but not intersecting points.

a. Tangential

b. Circumscribed

c. Perpendicular d. Inscribed

99. A machine part, operating in a corrosive atmosphere, is made of low carbon steel, cost P450 installed and lasts six years. If the part is treated for cession resistance it will cost P800 installed. How long must the treated part last to be as good an investment as the untreated part, if money is worth 8%?

a. 14.8 years

b. 13.9 years

c. 16.8 years

d. 17.2 years

100. Plan A requires a P100,00 investment now. Plan B requires an P75,000 investment now and an additional P50,000 investment later. At 9% interest, what is the breakeven point on the timing of the additional P35,000 later?

a. 7 years

b. 8 years

c. 6 years

d. 5 years

Answer Key (Handwritten)