Padilla, MCQs in Engineering Mathematics

MULTIPLE CHOICE QUESTIONS IN AND

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 a.10.67 sq. units b. 32 sq. units c. 48 sq. units d. 16.67 sq. units

 = 8

and its latus rectum.

3. The effective rate of 14% compounded compound ed semi-annually is: a. 14.49% b. 12.36% c. 12.94% d. 14.88% 4.

4  225 225 = 0

a. b. c. d.

is the equation of _______? Parallel sides Parabola Circle 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 numb er 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 the initial velocity? a. 2000 m/s b. 3000 m/s c. 4000 m/s d. 5000 m/s

, x= distance in meters, and t= time in seconds. What is

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 a. -1/m

− +  c.  d. – m

b.

 − in terms of 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 a. b. c. d.

∫ 

dx

1.051 1.501 3.21 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. b. c. d.

tan x – x + c x - tan x + c sec x 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 b y 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 a. 3 b. 4 c. 2 d. 8

+ =1. Determine the distance between directrix:  

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 man y 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. b. c. d.

−   → −−

Undefined 0 Infinity 1/7

201. What is the speed of asynchronous earth’ satellite situated 4.5x 107 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 its acceleration after an interval of 10 sec. (in ft/sec2) a. 2.10 b. 1.71 c. 2.25 d. 2.75

 =  ft/sec. determine  +

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 3x 2+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 a. 9 cm b. 18 cm c. 18 cm d. 12 cm

√  √ 

√ 

sq cm then its perimeter is

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 a. b. c. d.

, then x is equal to:

−√    √  √  √ +√ 

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 P 700

Canlubang P500

Batangas P800

P 200

P300

P400

Q.C Makati

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= d= a. c, d, a, b b. b, a, d, c c. c, d, b, a d. d, c, a, b 268. If

√  √  √    √  , b=3+

 =  =  , which of the following relationship is correct? − − − a. b. c. d.

x+z=y x=y+z x+y=z x-y=z

, c=

,

 ()− 

269. evaluate u= a. b. c. d.

2 9 6 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. b. c. d.

sin A sin B b 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 + i 2 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: a. b. c. d.

  =    =    =  ,

,

. Find a, n, and m.

2, 16, 4 16, 2, 4 4, 16, 2 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. b. c. d.

-101 011 -001 111

   

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˚ + .. + sin 2 90˚ a. Infinity b. 0 c. 44.5 d. Indeterminate 314. Find the value of P if it is equal to a. b. c. d.

0 1 2 4

˚+˚+˚+⋯+˚ ˚+˚+⋯+˚

 −√ + 315. =?

− a. b. c. d.

0.3 0.4 0.5 0.6

316. Find the value of a. 4 b. 2 c. 0 d. 1 317. Find the value of a. b. c. d.

3/2 2 3 1/2

318. Find the value of a. b. c. d.

25/48 125/48 125/16 125/8

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. b. c. d.

0 1 2 cot (A+B)

323. Solve for the following: a. -7a b. +7a c. -7-a d. +7-a

324. Simplify a. b. c. d.

 − −

+   −n − −

+  +−    − −

{      }

       

()    ( )   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. b. c. d.

sin cos sec csc

 

 a +

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 a. b. c. d.

+ ∫ +

dx

37.6 47.6 27.6 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 the x-axis a. 4/3πab2 b. 2/3 πab2 c. 4/3 πba2 d. 2/3 πa2 b

   =  about  

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 comin g 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. b. c. d.

21 -21 12 -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 D E 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=?

4-r 45˚

4+r

a. b. c. d.

378.

0.686 m 0.688 m 0.866 m 0.868 m

Differentiate the equation

 + +  b. + a.

 = +



c. d. 1

379.

Give the slope of the curve at point (1, 1)

  = −+

a. b. c. d.

1/4 -1/4 4 -1/3

a. b. c. d.

Evaluate b in the following equation log b 1024=5/2 2560 2 4 16

380.



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 t he 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 through the origin. a. b. c. d. 386.

 = 

and passing

)(  ) =  ((   )(  ) =   )(  ) =  ((   )(  ) =            =           =           =     ′′   ′ =    =   =   =   =    =   =   =    −  ==  −     == −   =   =    ==     =   =     )   =  (   )   =  (   ) =  ( = 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

a. b. c. d. 389.

/

when

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

a. b. c. d. 393.

  ==    == 

(  ) = 

394.

395.

396.

Solve

a. b. c. d. 397.

Solve the equation

a. b. c.

,

.

Solve the equation

a. b. c. d.

 =   = 

.

Solve the equation

a. b. c. d.

; when

  ) =   (     ==  −      ==   − ) =  (      = =      = =   =        ==      ==   )(  ) =  (    =      =     =     =      =   ==     =   

Solve the equation

a. b. c. d.

.

.

.

.

.

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

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 A. 1 B. 0 C. e

 

/ as x approaches positive infinity.

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 A. B. C. D.

410.

Find A.

/

/

if

/

if

.

.

.

√  √   √  √ −√     =     =               

B. C.

/

/

D. 411.

Find

/

if

and

.

A. B. C.

D. 412.

Evaluate the first derivative of the implicit function:

+ + + B. + − C. + + D. −

  

A.

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 A. B. C. D.

416.

  

 =    =    =    =            +  +    +  +    +  +    +  +     =       

What is the first derivative A. -

/

with respect to x.

of the expression

 = 

?

/

B. 0 C. -

/

D. / 417.

Find the derivative of A. B. C. D.

418.

Given the equation: A. B. C. D.

419.

/ .

, find

′ .

/

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 A.

/

if

.

/

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 A. 4.331 B. 3.474 C. 5.127 D. 6.445

 = 

is:

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 is to have a volume of 10 cubic meters. The material for its bottom cost P150.00 per p er square meter, and that for the sides is P60.00 P 60.00 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 altitude of a cylinder of maximum volume that can be inscribed inscribed in a right right circular 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 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 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 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, supp ort, 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 t he 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.

A. B. C. D. 452.

Evaluate A. B. C. D.

453.

                              ∫ +                     +         

Integrate:

Evaluate the integral of A. B.

.

C. D. 454.

+           /     /   ∫                      ∫            ∫   

What is the integral of

?

A. B. C.

D. 455.

The integral of A. B. C.

with respect to ;

D. 456.

Integrate A. B. C. D.

457.

Evaluate A. B.

.

.

C. ½ D. 458.

Evaluate A.

.

is:

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.

.

       Evaluate ∫  .  + A. ½       B.      C.     D.       . Evaluate ∫ + D.

463.

464.

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.




with limits from 5 to 6.

A. 81/182 B. 82/182 C. 83/182 D. 84/182 471.

Evaluate the integral of A. 0.022 B. 0.056 C. 0.043 D. 0.031

 + if it has an upper limit of 1 and a lower limit of 0.

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.


^

using lower limit of 0 and upper limit =

/

.

A. 2.0 B. 1.7 C. 1.4 D. 2.3 475.


  

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 A. 28 sq. units B. 46 sq. units C. 36 sq. units D. 54 sq. units

 =   

and the x-axis between

 = =  and

.

477. axis.

Find the area bounded by

 = /

, the lines

 =   =  and

, and the X-

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

. A. B. C. D.

479.

   



Find the area bounded by the -axis and

 = +   =   =

 = /

, 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. C. D. 481.

sq. units sq. units sq. units

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 , about the -axis.

 =   =   = ,

, and

A. B. C.

D. 486.

The area bounded by the curve . What is the volume generated?

and the line

= 

is revolved about the line

A. 186 B. 179 C. 181 D. 184 487.

 = 

 =

 = 

  =  = 

Given is the area in the first quadrant bounded by , the line What is the volume generated by revolving this area about the y-axis?



and the -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 axis. What is the volume generated when this area is resolved about the line

and the ?

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 , and the -axis.

= 

A. 1.2 B. 1.4 C. 1.6

 = 

, the line

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 line , with respect to the -axis.

= 



 =  

, -axis and the

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 happen is zero.

are mutually exclusive, then the probability that both events can

B. The probability that an event can happen is always positive and is less than one or equal to one.

     C. If

D. If events

506.

    =   

is an event which cannot occur in the sample space, the probability of &

are mutually exclusive, then

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

is zero.

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 distance from 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, hyperbola, which is parallel to its directrices, is known as: 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 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 any solid of revolution revolution is equal to the generating 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 amount of divergence between 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 the line of sight sight to the object, makes with the horizontal, which 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 median of a triangle triangle is the line line connecting a vertex and the midpoint of the opposite 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: as: A. orthocenter B. circumcenter C. centroid D. incenter

546.

The angular bisector of the sides of a triangle 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 procedure is to use: A. the law of cosines

, , and

, the most direct

B. the slope of the line C. the translation of axes D. the Pythagorean Theorem 571.

In finding the distance between two points procedure is to use:

, , and

, the most direct

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 A. straight angle B. obtuse angle C. related angle



radians is:

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. B.

is not equal to zero

= 

,

C.

 >   < 

D. 590.

Point of the the derivatives, derivatives, which which do not exist ( and so equals zero) is called: called: A. stationary point B. maximum points C. maximum and minimum point D. minimum point

591.

If the the second derivative of the equation of a curve is equal to the negative of the equation of that that same curve, the curve is: A. a cissoid B. a paraboloid C. a sinusoid D. an exponential



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 C. mass

× ×

velocity acceleration

D. ½ mass 618.

velocity2







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, “Th e 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



665.

A 10-lbm object is acted upon by a 4-lb force. What is the acceleration in ft/min2? A. 8.0 B. 9.2 C. 7.8

× × ×

10 to the 4th power ft/min2

10 to the 4th power ft/min2 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 2 00 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 ten sion 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

 =   

at time

 =

?

 =    

, and -component

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 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 If a wind of 40kph is blowing from 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. 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 inclined at an angle of 30° with the 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 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 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 is resting resting on a level surface. surface. If the coefficient 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 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 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 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 at the rate of 500 m/min 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/hr 2 for 1 hour, then decelerates at a constant -5 km/hr 2 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. B. C. D.

× −

 = ,  = ,  = ,  = ,

MPa;

MPa; MPa; MPa;

 = × −  = ×−  = ×−  = × −

m/m

m/m m/m 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 GPa. Poisson’s ratio µ is 0.30, determine the lateral strain of the rod. Use A. B. C. D.

 = .× −  = .× −  = .× −  = .× −

 = 

mm/mm mm/mm mm/mm

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. B. C. D.

733.

 =   =   =   = 

mm;

mm; mm; mm;

 =   =   =   = 

mm

mm mm

mm

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. B. C. D.

736.

 = .  = .  = .  = .

kN;

kN; kN; kN;

 = .  = .  = .  = .

kN-m

kN-m kN-m kN-m

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 density.

20m is known to be 350 kg. Find its

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 in meters. Determine the pressure, in kPa, at a depth of 5m.





is in kN/m 3 and is

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. B. C. D.

758.

.× − .×− .×− .× −

m3/s

m3/s m3/s m3/s

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



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 kn own 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%

Padilla, MCQs in Engineering Mathematics

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