Multiple Choice Questions in Engineering Mathematics by Perfecto b. Padilla Jr

MULTIPLE CHOICE QUESTIONS INMATHEMATICS PERFECTO B. PADILLA JR AND DIEGO INOCENCIO TAPANG GILLESANIA 1. What is the allowable error in measuring the edge of a cube that is intended to hold 8 cu.m, if the error of the compound volume is not to exceed 0.03m3? a. 0.002 b. 0.001 c. 0.0025 d. 0.0001 2. Find the area bounded by the parabola and its latus rectum. a.10.67 sq. units b. 32 sq. units c. 48 sq. units d. 16.67 sq. units 3. The effective rate of 14% compounded semi-annually is: a. 14.49% b. 12.36% c. 12.94% d. 14.88% 4. is the equation of _______? a. Parallel sides b. Parabola c. Circle d. Ellipse 5. A section in a coliseum has 32 seats in the 1st row, 34 in the 2nd row, 36 in the 3rd row, . . and 48 in the 9th row. From the 10th up to the 20th row, all have 50 seats. Find the seating capacity of this section of the coliseum. a. 908 b. 900 c. 920 d. 910 6. Smallest term that can be factored from a number a. Greater b. None of these c. equal d. lesser 7. How many horsepower are there in 800 kW? a. 2072.4 hp b. 746 hp c. 1072.4 hp d. 3072.4 hp 8. A man roes downstream at the rate of 5 mph and upstream at the rate of 2 mph. how far downstream should he go if he is to return 7/4 hour after leaving? a. 2.5 mi b. 3.3 mi c. 3.1 mi d. 2.7 mi 9. Find the angular velocity of a flywheel whose radius is 20 ft. if it is revolving at 20 000 ft/min a. 500 rad/min b. 750 rad/min c. 1000 rad/min d. 800 rad/min 10. Find the area of parabolic segment whose base is 10 and height of 9 meters. a. 60 m2 b. 70 m2 c. 75 m2 d. 65 m2 11. A line which a curve approach infinity but will never intersect. a. b. c. d. Parallel line Assymptote Inclined line 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 a. units c.218 hours b.324 hours d. find the length of the secant line. 200 sq. a. 3.0645 sq.5˚ c. 10 m/s b. Q=25 when t=0.0654 sq. 33 931. units c. 5 b.83 sq. units 24. 4. b=16. m 22. 9 23. Find the tangential velocity of a flywheel whose radius is 14 ft. 54. In an oblique triangle. if it is revolving at 200 rpm. 150 d.83 sq. BC=4 and the altitude to the hypotenuse is 1 unit. b.5˚ 26. What is its velocity at the maximum height? a.0654 sq. 225 sq.5˚ d. 1). 0 c. 250 sq. 17 593 ft/min b. Drain C can empty a full tank in 24 hours. 145 c. (0. 8 d. 2. units b. Find the area of the triangle. units d. 34 931. a.182 hours c. 175 sq. 54. m c. 36 931. units b. 185 b. 35 931. What is Q when t=6? a. 18 593 ft/min c. 175 29. and (8. If the distance from the point of tangency to the point of intersection is 6. 5. Q=75 when t=2. a. 24. 2. 1. Pipes A and B can fill an empty tank in 6 and 3 hours respectively. d. units d.0654 sq.5˚ b.available fencing material is 30 meters long. find the largest possible area of the lot. A ball is thrown vertically upward at a velocity of 10 m/s. a. Given a right triangle ABC. Mario starts .821 hours 30. a=25. 0). Angle C is the right triangle. 7 c. 19 593 ft/min d. Pedro runs with a speed of 20 kph. What is the increase in surface area if the radius of the original sphere is 50 cm. 5 m/s d. Find the measure of angle A. How long will an empty tank be filled if pipes A and B with drain C open? a. angle C=94˚06’.83 sq. m d. 31. 4) and whose axis is parallel to the xaxis. 1. 45. 3. units 25. Five minutes later. The volume of a sphere is tripled.? a. c. a. and the external distance of the secant line is 4. m b.83 sq. 12 593 ft/min 27. Find the equation of a parabola passing through (3. A tangent line intersects a secant line to a circle. 15 m/s 28. Ana is 5 years older than Beth. Stocks 36. 40. P41 454. 16 d. P40 454. 24 38. P134 350 b. 730˚ c. The line y=5 is the directrix of a parabola whose focus is at point (4. Find the simple interest rate. A man bought a machine costing P135 000 with a salvage value of P20 000 after 3 years. a. What is the accumulated amount of five years annuity paying P 6000 at the end of each year.5 . Find the length of the latus rectum. 27. a. 4 c.e. P17 504.40 b. Form of paper money issued by the central bank. d. 2. 8 b. 15. Check c. 25 kph c. Implicit derivative 37. how much is the loss or gain (i. 30 kph 32. 490˚ 39. The sum of two numbers is 21 and their product is 108.67% b.67% d. How much do ten P2000 quarterly payments amount at present if the interest rate is 10% compounded quarterly. 17. a. a. Cash d. 810˚ b. 16.29 41. 190˚ d. b.running to catch Pedro in 20 minutes. Find the sum of their reciprocals. the cost of equipment) if i=10%. 3). Logarithmic derivative b. with interest at 15% compounded annually? a.67% 35. 22. the product of their ages is 1.29 c.29 b.25 revolutions are how many degrees? a. a. P143 350 c.5 kph d. P1000 becomes P1500 in three years. T-bills b. c. P41 114. _________ is the concept of finding the derivative of an exponential expression. P17 771. a.13 c. P18 504. Find the velocity of Mario. In 5 years.29 d. If the man will sell it after 2 years. P153 350 d. a. P40 544. P71 504.5 kph b. Chain rule c. a. P163 350 34.67% c.13 33. Trigonometric derivative d.13 d. 18. Find its tangential velocity at the lowest point.21 d. ˚ ˚ a. If m=tan25˚. 30 42.10 d.76 c. 25 b.4856 m/s d. what will be its selling price after 5 years? a. Use declining balance method. In . 12. 20 c. How fast is the balloon receding from the observer 10 seconds later? a. 5 m/s .321 dx 47.76 50. 1.50 46. a. 3. 2.05 ft/sec d. 3. P40 794. 3000 m/s c.577 b. 16. P20 794. P245.4856 m/s b. –m 45.05 ft/sec b. a. Fin the eccentricity of an ellipse when the length of the latus rectum is 2/3 the length of the major axis. 4000 m/s d. a.051 b. How old is Beth now? a. d. c. P30 794.00 c. P20 794. P50 794. 2. P200. a.05 ft/sec 44. 2000 m/s b.76 d.05 ft/sec c. Use straight line method.76 b. while the lowest point is 3 ft above the ground.333 d. 0. P213. The balloon rises directly upward at the rate of 4 meters per second.643 48.4856 m/s c. and t= time in seconds. 1.times the product of their present ages.501 c. P236. If it’s selling price is expected to decline at the rate of 10% per annum due to obsolence. 5000 m/s 43.76 d. P40 794. 12. 15 d.76 b. What is the initial velocity? a. 0. 0. A VOM has a current selling price of P400.20 b. 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. A balloon is released from the ground 100 meters from an observer. find the value of ˚ ˚ in terms of m. Evaluate ∫ a. 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. P50 794. 1. 0. x= distance in meters. P50 400 c. 20. -1/m b. The highest point that a girl on a swing reaches is 7 ft above the ground.76 49.477 c. 5 tons b. consisting of quarters.51. 1. The pistons (A&B) of a hydraulic jack are at the same level. 1. 4123 mph 55. Exponential c.35 m/s2 54. Find the required force F at piston B to carry the load.3 π 53.21 c. 30 52. 151. 1. if a wind at 40 mph from the north is blowing. 243 mph d. Divide 120 into two parts so that product of one and the square of another is maximum. If a derivative of a function is constant.21 d. If pressure will be increased to 120 kPa. An air has an initial pressure of 100kPa absolute and volume 1 m3.75 m/s2 c.π . Logarithmic d. 532 mph c.21 b. 2. the total amount would be .875˚ b. the dimes were quarters and the quarters were nickels. The ratio of radii of cone and cylinder is 1:2 while the ratio of radius of cone to its altitude is 1:3. a. a.67 m/s2 b. 5. 131. Find the perimeter. Piston A carries a 500 kg load. Find the small number. a. 4. Pistol A is 100 cm2 while piston B is 500 cm2.875˚ 58. First degree b.4 π . nickels. 2700 mils is how many degrees? a. 6 56.75. 60 b. 3 d. In a box.2 π . a. A rectangular dodecagon is inscribed in a circle whose radius is 1 unit. 50 c. the function is: a. 8.5 tons 60. and dimes with a total amount of $2. 180˚ d. 1. a.5 tons d. 4 c. 270˚ c. 5 b. 0. If lateral surface area of cylinder equals volume of cone. find the groundspeed of the plane. 0. a. 7. there are 52 coins. Find its acceleration. Sinusoidal 57. What is the period? . A plane is headed due to east with airspeed 240 mph.2 m3 b.21 61. 1.05 m/s2 d. If the nickel were dimes. 3. .5 tons c. 342 mph b. find the new volume. A horizontal force of 80 000 N is applied unto a 120 ton load in 10 seconds.83 m3 c. 0.5 m3 59. 0. a. 6. 40 d. find the radius of the cone if the altitude of cylinder is 4.63 m3 d. What theorem is used to solve for centroid? a.5 c. Hexagon 67. x2-4y2+8x-4y-4=0 68. 1.5 hrs 69. 0 65. vertex at (2. d. y=arctan ln x.. If the sum of the areas is 100 sq.12 62. . ∫ a. tan x – x + c x . 2). c. 4x2-y2-8x+4y-4=0 b. How many quarters are there? a. 8 b. find the difference in length? a. If the pipe runs with the drain open.5 b. 0). A drain can empty a full tank in 6 hours. meter. b. 64.$3.35 secs. . 10 c. a. 24. x2-4y2-8x+4y-4=0 c. 3 hrs d. . 16 b. a. 20. Nonagon d. d.5 d. b. 4 hrs c. 5 d. b. Fin the 7th term in the series: . . b. 2. 2) and conjugate vertex at (1. 10 d. 20 71. a. A regular polygon has 27 diagonals.75. Castiglliano’s d.5 hrs b. 4x2-y2-8x-4y-4=0 d. Varignon’s c. c. Then it is a : a. 70. a. c. Find the equation. A stone is thrown vertically upward at 12 m/s.tan x + c sec x sec x tan x c. Pentagon b.45 secs. 2.15 secs. 2. Find y’. Heptagon c. Pascal’s 66. d. 16 c. A hyperbola has its center at point (1. 21. Find the time to reach the ground. A pipe can fill a tank in 2 hours. 63. a. Pappus b. Find the length of the larger base of the largest isosceles trapezoid if the legs and smaller base measure 8 units. 3. how long will take to fill-up an empty tank? a.95 secs. A 50 meter cable is divided into two parts and formed into squares. 1. Extracted . The general equation of a conic section whose axis is inclined is given by Ax2+Bxy+Cy2+Dx+Ey+F=0. 16 d. 3 min c. 40˚ d. 28. 3 b. the curve is a/an _____. It could mean a difference in value between a new asset and the used asset currently in service. cos4 θ – sin4 θ= ? a. 4 c. f”(a) = 0 d. implicit c. Parabola c. f”(a) < 0 c. A merchant has three items on sale namely: a radio for $50. 25. f”(a) > 0 b. Find the angle between 30N and 40N forces.d. cos 2θ c. 8 77. A function wherein one variable is not yet readily expressed as function of another variable is said to be: a. cos 4θ d.00. The time required for two examinees to solve the same problem differs by two minutes. a. 4 min d. a clock for $30. 2 min b.97˚ c. how many radios did she sell? a. 20 80. a. _______ is the loss of value of the equipment with use over a period of time. Hyperbola b. 30N. Loss b. 30˚15’25” 78. Three forces 20N.00 on the total sales. Determine the distance between directrix: a. symmetric b. Circle 73.96˚ b. At the inflection point where x=a a. Together they can solve 32 problems in one hour. and 40N are in equilibrium. Which of the following is true? a. cos(-θ)= cos θ d. cos 3θ 75. she has sold a total of 100 of the three sale items and has taken in exactly $1. exponential 76. How long will it take for the slower problem solver to solve the problem? a. Ellipse d. 2 d. explicit d. 80 c. tan(-θ)= tan θ c. When B2-4 Ac=0. 72. Depreciation c. Given an ellipse + =1. sin 2θ b. csc(-θ)= csc θ 81. At the end of the day.00 and a flashlight for $1. Gain d.00. a. sin(-θ)= sin θ b. 5 min 74. 4 b. f”(a) is no equal to zero 79. 000. a. Skew b. 1 275 cu. 11/3 b. Find the area bounded by the curve defined by the equation x2=8y and its latus rectum. P15 614. 16. 10 hrs b.72% c. Perpendicular 87. 19. a. Non-intersecting c. a. Parallel d. 1 257 cu. While the radius of the base is 20 inches and increases at the rate of one inch per second. which is due at the end of 7 months. Mass diagram c. Perfect competition c.84% d. Histogram 86. P46 729 d.35% b. Monopoly d. 74 b. 93 . 69 d. 81 c. 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. What is the effective rate corresponding to 18% compounded daily? Take 1 year =365 days.59 c. Ogive d. P16 311. If the product of the slopes of two straight lines is negative 1. 17. 11 hrs d. Frequency polygon b. 44 893 c. The graphical representation of the cumulative frequency distribution in a set statistical data is called? a. If you borrowed money from your friend with simple interest of 12%. 11 310 cu.78% 91. How long will it take Pedro to paint the same fence if he had to work alone? a. At what rate is the volume changing? a. 13 hrs c.26 d. 16/3 d. 32/3 c. P15 847. 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.82. The amount of P12 800 in 4 years at 5% compounded quarterly is? a. one of these lines are said to be: a.33 90. a.34 b. 15 hrs 88. in/sec d. P46 200 b. In how many ways can 2 integers be selected from the integers 1 to 100 so that their difference is exactly 7? a. 22/3 83. 11 130 cu. in/sec c. P14 785. 17. Elastic demand b. 45 789 89. Oligopoly 85. in/sec b. The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per second. find the present worth of P50 000. in/sec 84. a. Elasticity b. 8 b.19 b. 130 BTU 93. 9 b. 100BTU b. P2 584. 177. Plasticity 96. Ductility d. How should the man be willing to pay now for 12% -P10 000 bond that will mature in 10 years and pays interest semiannually? a. -3/2 cos 2 + C b. P59 049 b. 7 . A man expects to receive P20 000 in 10 years.42 m 99. What is its book value after 5 years? a. 110BTU c. P15 678. P17 567. 8 101. A machine costing P100 000 depreciates at 10% annually.42 m d. a. Evaluate ∫ a.92.05 c. P49 049 d. 6 95. The area of a rhombus is 24.25 c. P 12 698. Malleability c. P79 049 94.42 m b. 7 d.65 b. 7 c. P8 940. P69 049 c. -3 cos 2 c. The area of a rhombus is 24. 3/2 cos 2 + C d. A man wants to make 14% nominal interest compounded semi-annually on a bond investment. Find the length of the latus rectum of the parabola y2=-8x? a. P867. Find the maximum height which a cannonball fired at an initial velocity of 100 m/s at 30˚ above the horizontal. find the length of a side.45 100. a. a. 3 cos 2 + C 98.42 m c. One diagonal measures 6 units. 9 c. 6 d. 5 b. 137.95 d. a. A 2 lbs liquid has an specific heat of 1.82 97. 172. find the length of the other diagonal. 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.60 d. 6 c. One diagonal measures 6 units. How much is that money worth now considering interest at 6% compounded quarterly.2 Btu/ lb-˚F. How much heat is required to increase its temperature by 10˚C? a. 120 BTU d. 127. P11 025. P3 118. Above 10 d. d.33 x 105 N/m2 d.82 cm 12. units c.d. c. 1/2 d. -1/2 111. 30 km c. 4 109. 8. 8 102. Logarithm 110. 52 cm2 b. Less than 2 103. a.33 x 106 N/m2 112. If the total time of travel is 3 hours. From 2 to 5 b. √ 107. The volume of two spheres is in the ratio of 27:343 and the sum of their radii is 10. 60 km d. 6 b. Cologarithm d. 2 b. A father is now 41 and his son 9. Determine its amplitude. 2√ sq. find the total distance traveled by the banca. a. 6 b. A banca traveled at an average speed of 15 kph downstream and then back at an average speed of 12 kph upstream.28 cm 15. units d. √ sq. 40 km b. a. 1000 sq. 82 cm2 . 50 km 104. Find the radius of the smaller sphere.33 x 103 N/m2 b. 62 cm2 c. 2 c. a. From 5 to 10 c. units 106. a. 8. 12. Given y = 4 cos 2x. 4 c. -2 b. 8 d. 100 sq. A central angle of 45˚ subtends an arc of 12cm. find the lateral area. a. A rectangular hexagonal pyramid has a slant height of 4 cm and the length of each side of the base is 6 cm. Determine the vertical pressure due to a column of water 85 cm high.85 cm 108.58 cm 15. 3 c. The sum of the coefficients in the expansion of (x+y-z)8 is: a.33 x 104 N/m2 c. b. Derivative c. units b. 4 d. Find the area of the largest rectangle which you can inscribe in a semicircle whose radius is 10. What is the radius of the circle? a. 8. 5 d. Product b. After how many years will his age be just triple his son’s age? a. Find the sum of the roots 5x2 -10x + 2=0 a. The integral of any quotient whose numerator is the differential of the denominator is the: a. 5 c. 8. 7 105. 72 cm2 d. 1/2 b. What is the distance in cm. Pyramid c.66 d. This illustrates which axiom in algebra? a. Function c. A loan of P5000 is made for a period of 15 months at a simple interest rate of 15%.7 116.32 b. Plane angle .3 c. A 200 gram apple is thrown from the edge of a tall building with an initial speed of 20 m/s. Symmetric axiom c. 1/5 119. find the value of x. Correlation b. Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8. 180 joules c. What future amount is due at the end of the loan period? a. Cube b.5 d. It is a polyhedron of which two faces are equal. If a =b. 8. To compute for the value of the factorial. 12. in symbolic form (n!) where n is a large number. if an edge measures 8 cm? a. Prism d. 8. 8. P5 937. Parallelepiped 117. When two planes intersect with each other. 100 joules b. It is the measure of relationship between two variables. the amount of divergence between the two planes is expressed by the measure of: a. If arc tan x + arc tan 1/3 = π/4. a. What is the change is kinetic energy of the apple if it strikes the ground at 50 m/s? a. Reflex angle d. Stirlings Approximation formula d.54 b. between two vertices of a cube which are farthest from each other.93 118. P 5 842. Richardson-Duchman formula 115. Relation 120. 8. Dihedral angle c. Reflexive axiom c. the b = a. P5 900. P5 637. Diophantine formula c. 6.00 121. a. 1/3 c. polygons in parallel planes and the other faces are parallelograms. 8. 13. 210 joules 122. 81 joules d. a. Transitive axiom d. Replacement axiom b. 1/4 d. a.1 b.86 c. Equation d.50 114.50 d. we use a formula called: a. Polyhedral angle b.113. Matheson formula b. 54. Orthocenter d. Centroid 124.000 cu. The volume of ice will not change b. 1994 132. 3974 c. 53. A five-pointed star is also known as: a. Incenter c. Ice will become water c. 1 quarter circle 127. Centroid 129. 1 radian c. Orthocenter d. What is the original number? a. The sum of the digits of a two digit number is 11.1% d. The arc length equal to the radius of the circle is called: a. Each side of a cube is increased by 1%.4% c. π radian d. By what percent is the volume of the cube increased? a.123. which is known as: a. If the digits are reversed. what will happen? a. 228.2 b. 53. The altitudes of the sides of a triangle intersect at the point. 23. the medians intersects at a pint which is called the: a. A pole cast a shadow of 15 meters long when the angle of elevation of the sun is 61˚. For a given triangle. a. 34. 288. 1 grad b.25 m 130. 83 c. the resulting number is seven more than twice the original number. Pentatron d. One gram of ice at 0˚C is placed on a container containing 2. 3% b. Assuming no heat loss. All of the above 128. 2174 b. 282. MCMXCIV is a Roman numeral equivalent to: a. 238. what is the length of the pole? a.25 m c. Centroid b.2 d.2 . 53 133. 38 d. Incenter c. Circumcenter b. Orthocenter d. The median of a triangle is the line connecting a vertex and the midpoint of the opposite side. Quintagon b.8 c. If the pole has leaned 15˚ from the vertical directly toward the sun. Centroid b. 33. Some part of ice will not change d.24 m b. Circumcenter 126. Pentagram 125. 2974 d. Incenter c. A regular octagon is inscribed in a circle of radius 10. m of water at 0˚C. 52. Pentagon c.56% 131.000. The angular bisector of the sides of a triangle at a point which is known as: a. Find the area of the octagon.43 m d. 44 b. 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. b. c. d. 13 21 -17 -13 157. Determine the angle of the super elevation for a 200 m highway curve so that there will be no side thrust at a speed of 90 kph. a. 19.17˚ b. 17.67˚ c. 18.32˚ d. 20.11˚ 158. A ball is dropped from a building 100 m high. If the mass of the ball is 10 grams, after what time will the ball strike the earth? a. 4.52s b. 4.42s c. 5.61s d. 2.45s 159. Centrifugal force is _____ a. Directly proportional to the radius of the curvature b. Directly proportional to the square of the tangential velocity c. Inversely proportional to the tangential velocity d. Directly proportional to the square of the weight of the object 160. Each of the faces of a regular hexahedron is a _____ a. Triangle b. Square c. Rectangle d. Hexagon 161. Find the mean proportion of 4 and 36 a. 72 b. 24 c. 12 d. 20 162. Simplify the expression i1999 + i1999 where I is an imaginary number. a. 0 b. -1 c. 1+1 d. 1-i 163. In a club of 40 executives, 33 likes to smoke Marlboro and 20 like to smoke Philip Moris. How many like both? a. 13 b. 10 c. 11 d. 12 164. The graph of r=a+bcos θ is a : a. Lemniscates b. Limacon c. Cardioids d. Lituus 165. Solve for A in the equation: cos2A = 1- cos2A a. 15˚, 125˚, 225˚, 335˚ b. 45˚, 125˚, 225˚, 315˚ c. 45˚, 135˚, 225˚, 315˚ d. 45˚, 150˚, 220˚, 315˚ 166. Momentum is the product of velocity and a. Acceleration b. Mass c. Force d. Time 167. If 15 people can win prices in a estate lottery (assuming that there are no ties). How many ways can these 15 people win first, second,, third, fourth and fifth prizes? a. 4,845 Delayed annuity c. a.360 d. a. A point on the circumference of the wheel moves 30 ft in 2 seconds. x b. and 6 in. 91 169. Deferred annuity b. 44% b. 6 rad/sec d. a. 360. Find the ratio of an infinite geometric series if the sum is 2 and the first term is ½ a. csc 520˚ is equal to a. 185 mi . It is a series equal payments accruing at equal intervals of the time where the first payment is made several periods after. 125 d. Given a cone of diameter x and altitude of h. Simple annuity 176. cos 20˚ b. 105 177. 15 170. sin 20˚ 174. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone? a. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 seconds? a. 3. A load of 100 lb.… a. 88 d. Progressive annuity d. 46% c. csc 20˚ c. 12 d. 165 lbs b. Determine the tension in the rope. 90 c. which is stretched between wo rigid walls of 30 ft apart. y=x1/2+c d. a. the tangent line has a slope of 2x. 4 rad/sec c. tan 45˚ d. Exact angle of the dodecagon equal to ________ deg.280 c. How old is Ann now? a. Mary is 24. 116. 5 rad/sec 175. x=y2+c 173.b. 2 rad/sec b. 10. Due to the load. y=x2+c c. 194 lbs d. She is twice as old as Ann was when Mary was as old as Ann now. Find the equation of the curve at every point of which. a. 1/2 c. the rope sags 4 ft in the middle. 173 lbs c.P 4. 149 lbs 178. 7. 1/3 b. 150 c. 75 b.003 168. 16 b. A rotating wheel has a radius of 2 ft. 135 b. is hung from the middle of a rope. 65% 172. Find the 30th term of the A. Find the angular velocity of the wheel. 3/4 d. 17 c. 56% d. 1/4 171. What is the lowest common factor of 10 and 32? a. Volume strain 185. A balloon is rising vertically over a point A on the ground a rate of 15 ft/sec. Maximize the angle of elevation d. If an observer’s eye is 1. The tangent function of the angle of trajectory must be equal to one 183. 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.8 m d. When the .b.39 b. A block weighing 500 kN rest on a ramp inclined at 25˚ with horizontal. 172 mi 179. The force tending to move the block down the ramp is: a. 100 kN b.79 c. Longitudinal strain b. 180 d.51 m c. 288.828 m c. 3. Ellipse 186. 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. which of the following applies? a. how far should he stand from the base in order that the angle suspended bu the statue is maximum. Hyperbola c.97 d. 255 kN d. 12 and 14 units. 3.37 181. What is the value of log25+log35? a. The area of the largest circle is a.71 m d. Circle b. 16 π 182. A statue 3m high is standing on a base of 4m high. 4. 90 184. Shear strain d. 2 c. 3. a. 72 π b. Maximize velocity b. 7. Linear strain c. 320 b. 3.88 m 188. 167 mi c.5m above the ground. 8. To maximize the horizontal range of the projectile. 450 kN 180. 211 kN c.2 m b. The distance between the center of the three circles which are mutually tangent to each other externally are 10.41 m b. Parabola d. a. 3. How far from the throwing point well the ball attains its original level. A point B on the ground is level with and 30 ft from A.41 m 187. 23 π c. a. 200 mi d. 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. 882. 9. Maximize the angle of elevation and velocity c. 64 π d. 82. 86˚ 198. What is the height of the tower? a. 225 d.82 degrees between each other. 8/3 d. 0. 76. 73. 12 ft/sec d. at what rate is its distance from B changing? a. 1 023 b. Find the point in the parabola y2 = 4 at which the rate of change of the ordinate and abscissa are equal. 3 d.balloon is 40 ft from A.72˚ b.8. a. (4. 4. Two electrons have speeds of 0.31 m c. a. 73.02c b. 61 m 191. find x. 5. 1. 4) c. 4) 195. 94 550 000 miles 197.4. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0 a. π/2 ) )} is equal 193. A man finds the angle of elevation of the top of a tower to be 30 degrees.27˚ c. The diameter of a circle described by 9x2 + 9y2 = 16 is ______ a. 2 194.16 m d.31 m b. 94 335 100 miles d. 73.12c c. 5 b. 0.12˚ d. 000 miles and the eccentricity of the ellipse is 1/60. π/4 c. 7x-4=0 196. (-1. The major axis of the elliptical path in which the earth moves around the sum is approximately 186. 0. 0. The angle of inclination of ascends of a road having 8.09c d. 1) d.7c and x respectively at an angle of 60. 000. 4x+7=0 c.… a. 4x-7=0 d. 1 596 .25c 192. 13 ft/sec b. Find the equation of the axis of symmetry of the function y= 2x2-7x+5 a. Find the sum of the first term of the geometric progression 2. 4. If their relative velocity is 0. π/6 d. 7x+4=0 b. 91 450 000 miles c. 4 190.16. 93 000 000 miles b. 15 ft/sec c. 4/3 b. 4 c. 2) b. 10 ft/sec 189. He walks 85 m nearer the tower and find its angle of elevation to be 60 degrees.25% grade is _____ degrees. Arc tan{2 cos(arcsin to: a. a.65c. Determine the apogee of the earth a. π/3 b. (2. 2 046 c. 16/9 c. (1. 12x2+7x-1=0 d. 2/3 a. 1. Covert θ=π/3 to Cartesian equation a. 840 c.03 c. If (x+3) : 10=(3x-2): 8. x=31/2 x b. 4) with respect to the translated axis with origin at (1. 1 b. 90 in3 in3 30. In how many ways can the company choose from 9 men and 6 women who qualified for the position a. 0. Hg. 3y=31/2x c. 0. The area of the rectangle is: a.4 kph d. 122-7x+1=0 c. What is the speed of asynchronous earth’ satellite situated 4. 540 c. 480 d.5x107 m from the earth a. 0. 500x/ π n d. What is the equation? a. 76 cm. The volume of a gas under standard atmospheric pressure. 170 m2 c. 12 070.99. -1) b. The wheel of a car revolves n times while the car travels x km. 12x2-7x-1=0 208. The radius of the wheel in meter is: a.0 kph c. 110 in3 210.05 b.00. 9/2 b. 12 000. 11/2 d. A semiconductor company will hire 7 men and 4 women. 11 777. A piece of wire is shaped to enclose a square whose area is 169 sq cm. 7/2 200. 0. Find the coordinates of the point P(2. 156 m2 204. (1. -2. 165 m2 b. 2 d.01.04 d. 0.02 206. Evaluate ( a. 5 000x/ π n 209. The roots of a quadratic equation are 1/3 and ¼.0 kph b. 1) 207. find (2x-1).2 kph 202. 1. …. 3 . 190 in3 b. Infinity d.4 205. 0 c. a. 11 070. if the temperature is unchanged? a. (-1. 1) d. It is then reshaped to enclose a rectangle whose length is 15 cm. Find the sum of the infinite geometric progression 6. What is the volume when the pressure is 80 cm. 12x2+7x+1=0 b. Hg is 200 in3. 4 c. -1) c. 500 00x/ π n c. 3) a. Undefined b. 5/2 c. Find the 100th term of the sequence. (1. 680 b. a. y=31/2 x 203.199. (-1. 1/7 ) 201. d. 10 000x/π n b. 175 m2 d. y=x d. 2. Venn diagram 212. 7:72 218.100 b. b. 290 b.75 214.150 c. What is the temperature. (in ft/sec2) a. 2 ft/sec b. a. 56% d. 2.25 d.78% 15% 217.939. cosA=3. Argand diagram c. 15% when compounded semiannually will have effective rate of: a.571x.12 ft/sec c. 2:7 c. Division b. What is the average acceleration? a. Find the ratio of the area of the rectangle to the area of the square. we use a diagram to represent a complex plane commonly called: a. Funicular diagram d. The flowerpot and the glass hit the ground at the same instant b. 2. 0. 0. and sin2A=3. expressed in degrees Kelvin? a.10 b. De Moivre’s diagram b. 2. Is sinA=2. The glass hits the ground before the flowerpot d. a. 4:9 b. while traveling in a straight line. find the value of x. The velocity of an automobile starting from rest is given by ft/sec. 295 216.39 ft/sec d.71 c. 5:9 d. The flowerpot hits the ground first with a higher speed than the glass 220. Central tendency d. A comfortable room temperature is 72˚F. Which of the following is true? a. An automobile accelerates at a constant rate of 15 mi/hr to 45 mi/hr in 15 seconds. c. by how much is its area decreased? a. 2. just as it passes the third-floor window someone accidentally drops a glass of water from the window. determine its acceleration after an interval of 10 sec.02% 18. In complex algebra. 0. Certainty c.06x. 15. Dispersion 213. If the radius of the circle is decreased by 20%.93% 16.250 . 2. 26% 219. 46% b.93 ft/sec 215. A flowerpot falls off the edge of a fifth-floor window. 1. 36% c. 275 d. 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. 263 c. The quartile deviation is a measure of: a. The flowerpot hits the ground at the same time as the glass c.211. d. 13 222. A man in a hot air balloon drops an apple at a height of 50 meters. Co-terminal arcs c. Equal terms 229. a. Polar distance 227. In Plain Geometry. Coordinate d. If cosθ=-15/17 and θ is in the third quadrant. 11 d. 4 c. a. 1. 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. With what speed in meters per second does it strike the ground? Assume g=10m/s2. Unequal terms b. 1. 1. a. Mantissa c. Briggsian logarithm d. Conjugate arcs b. 1510 kN-m 226. 151.57 m d. 3/4 c. 171. Napierian logarithm 228. How many terms of the sequence -9. It represents the distance of a point from the y-axis a.73 231. sin B= 7/25 and B is in the first quadrant. What is the maximum moment of a 10 meter simply supported beam subjected to a concentrated load of 500kN at the mid-span? a.350 221. Half arcs d.d. find sin (A+B) a. You find 7% and 12% solution on the shelves.53 c. 141.7182818…. find cos θ/2. If sin A=4/5 and A is in the second quadrant. find the highest point reached by the apple. Ordinate b. 4/5 224.47 m 223. Terms that a differ only in numeric coefficients are known as: a. Characteristic b.55 m c. two circular arcs that together make up a full circle are called: a. 3/√ 225. -8/√ c. 1050 kN-m d. -1/√ b. 1250 kN-m b. Abscissa c. 12 b. -6. 1.45 m b. The logarithm of a number to the base e (2. Unlike terms d. Like terms c. 2/√ d.43 b.0 is called a. For a particular experiment you need 5 liters of a 10% solution. 161. . 3/5 b. 1520 kN-m c. Congruent arcs 230. 2/5 d. A mango falls from a branch 5 meters above the ground. If the balloon is rising at 15 m/s. -3 … must be taken so that the sum is 66? a.63 d. 0. a. altitude=1/3h d. Radius=2/3r. If the first is totally evaporated in 6 weeks. Distractive waves are produced c. 42/5 weeks 236. a. 0. Constructive interference always results 233.099 b. 50 hp d. Degree d. 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. Find the fourth term of the progression ½ . c. 6 235. 7 b. a. 4 weeks c. An angular unit equivalent to 1/400 of the circumference of a circle is called: a. Radius=1/3r. 1/10 d. altitude=2/3h 239. b. but constant rates. 48 hp c. 5 c. What size of motor is required to lift 800 lbs in 40 seconds through a distance of 40 feet. 3. Mil c. Radius=2/3r. 56 hp 238. 1/11 c.a. 58 hp b. Radius=1/3r. Determine the number a. Ten less than four times a certain number is 14. Total mechanical energy b. 0.125 … a. 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. The phase difference is always zero b. Total potential energy c. Radian 240.2. 10 m/sec 14 m/sec 12 m/sec 8 m/sec 232. a. Semi-monopoly . If it takes 30 seconds for a 10 hp motor to lift 100 lbs through 50 feet. 0. and the second in 7 weeks. when will be the second be ½ the volume of the first. d. 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. 4 d. Grad b. Total kinetic energy d. Standing waves are produces d. altitude=1/3h c. Monopoly b. altitude=2/3h b. a. Equal volumes of two different liquids evaporate at different.5 weeks b. Total momentum 234. 0. When two waves of the same frequency speed and amplitude traveling in opposite directions are superimposed. Perfect competition c. 5/42 weeks d.102 237. The work done by all the forces except the gravitational force is always equal to the _____of the system a. 1. 12 years c. 100 meters b. 200 meters d. In a certain 25 inch TV set. 300 meters c. 18 years d. The replacement of the original cost of an investment a. one calibrated in Celsius and the other in Fahrenheit. the ghost is about 1 cm. 41 meters c.013 psi d. 14. 1 atm of pressure is equal to _______. On a certain test. The density of ivory soap is unity d. a. 53 meters d. a. 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. 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. Ivory soaps floats in water because: a.d. Payoff . 7/13 d. All matters has mass 242. the numerical reading obtained on the Fahrenheit thermometer. 37 meters b. 2117 psi 247. and the sound of the splash was heard three seconds later. Oligopoly 241. Is less than that obtained on the Celsius thermometer c. May be greater or less than that obtained on the Celsius thermometer d. 101300 Pa b. what part of the group of students passed the test? a. to the right of the principal image of the reflected signal arrives 1 microsecond after the principal signal. The specific gravity of ivory soap is greater than that of water c. 5/9 b. 4/7 243. are used o measure the same temperature. 400 meters 244. Is greater than that obtained on the Celsius thermometer b. A stone is dropped into a well. Is proportional to that obtained on the Celsius thermometer 246.7 bars c. 20 years 248. Two thermometers. 14 years b. Breakeven c. The specific gravity of ivory soap is less than that of water b. What is the difference in the path length of the reflected and principal signals in this case? a. the average passing score is 72 while the average for entire test is 62. What was the depth of the well? a. 30 meters 245. 6/11 c. Capital recovery b. 4 π cubic units 251. An oil well that yields 300 barrels of cure oil a month will run dry in 3 years. $190. 2. $150. it is said that the crow dropped a pebble which was a perfect sphere 3 cm in radius into the can. The spherical excess of a spherical triangle is the amount by which the sum of its angles exceed a. $253. 10 cu m d. When comparing leasing against outright purchase of equipment. π cubic units d.3√ dollars per barrel. π/4 cubic units c. Mean value c.650 d. If the can was 6 cm radius. 2. Find the volume of the solid above the elliptic paraboloid 3x2+y2=z and below the cylinder x2+z=4 a. Leasing offers certain tax advantages 250. 1 cm c. Leasing reduces maintenance and administrative expenses c. If is estimated that t months from now. 1.d. 3. the area of three adjacent surfaces of a rectangular block are 8 sq cm. Leasing frees needed working capital b. Return on investment 249.5 cm 257. Less than 0 . -1 254. 1/3 b. 3 cm d. what was the rise in water level inside the can after that pebble was dropped? a. 360˚ d. 20 cu m 256. 270˚ 255. 90˚ c. Deflection 253. Find the maximum and minimum values of 3sinθ for 0˚ a. A point on the graph of a differentianble function where the concavity changes is called a point of ______ a. Leasing offers less flexibility with respect to technical obsolescence d.324 252. If the oil is sold as soon as it is extracted from the ground. When a line y=mx+b slopes downwards from left to right. Local minimum value d. 0 c. which of the following is not correct? a. what will be the total future revenue from the oil well? a. Inflection b. 1. the slope m is a. the price of crude oil will be P(t)=18 + 0. -2 d. 180˚ b. 2π cubic units b. the volume of the rectangular block is a. 40 cu m c. 10 sq cm and 20 sq cm.612 c. In the story about the crow who wanted to drink water from a cylindrical can but could not reach the water.550 b. 2 cm b. $207. 200 cu m b. A line perpendicular to a plane a. When the same polynomial is divided by (x-4). 4x-1 262. the remainder is 3. Value in radians c. Equal to 1 258. -2x-8 c. √ d. six 10-passenger mini buses and 12 drivers. The raw materials have to be transported to three production points in Dasmarinas Cavite. of which 10 tons are stored in warehouse in Quezon city.b. x+5 b. If the area of an equilateral triangle is 9√ sq cm then its perimeter is a. Cosine 263. 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. 260. A certain electronics company has 16 tons of raw materials. 7 cars and 5 mini buses √ ) c. the cost per ton for transporting the raw materials from the two warehouses to the three production points areas as follows To/Fro m Damarin Canluba as ng Batang as . When a certain polynomial p(x) is divided by (x-1). Canlubang Laguna and Batangas city in the amounts of 5. How should the transport company use their cans and mini buses in order to carry the maximum number of passengers each day? a. 9√ cm b. Tangent d. Equal to 0 d. Makes a right angle in the plane which passes through its foot c. If the surd (√ x is equal to: . 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. 18√ cm d. Is perpendicular to every line is the plane d. Is perpendicular to only two intersecting lines in the plane b. 9 cars and 3 mini buses b. 18 cm c. 3 cars and 9 mini buses c. The cars can make 14 trips a day while the mini busses can make 10 trips a day. The transport company has nine 5-passenger cars. Find the remainder when the polynomial is divided by (x-1)(x-4) a. and 6 tons are stored in warehouse in Makati. √ √ √ 264. -3x+15 d. then √ a. 7 and 4 tons respectively. Makes a right angle with every line is the plane 259. √ b. 12 cm 261. remainder is 12. 6 cars and 6 mini buses d. Greater than 0 c. | | c. x+z=y b. 89 c. 21 b. c. a.C to Dasmarinas. c and the respective opposite angles are A. b.C to Batangas. 35 272. 9 300. 14 c. c.00 d. e= no of tons to be shopped from Makati to Canlubanga and f= no of tons to be shopped from Makati to Batangas. b. a d. a2=b2+c2-bc cos A b. a. a. c=√ √ . b. c=no of tons to be shipped from Q. find the product MN of the following matrices M=| . A number when divided by 6 leaves a remainder of 5. Evaluate: I= ∫ ∫ a. If none of those examinees fail both subjects and there are four examinees who passed both subjects. d=√ √ a. which of 271. a. b b. d. x+y=z d. b=no of tons to be shipped ftom Q. | | ( ) 2 9 6 8 270. a2=b2+c2-2bc cos A c. 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. b. 8 300. find the number of examinees from that school who took the examinations a.00 c. If the following relationship is correct? a. d.P 700 P500 P800 P 200 P300 P400 267. 7 300. HINT let a=no of tons to be shopped from Q. 3 d. x=y+z c.C to Canlubang. x-y=z 269. c and the respective sides are a. d= no of tons to be shopped from Makati to Dasmarinas. | | b. when divided by 5 leaves a remainder of 4.00 b. c c. evaluate u= a. c. d. by 4 leaves a . 88/3 b. 79/3 266. a2=b2+c2-2bc cos B cos C | | N=| a. B and C. a. c. d. | | d. b. b Q. b=3+√ . d.00 268.C Makati Find the minimum possible transportation cost. Which of the following is a correct relationship for any triangle whose sides are a. a2=b2+c2-2bc sin A d. 10 300. 28 d. Arrange the following surds in descending order: a=√ √ . 265. 29 b. 825. Transcendental number 274. Conjugate circle d. 59 273. 845.4x 10-10 b. 4. Irrational number d. Radicals b. Exponent b. 7. Least common denominator c. Coefficients d. An arc equal to one-fourth of a circle is called a ____ a.94 inches c. 842. a. One is to fifty-two and one half as three and one-third is to ______ a. m c. m represents the _______ a.6141 radian d. If soldering lead contains 63% silver.1614 radian c. The logarithm of a number to a given base is called the ______ a. 1. a. Find the smallest possible value of the number. Quarter circular arc b. Quarter circle c. If angle θ=2. Least common factor d. Distance from a point b.2x10-10 275. 49 d. Base d.94 inches 280. 6. Greatest common factor 276. q d. Complimentary circle 281.94 inches b. 1.371x10 -10 becomes ______ a.remainder of 3. 185 b.4 c. 4.4 b. ______ grams of soldering lead can be made from 520 grams of silver.03 inches d. _________ are irrational numbers involving radical signs a. Slope of the line 278. a. The __________ of a and b is the smallest positive integer that is a multiple of both a and b. 1. and by 2 leaves a remainder of 1. none of the choices 279. The hypotenuse of an isosceles right triangle whose perimeter is 24 inches is ____ inches. Matrix 283. Coordinate of the line c. the multiplicand is _______ a. Index c. n b. In the equation ÿ=mx+b”.4161 radian 282. 175 . by 3 leaves a remainder of 2. a.3x10-10 d. When rounded off to two significant figures. 4.2 d. 4x10-10 c. In the equation “n x m=q”.5 277. 7. 9. 852. 1. the number 4. Least common multiple b. Surd c. 39 c.1416 radian b. then angle (180˚-θ)= __________ a. Each block measuring 20cm x 20 cm.44 d. less than or equal to 288. then x _____z. sine 289. then (a+c) is _______ of (b+d) a. sin A b. Each block measuring 20cm x 20 cm.44 sq m d. Assuming all the darts hit the dartboard.44 sq m c. greater than c. Less than b. Greater than c.0168 292.54 . 309. 165 d. what is the probability of getting a total score of 11? a. less than b. 100 c. If x >y and y>z. equal to d. The number on each block is the score earned when a dart hits that block.64 b. a percentage is a fraction whose denominator is ____ a. 0. gets a score of zero. Complimentary b. Assuming all the darts hit the dartboard and with two darts.04 c. and c _______is equal to b( ) a. and each circle passes through the center of the other. cosine b. 0. The dartboard has nine numbered blocks. 0. 10 d. Less than or equal to 286. sin B c. Each of the circles has a radius of 9 meters. what is the probability of getting a score of zero with one dart? a. 155 284. a. A dart. Find the area of the swimming pool. 0. if a>b and c>d. Equal to d. The number on each block is the score earned when a dart hits that block.0328 c. Supplementary c. b. 0.0128 b. Adjacent angles whose sum is 90 degrees are said to be _____ a. b d. 0. A dart. 209. which hits the unnumbered portion of the dartboard. 10000 290.c. If any given triangle with sides a. A swimming pool is constructed in the shape of two partially overlapping identical circle. 1000 b. Explementary d.44 sq m 291. 0. cotangent d. tangent c. a. Reflex angles 285. The dartboard has nine numbered blocks.44 sq m b. 509.228 d. a 287. 0. the following Fourier series equation represents a periodic ____wave i(x)= i + i cos x + i2 cos 2x+ i3 cos 3x +…+i sin x + i2 sin 2x+ i3 sin 3x+… a. 409. gets a score of zero. which hits the unnumbered portion of the dartboard. Q. 420 b. –cos 2y 296. 2. the number of female workers will increase to 65% of the total number of workers. P2-Q2=A2+B2 b. and B not involving any of the trigonometric functions of angle t. derive another equation showing the relationship between P.4 hp . From the given equations. what is the probability of getting a score of seven with one dart? a. 16.5% b. 52. A. 82. b. 4 4. 450 c. 2. What horsepower. If 100 new female workers are hired. 72. 40. n. 13.5% d. During installation. A rectangular metal sheet measures 22 ft long and 2R ft wide. 0. 4 16. 16. 16 297. 0. If a and y are complimentary. –cos 2x d. 0.70 294.47 ft c. 13. 12. sin 2x b. each circle measuring R/3 ft.293.56 ft d. a. three identical circles were cut.5% c.4 hp b. 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. Assuming all the darts hit the dartboard. 2. If the efficiency of the input multiplied by 100%. 490 299. the ratio of the number of male to female workers is 2:3.4 hp c. gets a score of zero. radius. 480 d. An elevator can lift a load of 5000 Newtons from ground level to a height of 20. Q= A cos t – B sin t. and m. which hits the unnumbered portion of the dartboard. 0. .10 c. The dartboard has nine numbered blocks. 14. If the area of the remaining metal sheet is 66 sq ft. a. A dart. P2+Q2=A2+B2 298. . what is the efficiency of the pulley? The tower section weighs 1000 kg a.04 b. 1. Find a.56 ft 295. Each block measuring 20cm x 20 cm. hp can the elevator develop? a. Given: P= A sin t + B cos t. Find the original number of workers in the factory. Given: a. d. find the value of P if: P= cos (540˚+x) sin(540˚+y) +cos(90˚+x)sin (90+y) a. .07 d. a. P2+Q2=A2-B2 c.0 meters in 10 seconds.56 ft b. find R. 2 2. From this rectangular metal sheet.5% 300. c. cos 2x c. P2-Q2=A2-B2 d. 62. 4. In a certain electronic factory. The number on each block is the score earned when a dart hits that block. find the centrifugal force in Newtons. 10000N 303.85% . 180 hours b. 0. 42 c.53 cm a. d. log nM b. 35 d. 160 hours c.0 meters/sec2? a. find the percentage increase in the cost of running the shop. 24 b.44 d. 10. 6 000N 302. and the miscellaneous costs are unchanged. M log n 306. Give the area of a triangle in square meters when the base is equal to 24.0 meters at a speed of 20 meters per second. How long will it take both crews to finish the same job working together? a. 28. 8 000N d.4 hp 301.062484 b. (a+x)(x-a) 309.85% d. a. The cost of running an electronic shop is made up of the following: Office rental=40% Labor=35% Materials=20% Miscellaneous=5%. 1/8 d. 2x-2a d. 0. 40000N b.1252 c. Evaluate the value of the determinant | | a. Give the factors of a2-x2 a. a. labor increased by 15%. If the same car in problem 301. c. b. -101 011 -001 111 308. 16. If the office rental is increased by 24%. One of the sides is equal to 56. 12 000N b.85% c.85% b. 1/2 b. 30000N c. 2a-2x b. (a+x)(a-x) c. 140 hours d.d. 20000N d. log Mn is equal to a. 1252. required to move a car with 1000 kg mass with an acceleration of 12. 18. log Mn c. 120 hours 2 304.6cm and the height is equal to 50. 1/4 c.1 310. with 1000 kg mass is driven around a curve with radius of 10. What is the force in Newtons.8 cm. 12 305. n log M d. 1/16 307. 10 000N c. 2877. Crew 1 can finish the installation of an antenna tower in 200 hours while crew 2 can finish the same job in 300 hours. Evaluate the limit of x +3x-4 as x approaches the value of 4 a. 15. The volume of a cube is reduces to ______ if all the sides are halved a. cost of materials increased by 20%. 27. 1 =? =? a. d. 0. d.5% 312. 47. 360 degrees c. √ 3/2 2 3 1/2 318. Simplify the following: a. b. 2 c. c.6 316. 37. Find the value of a. 0 1 2 cot (A+B) . Find the value of a.5% b. d. ( ) 25/48 125/48 125/16 125/8 319. 8 d. d. d. b. tan B sec B cot B csc B 322. 720 degrees 313. Find the value of √ √ a. 180 degrees b. 4 c. how much discount was given to the customer? a. Indeterminate 314.4 0. Simplify ( ) a. Find the sum of the interior angles of a pentagram a. b. 4 c. 2 b. c. Find the value of a. d.. 540 degrees d. √ 315. 4 317.5 0. b. 0 1 2 4 a.5% d. Find the value of P if it I equal to sin2 1˚ + sin22˚ + sin23˚ + . The selling price of a TV set is double that of its net cost. b. 8 d. b. + sin2 90˚ a. c. c.5 d. 16 320. 30. 2 b.3 0. 16 321. Infinity b.5% c. If the TV set is sold to a customer at a profit of 255 of the net cost. c. 0 c. c.311. b. 44. Find the value of P if it is equal to a. 0 d. 0. 0. 324. when rounded off to three significant figures yielded a value of 3. 149. 6785768. Round off: 0. 0. 0.2800 c.003 d. 325.00310 c.003086 to two significant figures a. c. Simplify { * +} a. 0.105 b.3x10-8 b. 2. 3. 2.10 to 3.101 to 3.101 to 3.2814 to four significant figures a. 6785768.34 b.3 c. c.6 .342 to the nearest one tenth a. 328. 3. 2. Round off: 149. 326. Round off: 30 562 to three significant figures a. Round off: 6785768. b.323. b. Round off: 2. Simplify ( ) ( ) a.00310 331.2000 332.00300 d.105 c. Round off: 0.0 d. 3.371x10-8 to two significant figures a. 3.691 to one decimal place a.109 330.00309 c. 329.00308 b. d. 34. 0. 34. d. 35.10. b.0x10-8 d. what was the original range of values of A? a. Round off: 34. 30 400 d.0000 d. 7000000. If A was originally a range of numbers with four significant figures which. 6785770. 30 600 c.00386 to three significant figures a.101 to 3. 0. 30 500 b.00 a.00311 d.2814 b. 2. Solve for the following: d.104 -7a +7a -7-a +7-a 327. 30 300 333.5x10-8 c.4x10-8 c. 0. 34.00308 b. The curve traced by a point moving in a plane is shown as the _____ of that point. such as air. 67. 121. .69 d. which is 120 meters above the water level at a velocity of 36 km/hr. the splitting apart of the heavy nuclei of uranium is called a. 148. Round off: 149. cos c. 148. A stone is thrown outward. 338. the refracted ray lie _____ to the perpendicular than does the incident ray. 3000x108 m/sec d.274 m c. Fission c. The speed of light is closest to: a. Pattern c. sin b. Closer b.274 m d. Diffusion 337. Perpendicular 336. 148 c. 150 d.274 m 342.46 meters b. at an angle of 30 with the horizontal. 141.70 c. 149 b. 3x108 m/sec 335. a. into the river from a cliff. how far from the cliff will the stone strike the water? a. Locus d. Parameter b.5 d. sec d. c. Farther c. 47. at an angle of 30 with the horizontal.69 b. Parallel d. a. b. 161. (a-b)3 is equivalent to which of the following? a. Which of the following is equivalent to the expression: a. A parabola which opens upward and whose vertex is at the origin is defined by what equation? a. csc 341. When a ray of light is incident from a medium. 147 d. 149.b. into the river from a cliff. like water.691 to two decimal places a. Neutron d. In nuclear energy. Round off: 149. Fusion b. Formula 344. 57. A stone is thrown outward.4 334.46 meters c. 149. 30x108 m/sec b. b. 77. 131. 148.46 meters 343. 300x108 m/sec c. At what height above the water level will the stone start to fall? a.691 to the nearest integer a. d. which is 120 meters above the water level at a velocity of 36 km/hr. 149. to a denser medium. 148.7 c.274 m b.46 meters 339.70 340. 8). Area of a triangle is given by the formula a. sin(A+B) b.d. sinAcosB + sinBcosA= ? a. Maturity value c.687 350. 221/512 d. C=9/5F+32 d. 1. 1. 1). Find the value of log 48 a. Solve by using trigonometric functions. cos(A-B) c.21 ft c. Find the volume generated by revolving the ellipse whose equation is a. Given log2=0. Payment for the use of borrowed money is called a. a. Evaluate ∫ a. 34. 345.21 ft . (0. cos(A+B) 351. d. 50 sq units 349.6 27. cosh2x+sech2 x c.30 and log3=0. 5). c. 25 sq units b. the coordinates if the vertices of a square are (1. which relationship is correct? a. 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. What is the area of the square? a.477.6 348. dx 37. d. d. 231/512 b. 3/4bh 347. bh c. and (-3. 24.6 57. sin(A-B) c. If the freezing point of water is zero deg Celsius or 32 Fahrenheit.6 47. C=5/9F+32 353.681 b. 16 sq units c. and its boiling point is 100 deg Celsius or 212 Fahrenheit. Find the total length of the guy wire if an additional three feet is to be provided for splicing. Loan b. 235/512 354. b. cosh2x-sech2x b. 1/4bh d. about the x-axis 4/3πab2 2/3 πab2 4/3 πba2 2/3 πa2b 355. 32 sq units d. F=5/9C+32 c. sech2x-cosh2x d.685 d. 1.21 ft b. c. F=9/5C+32 b. (4. b. What is the probability of obtaining either four or five heads if a fair coin is tossed 10 times? a. 1. 233/512 c.683 c. 44. In the Cartesian coordinate. sech2x+cosh2 x 352. sinh2 x+tanh2 x= ? a. Rate 346. Interest d. 4). 1/2bh b. The slope of a family of curves at any point (x. ( ) ( ) c. 30. 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. Reduce the following complex fraction into simple functions b. 33. Find the equation of the curve that is passing through point (1. 300 m 357. 25. 360. ( ) ( ) 358.64 c. 356. y) is equal to (x+1)(x+2). 1). a. 35. 200 m b. + 361. 356.64 b. 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. 352. How far will the ball travel before coming to rest if the ball continues to fall in this manner? a. Find the equation of the curve that is passing through the point (-3.45 m/sec 362. 365. ( ) ( ) d. After the 10 second period. ( ) ( ) b.45 m/sec c. what is the final velocity. – d.d.45 m/sec b. v in m/sec of the missile? a. b. what is the acceleration of the missile in m/s2 ? a.45 m/sec d. c. 256. y) is equal to 3x4-x2.64 .21 ft a. d. 250 m d. c. – b. + c. Reduce the following complex fraction into simple fractions a. 225 m c. 359.64 d. d. After the 10 second period. The slope of a family of curves at any point (x. 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. -3/2) a. 39. 369. 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 0.28M d. b. $54 M 364. P235630 b. nlogM . 366. P352630 c. 21 b.28M c. $74 M c. $84 M d. $64 M b.28M 365. 12 d. $43. P325630 d. Find the derivative of y with respect to x in the following equations a. Find the value of y’ at x=1 of the equation a. Solve for the values of a in the equation a8-17a4+16=0 a. b. P253630 368. if the cable shall be depreciated over a period of 15 years with zero salvage value. PV factor=22. c. ( ) c.363. All of the choices 370. Simplify the following expression: a. Log(MN) is equal to a. This amount includes freight and installation charges that are estimated at 10% of the above total price. what is the annual depreciation charge? a. c. logM-N b.563 a.28M b. A consortium of international telecommunication companies contracted for the purchase and installation of a fiber optic cable linking two major Asian cities at a total cost of US$ 960M. -21 c. $41. b. d.5% interest. d. $42. $44. what is the depreciation charge during the 8th year using the sum of the year’s digit method? a. This amount includes freight and installation charges that are estimated at 10% of the above total price. A consortium of international telecommunication companies contracted for the purchase and installation of a fiber optic cable linking two major Asian cities at a total cost of US$ 960M. if the cable shall be depreciated over a period of 15 years with zero salvage value. Given the sinking fund deposit factor of 0. -12 367.0430 at 6% interest where n=15. d. log M+N c. 9557 b. while the probability that the signal being received correctly at C is 0. The probability that the signal being sent from A is receives correctly at B is 0.965. 3 d. 4 374. a. a dot signal is also received at C?(Express your answer up o four decimal places) a. Sin215˚+sin275˚ a.6˚ 376.986 c.98.signal. Find angle AED.9457 c.6˚ b. b. 373. ABCD is a square and BEC is an equilateral triangle. from where it is retransmitted to station C.4957 d. 140˚ D . 150˚ c. 120˚ d.869 375. 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. 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.5947 d. θ=43. Large circle r=4m. what is the angle of refraction in the glass? a. NMlog10 371.896 b. 0.8. small circle r=radius=? 4-r 45˚ 4+r . 2 c. y’=? 372. 0. c. 0. respectively through the first and second medium. 0. - A eeeee d. θ=53. What is the probability that when a dot signal is transmitted from A. In the ECE board examinations. the probability that an examinee pass in each subject is 0. 0.6˚ d. A Morse code transmitter at station A sending out either a dot or dash B B C 377.689 d. θ=23. What is the probability that he will pass in at least 2 subjects? a. 0. If a. 75˚ b. logM+logN e. θ=33. 0. In the figure shown. 0.25. 1 b. The signal is received at station B.6˚ c. Solve for the radius of the circle shown. b. c. b.a. 1 379. a. 387. b. d. 16 381. a. c. [ ] a.688 m 0. Obtain the differential equation of all circles with center on line and passing through the origin. . Obtain the differential equation of all parabolas with axis parallel to the -axis. Evaluate b in the following equation logb 1024=5/2 a. 0. c. 383. c. Obtain the particular solution of when . d. b. . d. 4 d. . [ ] d. 378. b. d. Determine the differential equation of the family of lines passing through the origin. d. Obtain the differential equation of the family of straight lines with slope and -intercept equal. 2 c. a. d. a. 384. Obtain the differential equation of all straight lines at a fixed distance from the origin. a. [ ] c. Give the slope of the curve at point (1. c. b. [ ] b. ( ( ) ) 386. 1) a. 385. 388. 2560 b.866 m 0. 1/4 b.686 m 0. 382. -1/4 c. -1/3 380. c. b. b. c. a. 4 d. d. / a. d.868 m Differentiate the equation a. What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the -axis. c. Obtain the differential equation of all straight lines with algebraic sum of the intercepts fixed as . c. a. d. b. 392. a. 391. b. a. b.a. a. c. Solve the equation 395. b. Solve the equation 399. d. 398. c. 394. d. c. ( ) a. b. Solve the equation . . d. Obtain the general solution of . c. . b. d. Solve the equation . when . a. | | | | | | | | . a. b. c. 389. Solve the equation . b. Solve 396. 390. Obtain the particular solution of . b. d. a. d. Solve the equation . b. c. b. d. c. a. Obtain the general solution of the differential equation . b. a. c. . c. d. d. 393. Solve the equation . c. d. 397. c. d. MARK ADRIAN C. MULTIPLE CHOICE QUESTIONS IN . a. <MATHEMATICS> <DIEGO INOCENCIO TAPANG GILLESANIA> ENCODED BY: BORBON. d.Solve the equation . c. 400. b. infinity 406. C. 1 Find / as x C. undefined A. 1/7 B. infinity 405. D. indefinite . 3 A. C. 0 409. D. D. 1 D. Evaluate the limit approaches positive infinity. 1 D. 16 403. B. A. ½ Evaluate the following limit. 2 B. 0 D. Evaluate the limit . 8 407. 2 . 0 . . B. 0 A. C.401. infinity . D. 0 D. Evaluate the limit: B. Evaluate A. 0 C. / if . 5/2 404. A. e B. 1 Simplify the expression: B. C. 2/5 408. -1/2 A. /( C. Evaluate the following: B. 0 Evaluate: . B. C. A. C. 2 402. . infinity D. 0 A. Find the derivative of with respect to x.410. / of B. / D. A. / A. . What is the first derivative the expression ? B. 414. C. Find the derivative of A. / / 417. A. D. and D. B. Find / if √ D. √ B. what is the derivative of ? /√ / √ C. √ / if C. Evaluate the first derivative of the implicit function: . 413. D. B. B. / √ √ Find . D. / . Find the derivative of the function with respect to x. C. If is a simple constant. / / C. - / / D. B. . A. C. 412. - C. C. A. - A. A. √ 411. B. 0 D. 415. 416. - C. C.23 D. -1 . Find the derivatives with respect to x of the function √ . 426. A. - The derivative of C. C. /√ A. A function is given below. . D. x/ C. B. /x B. C. Evaluate the differential of A. √ . Find / A. 5 D. - /√ B. - If Find / : . to the ½ D. 2/x 422. 421. .418. 425. 1/2x A. A. D. / if D. - /√ 424. B. B. D. Given the equation: find . 420. is: B. - D. D. B. - 419. C. Differentiate power. √ / B. 2. what x value maximizes ? A. / 423. - C. 1 . B. what is / ? A. A. - /√ C. 00 if not more than 150 persons will join. 70 & 50 D. Find A. D. Find the minimum number of copies distributed from 1995 to 2002. 190000 If the sum of two numbers is . 2000 432. C. 10200 431. Given the following profit-versusproduction function for a certain commodity: Divide 120 into two parts so that the product of one and the square of the other is maximum. 80 & 40 A. Determine the maximum profit. Find the quantity for which the cost is a minimum. 1000 A. 200000 A. If to the 3rd power the maximum value of . ⁄ D.00 per person in excess of 150. 430.427. 433. 9800 D. ⁄ A. 250000 B. 550000 C. 0 B. D. . B. ⁄ C. A. however the cost per person will be reduced by P 5. 3000 B. 2 C. 1500 B. 429. 7500 428. 150 . 100 & 120 ( ) Where P is the profit and x is the unit of production. find the minimum value of the sum of their squares. 75 D. How many persons will make the profit a maximum? C. 1 B. Find the numbers. where is in years. 60 & 60 B. The number of newspaper copies distributed is given by . ⁄ The cost C of a product is a function of the quantity of the product given by the relation: . -1 A. A certain travel agency offered a tour that will cost each person P 1500. 9850 C. How far from should he land if he can row at the rate of 6 kph and walk at the rate of 7. 3. north of a river which runs due east.331 B. If an observer’s eye is 1. D. 3 km 436.5 km from the nearest point on a straight shore . how far should he stand from the base in order that the angle subtended by the statue is a maximum? A.434. 31.71 m B.5 kph? An iron bar 20 m long is bent to form a closed plane area. 1 km B. What is the largest area possible? A. 1 The shortest distance from the point (5.127 D.5 m above the ground.41 m B. 250 D. 3. C. 2/3 A. 3.56 square meter D.83 square meter C. He wishes to reach.41 m C. 5. Where should the station be located so that the amount of pipe is a minimum? 437. 225 C. 4 km east of D. which is 4.445 Two cities and are 8 km and 12 km. 28. A statue 3 m high is standing on a base 4 m high. City being 15 km east of . respectively. 21. A pumping station is to be constructed (along the river) to supply water for the two cities. a point situated on the shore 9 km from . 9 km east of 438. 3 km east of C. 4. 5 km A Norman window is in the shape of a rectangle surmounted by a semicircle. A.51 m A. A boatman is at . 4. 6 km east of 435.10) to the curve is: B. 6. 8 km A. 1/3 D.56 square meter B. 3. 25. ½ .474 439. in minimum time. C. 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? D.68 square meter C. what is its base radius. 137 square meter C. A. D. 63. 18. ⁄ B. 3. 10 cm An open top rectangular tank with square bases is to have a volume of 10 cubic meters. 3 meters The volume of the closed cylindrical tank is 11.500 A. 2. 150 square meter D. 16 cm C.500 D. 12 cm 442. 32.41 cm B. 28. 62. inches? A. ⁄ B. 16.14 cm B. The material for its bottom cost P150. in m? D. 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? capacity of 16823cc.500 441. inches. ⁄ 445. The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of radius and height is: 446.3 cubic meter.28 cm 444. that can be made into a closed cylindrical can having a volume of 108 cu.88 B. The most economical height is: A. 65. How long is the 4th side. Find the height of the box to use the least amount of material. ⁄ A.44 A rectangular box having a square base and open top is to have a B. C.200 C. when the area of the trapezoid has the greatest value? A.00 per square meter. in sq. 120 square meter C. Three sides of a trapezoid are each 8 cm long. 1. and that for the sides is P60. 64.5 meters 443. . If the total surface area is a minimum.5 meters A. 15 cm D.74 cm C. 1.440. 2 meters What is the least amount of tin in sheet.00 per square meter. 125 square meter B. D. 56 m D.25 m 448. 450. 592.59 cubic inches 449. B. 579. 0.346 cfs D. 1. 0.50 cubic inches 452. A load of 40kN is to be raised by means of a lever weighing 250N/m. 4. What is the volume of the largest box that can be so constructed? Integrate: A. . C. The material for the sides cost P 2000. 622. 17. 430 cfs A. Evaluate ∫ D.486 cfs C. If the load is placed 1 m from the support.52 m B.19 m D. D.002 feet per second. B.49 cubic inches B. A. 18.73 m D. which is supported at one end. As increases uniformly at the rate of 0. Evaluate the integral of A. .95 cubic inches B. A. how long should the lever be so that the force required be a minimum? C.300 cfs B. 451.12 m C. Find the radius so that the cost is least.447. 5.89 m A cylindrical steam boiler is to be constructed having a capacity of 1000 cu.43 m B. 1.22 C. 0. A box is to be constructed from a piece of zinc 20 inches square by cutting equal squares from each corner and turning up the zinc to form the side.00 per square meter. 453. 4.00 per square meter and for the ends P 3000. C. 20. 599.66 D. C. 3. at what rate is the expression (1+ ) to the 3rd power increasing when becomes 8 feet? A. m. 13. A. - B. A. Integrate D. A. A. ½ D. C. 456. ½ . D. ⁄ Evaluate ∫ . with respect to C. B. √ ] √ D. D. . What is the integral of ? B. ½ D.458. C. - 455. ⁄ B. B. arcsec D. C. C. 459. B. C. arcsin A. . [ . The integral of is: . B. 457. Evaluate ∫ C. 454. ½ B. ⁄ A. . Evaluate ∫ A. D. . Evaluate ∫ B. A. .∫ Evaluate ∫ 462. D. arctan 461. ½ 460. √ A. A. C. Evaluate ∫ C. C. 463. has an upper limit of 1 and a lower limit of 0. √ B. B. 84/182 B. C. C. 465. C. A. ½ D. 470. √ Evaluate ∫ 468.467. D. C. - B. D. A. . 466.√ 469. Evaluate ∫ A.258 A. . A. 82/182 . D. B. √ Evaluate ∫ Evaluate the integral of with limits from 5 to 6. A. 0.186 B. Evaluate the integral of if it D. D. . - C. 83/182 A. Integrate the square root of . B. 81/182 B. 464. 0. 0. C. 0. . D. C.114 D. D.143 Evaluate the integral of . A. Evaluate the integral of with limits from 0 to . Evaluate ∫ . C. - 471.√ . 857 C. 6.3068 B. A.8 C. units D. 476. . 0. 1. 0. 0. Find the area of the region bounded by the curves and A. units D. C. D. 21. 0. Find the integral of if lower limit = 0 and upper limit = . units A. 0.6 D. 478. 6. 2. 36 sq. A.567 sq. . Evaluate the integral of using lower limit = 0 and upper limit = . 2.2 B. 0. the lines and and the X-axis.0 475. units B.5046 479. 46 sq.648 D. 0. Evaluate the integral of using lower limit of 0 and upper limit = . 6. units C. A.783 B. 0. .056 C. 0. 0.022 B.A.4 473. 0. Using lower limit = 0 and upper limit = . the -axis. 19. 6.6 .043 D. units C. B. A.456 sq. 54 sq. Find the area bounded by the -axis .3 D. 0. what is the integral of ? 477.539 474. Find the area bounded by . A.478 sq. units A. units B. and Find the area under the curve and the x-axis between .7 B.4105 D.6107 C. 25. 1.567 sq. 20. and .4 C.031 472. 28 sq. 22. 62 /5 sq. A.B. 181 Find the area enclosed by D. 482. D. What is the volume generated by revolving this area about the y-axis? . about the -axis. units 485. sq. sq.1 D. units B. A. the line and the -axis. A. 56. √ B. units D. C. 184 A. 179 D. C. Find the area of the region bounded by one loop of the curve . 26 B. 28. Find the area bounded by the curve Find the volume generated by rotating the region bounded by . 186 A. What is the volume generated? C. 487. B. 62 /3 sq. 12. B. units C. C. units sq. D. 481. 30 A. C. D. B. and .8 484. Given is the area in the first quadrant bounded by . 28 The area bounded by the curve and the line is revolved about the line . What is the area within the curve ? 486. 32 483. A. . 62 sq. sq. units Find the curved surface (area) of the solid generated by revolving the part of the curve from to about the -axis.2 480. units D. C. 5/62 sq. units C. B. 2.A.5. 1. the -axis and the line is revolved about the line .9. 28.12. (0.6.8) A.5) A.3) D. 50. the line .6) 492.8. -axis and the line .12. (0. (0.4 C. What is the volume generated when this area is resolved about the line ? A. (0.6) C. 51.26 A. (2. Given is the area in the first quadrant bounded by . and the line . B.75 A solid is formed by revolving about the -axis. (0. 1. (1.2 B. Find the moment of inertia of the area bounded by the parabola .067 .0. (0. (1.6) D.8 A. Find its centroid.81 489.to .26 491. D.4) B. (2.6 494. 1. with respect to the -axis. D.6) 488. Find its centroid. 2. 1.61 493.25) D. 52. D. 27.4.8.. and the line . How far from the -axis is the centroid of the area bounded by the curve .83 A. in the second quadrant. C.41 B. bounded by the curve . C. D.26 The area in the first quardrant. (0. (0. the line and the -axis.4.24 B. 2. 25.26 C.07 A.75) 490. B. 1.32 A solid is formed by revolving about the -axis. 53.2. 2. 26. C. Find the centroid of the solid formed.5) C. and the -axis. the -axis. the area bounded by the curve . the area bounded by the curve . the -axis.6) Find the length of the arc of from . B. 497.305 ft-lb D. 498.500 kg-m B. that is 8 feet in diameter and 9 feet tall. 10. 12. 22. 562.457 kg-m D.50 kg per meter has a leaky 15-liter bucket attached to it.256 kg-m B.2 kg-m B.878 495.421 ft-lb B. 0. 0.5 kg-m D. How much work is done in winding up the last 20m of the cable? A. if it is emptied at a point 1 foot above the top of the tank? A.316 ft-lb The velocity of a body is given by . If the bucket is full of liquid when 30 meters of chain is out and half-full when no chain is out. 2.021 N-m 496. Assume a force of 6 N is needed to hold it at a length of 11 cm. The distance covered in meters between and second is close to: A.2 kg-m C. and is filled with a liquid that weighs 800 kg per cubic meter. 356.800 kg-m A.968 D.866 kg-m B. 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. 0.448 ft-lb C. 0. 56. 1. 21. A conical tank that is 5 meters high has a radius of 2 meters. 54.B. where the velocity is given in meters per second and is given in seconds.244 C. 49. 52. 9. How much work is required to pump all the water from a right circular cylindrical tank. -5 .21 N-m 499.3 kg-m 500. 21.896 kg-m C.667 kg-m A uniform chain that weighs 0.456 kg-m C. 689. A. 15.1 N-m D. Find the work done in stretching a spring of natural length 8 cm from 10 cm to 13 cm. 23. A 60-m cable that weighs 4 kg/m has a 500-kg weight attached at the end. 2 B. 458. How much work is done in discharging all the liquid at a point 3 meters above the top of the tank? A. D. 21 N-m C. 502. Which of the following is not a property of probability: A. its reciprocal 506. If events & exclusive. then the probability that both events can happen is zero. The probability that an event can happen is always positive and is less than one or equal to one. D. corollary C. sector A. axiom D. unchanged C. All circles having the same center but with unequal radii are called: . none of these 504. multiplied by m 507. 5 D. Any number multiplied by ________ equally unity. -2 501. the determinant of the matrix will be: B. A. a set of random events An angle greater that a straight angle and less than two straight angles is called: A. it depends are mutually D. C. tangent C. reflex angle D. If events and are mutually exclusive. infinity D. itself C. acute angle B. postulate B. a fuzzy set C. then B. the sum is equal. right angle A. a set of random variables A line segment joining two point in a circle is called: A. the set of possible outcomes of an experiment is termed as: B. theorem B. zero 503.D. 505. If equals are added to equals. a sample space C. D. If is an event which cannot occur in the sample space. obtuse angle C. arc In probability theory. A. the probability of is zero. If every element of a column (or row) of a square matrix is multiplied by m. B. chord 508. altitude C. parallel A. oblique C. concentric circles 509. decagon D. coplanar B. 514. A rectangle with equal sides is called: B. a parallelogram . The sum of the sides of a polygon is termed as: A. is: A quadrilateral with two and only two sides of which are parallel. scalene triangle D. equilateral triangle C.A. a rhombus B. tangent circles D. rhombus 512. dodecagon C. apothem D. In a regular polygon. apothem A line that meets a plane but not perpendicular to it. perimeter B. trapezoid D. pentedecagon B. trapezoid A. encircle C. altitude C. isosceles triangle 510. a square A polygon with fifteen sides is called: B. radius 511. nonagon C. square B. parallelogram C. D. the perpendicular line drawn from the center of the inscribed circle to any of the sides is called: B. D. median 515. rhombus A triangle having three sides equal is called: B. collinear 516. in relation to the plane. quadrilateral D. concyclic 513. A. parallelogram C. circumference A. a rectangle A. A quadrilateral whose opposite sides are equal is generally termed as: A. is called: A. which touches the conic at only one point A. lying on the plane The section of the sphere cut by a plane through its center is termed as: C. oblique to the plane C. the angles opposite to each other are termed as: B. perpendicular to the plane D. axis 524. The locus of the point which move so the sum of its distances between two fixed points is known as: A. big circle The chord passing through the focus of the parabola and perpendicular to its axis is termed as: D. which is parallel to the normal In two intersecting lines. a sector A. great circle A. inscribed angle 522. a parabola Point which lie on the same plane. are called: B. a hyperbola C. coplanar D. A tangent to a conic is a line D. 523. which passes inside the conic . opposite angles C. vertical angles C. latus rectum A. C. C. incircle 519. a segment 518. C. horizontal angle A. coplanar D. A normal to a given plane is: 525. B.517. directrix Line that pass through a common point are called: B. small circle D. concurrent D. a tangent B. concurrent 521. congruent 520. collinear B. collinear C. a circle A. a secant D. congruent A. translated axis B. parallel to the plane A. A part of a line included between two points on the line is called: B. an ellipse B. quadrants D. quadrants A. The locus of a point that move so that its distance from a fixed point and a fixed line is always equal. a circle C. a parabola A. a circle C. a parabola B. the polar angle is positive when: A. a parabola A. 532. A. a circle D. an ellipse D. is known as: D. none of these 529. axis C. octants C. the distance from a point to the pole is known as: A. an ellipse B. which are known as: The plane rectangular coordinate system is divided into four parts which are known as: 533. an ellipse 528. measured counterclockwise D. A.D. which moves so that it is always equidistant from a fixed point. -coorcinate . axis 530. an ellipse B. a parabola D. The locus of a point. a circle C. measured clockwise B. measured at the terminal side of D. D. coordinates B. coordinates 531. In polar coordinate system. A conic section whose eccentricity is less than one (1) is known as. octants B. a hyperbola C. A conic section whose eccentricity is equal to one (1) is known as: In polar coordinate system. radius vector C. polar angle A. a hyperbola 527. all of the above 526. is known as: B. a hyperbola The rectangular coordinate system in space is divided into eight compartments. a hyperbola C. -coordinate B. This is commonly known as: D. skew . a parabola A. conjugate axis B. equal to the negative reciprocal of the other The axis of the hyperbola. Second proposition of Pappus A. parallel B. congruent 539. major axis The volume of any solid of revolution is equal to the generating area times the circumference of the circle described by the centroid of the area. When two lines are perpendicular. A. The curve represented by the equation is: 538. is known as: C. major axis D. when extended. one of these lines are said to be: A. minor axis A. C. conjugate axis D. will pass through the interior of the polygon. Cavalier’s Principle A. the slope of one is: D. transverse axis 537. Which of the following statements is correct? A. First proposition of Pappus The axis of the hyperbola through the foci is known as: B. transverse axis 541. A polygon is _____ if no side. isopometric D. A. equal to the negative of the other 536. a circle 535. all equilateral triangles are similar B. Simpson’s Rule B. all rectangles are similar 540. minor axis If the product of the slopes of any two straight lines is negative 1. C. a line B. an ellipse C. equal to the other C. all isosceles triangle are similar D. which is parallel to its directrices. all right-angled triangles are similar D. equal to the reciprocal of the other B. equilateral C. C.534. convex B. bearing D. pentatron C. angle of depression A. The arc length equal to the radius of the circle is called: A. annulus . angle of elevation B. these medians intersect at a point which is called the: 548. centroid D. 1 grad The median of a triangle is the line connecting a vertex and the midpoint of the opposite side. D. A. pentagram D. 1 quarter circle C. disk C. dihedral angle B. centroid D. non-intersecting B. orthocenter 545. D. incenter 547. The angular bisector of the sides of a triangle intersects at the point which is known as: 549. acute angle C. incenter C. The area bounded by two concentric circles is called: A. incenter 546. which is above the eye of the observer is called: C. orthocenter C. The angle which the line of sight to the object. the amount of divergence between the two planes is expressed to be measuring the: C. C. plane angle A. orthocenter D. quintagon B. circumcenter When two planes intersect with each other. circumcenter radian A. For a given triangle. circumcenter D. 544.542. polyhedral angle B. reflex angle 543. pentagon A. centroid The altitudes of the side of a triangle intersect at the point known as: A five pointed star is also known as: B. makes with the horizontal. 1 radian B. perpendicular A. ring B. centroid D. congruent arcs D. It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms A. It represents the distance of a point from the -axis. vertices B. secant line 551. diagonals B. The altitudes of the sides of a triangle intersect at the point known as: A. orthocenter D. abscissa C. coterminal arcs A. incenter 552. physical life D. polar distance D. latus rectum C. two circular arcs that together make up a full circle are called: A. A. D. ellipse C. The length of time during which the property may be operated at a profit is called: In Plain Geometry. circumcenter C. tetrahedron B. sides A. life B. 554. Prisms are classified according to their _____. prism B. tangent line D. sector 550. parabola D. prismatoid 556. coordinate B. half arcs C. bases 555. axis of parabola C. What is the graph of the equation ? 557. hyperbola .D. ordinate A. conjugate arcs B. frustum C. length of time C. economic life 553. The line passing through the focus and perpendicular to the directrix of a parabola is called: A. circle B. a parabola B. zero A. diagonals D. hexagon D. paraboloid D. cylindrical surface C. triangle C. 560. How many faces have an icosahedron? A. circle The locus of points generated when a circle is made to roll externally along the circumference of another circle. Folium of Descartes A. if the eccentricity > 1. locus of a point D. vertices C. isogonal trajectories C. angles 559. is called: . sides C. 566. infinity C. Cardioid 563. a circle C. a hyperbola A. In a conic section.558. 16 B. square B. An arc length. A. none of these D. A. Epicycloid B. Each of the faces of a regular hexahedron is a: A. 18 C. an ellipse 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: B. spherical surface The family of curves which intersect a given family of curves at an angle less than 90° are called: D. Cissoid of circles Polygons are classified according to the number of: B. acute angle D. 562. which is equal to the radius of the circle. 564. 22 A line perpendicular to the -axis has a slope of: 565. 561. orthogonal trajectories A. intersecting curves B. 20 D. unity B. the locus is. A. one would use The area of a region bounded by two concentric circles is called: D. 1 radians B. the law of cosines To cut a right circular cone in order to reveal a parabola. the inverse square law C. 1 degree 567. supplemental polygon A. the Pythagorean Theorem B. the law of cosines 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. 2 radians In finding the distance between two points and . the Pythagorean Theorem A. the law of sines B. the translation of axes 572. 570.A. the law of cosines D. parallel to the axis of symmetry 569. parallel to an element of a cone and intersecting the axis of symmetry B. perpendicular to the axis of symmetry D. ellipse D. hyperbola D. parabola . the translation of axes D. annulus D. washer C. given only the lengths of the sides. the slope of the line Polygons with all interior angles less than 180° are called: C. circular disk 573. the most direct procedure is to use: C. B. concave polygon C. ring C. convex polygon 568. the law of tangents A. circle C. B. C. the slope of the line A. To find the angles of a triangle. acute polygon In finding the distance between two points and . it must be cut B. B. the most direct procedure is to use: D. A. at any acute angle to the axis of symmetry 571. 1 radian A. spiral of Archimedes C.574. its curve is symmetric with respect to the: circular motion about an axis. hexagon D. while travelling at a constant speed. all points of which are the same distance from a point within. focal width 581. circumference C. -axis B. latus rectum 577. 575. related angle D. square B. obtuse angle C. helix B. minor D. one C. If the equation is unchanged by the substitution of – for . infinity D. hypocycloid D. parallel to the axis? A. called the center: A. a chord which contains a focus and is in a line perpendicular to the major axis is a: 580. C. One-fourth of a great circle: A. circle B. line 45° with the axis D. In general triangles the expression / / / is called: B. A. cone . zero A. law of sines 578. reflex angle In an ellipse. Euler’s formula D. . origin C. -axis A. radius C. conjugate axis radian but less A. arc A. What type of curve is generated by a point which moves in uniform A plane closed curve. chord 582. An angle more than than radians is: D. 576. law of cosines C. straight angle B. cycloid A line which is perpendicular to the -axis has a slope equal to: 579. perimeter A. either B. Pythagorean theorem The sum of the sides of a polygon: B. maxima B. the curve is: A. At the minimum point. collinear 587. is not equal to zero D. 590. positive A. The volume of a circular cylinder is equal to the product of its base and altitude. maximum and minimum point 586. C. point of intersection B. C. point of intersection D. minimum point 591. infinity C. Point of the derivatives. If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve. circle The point on the curve where the first derivative of a function is zero and the second derivative is positive is called: D. quadrant 583. zero B. coplanar C. postulate B. D. which do not exist ( and so equals zero) is called: A. point of inflection B. oblique D. A. trigonometry B. corollary B. negative The study of the property of figures of three dimensions. parallel 584. physics D. At the point of inflection where . B. minima C. A. minima A. point of inflection D.C. a cissoid . maxima Points that lie in the same plane: B. A point on the curve where the second derivative of a function is equal to zero is called: A. maximum points D. stationary point C. solid geometry A. plane geometry 589. sphere A. theorem C. 588. 585. axiom C. the slope of the tangent line is: D. B. a sinusoid D. a paraboloid C. . an exponential MULTIPLE CHOICE QUESTIONS IN <PHYSICS> <DIEGO INOCENCIO TAPANG GILLESANIA> ENCODED BY: BORBON. MARK ADRIAN C. The product of force and the time during which it acts is known as: 597. acceleration B. 599. statics C. mass A. 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. energy D. mechanics B. dynamics B. kinematics Which of the following is not a vector quantity? A branch of physical science that deals with state of rest or motion of bodies under the action of forces is known as: A. A. translation B. work is defined in terms of the force acting through a distance. kinetics C.592. 595. center of inertia D. displacement C. velocity D. impact C. mass A. torque B. The study of motion without reference to the forces which causes motion is known as: A. 594. The rate at which the work is done is called: B. 596. kinematics D. rigidity B. kinetics 593. D. kinetics A. momentum A. weight 598. impulse In physics. plane motion D. rotation C. force C. power The property of the body which measures its resistance to changes in motion. work B. momentum A. center of gravity . The point through which the resultant of the disturbed gravity force passes regardless of the orientation of the body in space is called: C. statics D. what will happen? C.4 603. the volume of the ice will not change D. This concept is known as the: . some part of the ice will not change C. B. 15. specific weight D. the sum of the pressure. D. m.000.2 C. center of attraction B.2 606. Newton’s Second Law of Motion says that the rate of change of momentum with respect to time is: B. C. speed and amplitude travelling in opposite directions superimposed. Assuming no heat loss. the potential energy per unit volume. Ivory soap floats in water because: A. the phase difference is always zero C. constructive interference always results A. standing waves are produced B. 62.2 D. momentum 602. ice will become water A. and the kinetic energy per unit volume has the same value.600. 20. 32.000 cu. density 601. A. unit weight One (1) gram of ice at 0°C is placed on a container containing 2. the specific gravity of ivory soap is less than that of water 604. The momentum of a moving object is the product of its mass ( ) and velocity ( ). of water at 0°C. destructive interference always results The acceleration due to gravity in the English System or ft/s2 is: B. When two waves of the same frequency. all matter has mass Any two points along a steamline in an ideal fluid in steady flow. power B. the density of ivory soap is unity D. the specific gravity of ivory soap is greater than that of water The specific gravity of the substance is the ratio of the density of the substance to the density of water. all of the above 605. Another term for specific gravity is: D. D. moment of inertia C. force A. relative density A. energy C. What is the name of the vector that represents the sum of two vectors? C.A. maximum at the wall C. Faraday’s law of forces D. proportional to the depth of submergence B. watt per meter Kelvin 612. gravity D. Newton’s first law of motion 608. surface tension 613. equal to zero . Hydraulic theorem 607. Inelastic collision in which the total kinetic energy after collision is _____ before collision. C. proportional to the weight of the body A. ¼ maximum halfway out on the beam A leak from a faucet comes out in separate drops. constant along the beam B. per second C. an acceleration which is directly proportional to the resultant force and inversely proportional to the mass of the body. resultant 611. Whenever a net force acts on a body. A. Bernoulli’s energy theorem D. equal to the weight of the fluid displaced Kinematic viscosity in SI derived unit is described as: D. maximum at the free end 610. Pascal-second B. scalar D. independent of the volume of the body A. The loss of weight of a body submerged in a fluid is: A. air resistance In a cantilever beam with a concentrated load at the free end. B. Hooke’s law of equilibrium C. tangent C. viscosity of the fluid D. Newton per meter 609. it produces an acceleration in the direction of the resultant force. the moment is: A. tensor D. Which of the following is the main cause of this phenomenon? A. Fluid theory A. m. Pascal’s theorem B. Newton’s second law of motion C. B. This theory is popularly known as: B. sq. A. 616. less than C. mass acceleration A. equal B.81 liters . A flowerpot falls off the edge of a fifth-floor window. B. B. and = absolute temperature in degrees Kelvin. a parabola C. a part of a circle D. one inch C. = volume. D. The flowerpot hits the ground at the same time as the glass. ½ mass B. C. The flowerpot and the glass hit the ground at the same instant. which of the following is constant? A. ½ velocity B. mass velocity C. 619. plasticity 615. A. a hyperbola 620. One mole of gas at standard temperature and pressure (STP) conditions occupies a volume equal to: A.614. Which of the following is true? velocity2 In an ideal gas where = pressure. one foot 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. elasticity D. 617. one centimeter B. The glass hits the ground before the flowerpot. Kinetic energy equals: A. malleability C. The path of the projectile is: B.4 liters B. 9. One Joule of work is done by a force of one Newton acting through a distance of: A. 22. The flowerpot hits the ground first and with a higher speed than the glass. greater than D. D. Just as it passes the third-floor window someone accidentally drops a glass of water from the window. ductility 618. an ellipse D. C. one meter D. modulus of flexure C. The reciprocal of bulk modulus of elasticity of any fluid is called: The ratio of the uniform triaxial stresses. This hypothesis is popularly known as: A. Bernoulli’s principle C. 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. ductility 625. volume stress B. compressibility A. “The orbit of satellite is an ellipse. Compton’s hypothesis 622. D’Alembert’s principle D.5 liters 621. hardness B. Archimedes’s principle B. to the change in volume at equal stress in all directions is: A. coefficient of restitution 623. D. eccentricity 627. “Equal volume of all gases under the same conditions of temperature and pressure contain the same number of molecules”. 332 liters D. .C. D. malleability A. According to the laws of Johannes Kepler. shape factor C. modulus of rapture D. 2274. This principle is known as: A. Avogadro’s hypothesis C.” The shape of the ellipse depends upon its: “The resultant of the external force applied to an object composed of a system of particles. lengths of latera recta Calorie is the amount of heat required to increase the temperature of _____ of water by one degree centigrade. apogee and perigee A. is equal to the vector summation of the effective forces acting on all particles”. bulk modulus of elasticity B. ascending and descending nodes 624. C. toughness B. volume strain 626. This implies the resistance to shock or difficulty of breaking and express the work per unit volume required to fracture a material. 1 kg A. D. Debye-Sear’s hypothesis D. Dalton’s hypothesis C. Gauss-Jordan principle B. decrease as the distance of the axis moves farther from the centroid D. 1 mg To maximize the horizontal range of the projectile. shear strain D. maximize the angle of elevation and velocity B. maximize the angle of elevation It describes the luminous flux incidence per unit area and is expressed in lumens per square meter. explosion B. 631. C. The distance that the top surface is displaced in the direction of the force divided by the thickness of the body is known as: Formation of bubbles in a lowpressure area in a centrifugal pump and later their sudden collapse. illuminance C. Coulomb’s law 633. radiance The moment of inertia of a plane figure: According to this law. which of the following applies? D. C. is called: A. luminous intensity D. linear strain 644. A. law of universal gravitation B. Newton’s law C. the tangent function of the angle of trajectory must be equal to one C. is zero at the centroidal axis A. B. 1 gram A. 1 lb 628. D. cavitation C.B. volume strain D. D. “The force between two charges varies directly as the magnitude of each charge and inversely as the square of the distance between them. longitudinal strain C. The hardness of steel may be increased by heating to approximatelyv1500°F and quenching in oil or water if . luminance 629. maximize velocity A. increase as the distance of the axis moves farther from the centroid B. compression B. is maximum at the centroidal axis 630. corrosion A. inverse square law 632. force. The greatest unit pressure the soil can continuously withstand: A. impeller type Galvanized iron is a term referring to iron coated with: C. the steel has been hot rolled instead of cast 645. velocity. bearing strength C. point of raptue B. D. Which of the following is not true regarding the Blasius boundary layer solution/ A. fusion welding 647. A. magnesium D. the carbon content is above 3. B. acceleration. zinc The impulse and momentum principle is mostly useful for problems involving. demineralization process B. ultimate strength . C. lime soda treatment B.0% D. and time A process of welding metals in molten or in vaporous state without application of mechanical pressure or blow. specific speed B. the carbon content is below 0. tin A. overall efficiency C. It is valid only for potential flow A.2% D. It is valid for laminar flow D. TIG welding A. It is an approximate solution 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: D. force.A. Used as a guide to selecting the most efficient centrifugal pump: 649. Bernoulli’s equation A.0% C. velocity. acceleration. aluminum 646. cold welding C. and time D. and acceleration 650. Such welding may be accomplished by the oxyacetylene or by hydrogen flame or by electric arc. force. and time B. It is called: B. the carbon content is from 0. It permits one to calculate the skin friction on a flat plate C. C. thermal treatment 648.2% to 2. MIG welding B. velocity. ion exchange treatment 651. internal energy Heat transmission carried by the movement of heated fluids away from a hot body. conduction B. when there is no tendency towards spontaneous change D. yield point C. A. entropy decrease of the system 657. The power output of the engine is increased through: . shell and tube cooler B. In energy transformation process in which the resultant condition lacks the driving potential needed to reverse the process. convection A. B. plate cooler 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. absorption 653. disk cooler 654. plenometer C. boiler C. D. anemometer The sum of the three types of energy at any point in the system is called: A. the measure of this loss is expressed as: D. entropy increase of the system D. enthalpy An instrument used for measuring high temperature gas A. The system is safe to be in thermodynamics equilibrium: A. pyrometer 659. steam generator B. unfired pressure vessel C. enthalpy increase of the system C. specific bent ratio of the moment D. boiler or steam generator 655. when all its parts are at the same temperature 658. if it has no tendency to undergo further chemical reaction C. pressure heads 656. Bernoulli’s theorem B. radiation cooler B. radiation B.652. manometer D. A. as in the heating of water by a hot surface: D. The type of cooler extensively used for medium and large size diesel engines: C. when the system is not accelerating D. dew point 661. This hardness is A. An instrument used for measuring specific gravity of fluids: A. the total number of pounds of salt (sodium chloride) in the water per million pounds of water D. hygrometer B. flowmeter A. 663. ½ velocity On the hoist or load block or some equality visible space of every hoist designed to lift its load vertically shall be legibly marked: 664. dry bulb temperature D. turbo-charging C. its electrical voltage C. super-charging 660. The equilibrium temperature that a regular thermometer measures if exposed to atmospheric air is: B. its motor hp or kW The hardness of water is given in ppm (parts per million.. i. wet bulb temperature D. . psycrometer B.e. time B. its brand and model D. pounds per million pounds of water). Momentum = Force A. _____ A. all of these D. the total number of pounds of calcium and magnesium bicarbonate in the water. velocity2 C. hydrometer D. the total number of pounds of sodium bicarbonate in the water per million pounds of water. °C C. scavenging C. B. the total number of pounds of dissolved solids in the water per million pounds of water B. its rated load capacity 662.A. velocity C. .MULTIPLE CHOICE QUESTIONS IN <MECHANICS> <DIEGO INOCENCIO TAPANG GILLESANIA> ENCODED BY: BORBON. MARK ADRIAN C. and whose altitude is 0. that will cause an acceleration of 2.2. 670. 106 N C. whose coefficient of 671. 7. Calculate the tension needed to give the skier’s 54-kg body an acceleration of 1.5 N A. B.41 seconds C.2 m/s2.60. 667. 5. A 50-kilogram block of wood rest on top of the smooth plane whose length is 3 m.45 sec 10 to the 4th power ft/min2 666. 4. 1. 82 D.4. 6.8 10 to the 4th power ft/min2 D.75 sec B. A body weighing 40 lbs. 304 N D. starts from rest and slides down a plane at an .50m/s2 ? 669.665. 53.35 sec C.2 10 to the 4th power ft/min2 C. 202 N A.0 10 to the 4th power ft/min2 B.51 seconds D. 343. 8. 77 C. D.8 m.51 seconds B. 403 N B.2 N C. The truck bed is located with boxes. 4.637 friction with the bed is 0.8 N B.37 sec A. If the coefficient of friction is 0. 87 What horizontal force P can be applied to a 100-kg block in a level surface with coefficient of friction of 0. What is the shortest time that the truck can be brought to a stop such that the boxes do not shift? A. How long will it take for the block to slide to the bottom of the plane when released? A. 72 A skier wishes to build a rope tow to pull herself up a ski hill that is inclined at 15° with the horizontal. 2. A pick-up truck is travelling forward at 25 m/s. 2. 2. 2. A 10-lbm object is acted upon by a 4-lb force. D. 224. Neglect friction. determine the force parallel to the incline that must be applied to cause impending motion down the plane. What is the acceleration in ft/min2 ? A.5 N A 40-kg block is resting on an inclined plane making an angle 20° from the horizontal. 446. 9.14 seconds 668. 2. what is the smallest radius it can travel so that the friction will not be necessary to resist skidding? . The coefficient of kinetic friction between the 200 N block and the inclined plane is 0. passing through the pulley and connected to another block weighing 100 N moving vertically downward. The block is connected to a cable initially parallel to the plane.576 kN A. 9. B. Which of the following most nearly gives the acceleration of the system? 676. 2. Coefficient of friction between the tires and track is 0.478 kN D. D. 50 m B. 19. If the car’s velocity is 10 m/s. 1.3. 18.10. 15 m D. A.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.950 lb B. Compute the normal force on each of the front wheels of the car.63 ft C. What is the tension in the supporting cables? C. 34 m A. 6 kN 673.3. 34. 39. An elevator weighing 2. 5. If a car travels at 15 m/s and the track is banked 5°. 675. B. C. 2.000 lb attains an upward velocity of 16 fps in 4 sec with uniform acceleration.33 ft D. 7. The car is brought to rest from a speed of 54 kph in 5 seconds by means of the brakes.angle of 30° with the horizontal for which the coefficient of friction µ=0. How far will it move during the third second? 674. 60 m C.541 kN C.150 lb A block weighing 200 N rests on a plane inclined upwards to the right at a slope of 4 vertical to 3 horizontal.495 lb D. A.99 ft B. what is the smallest radius it may travel without skidding? A.250 lb A car travels on the horizontal unbanked circular track of radius . 24. 18° C.5° C. A vertical bar of length with a mass of 40 kg is rotated vertically about one end at 40 rpm. 229.A. 262. 5. 39° 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. 30° D. D. What is the maximum angle of tilt for the seats if the carousel operates at 12 rpm? B.2 rad/s A. The seats have a mass of 75 kg. 3.2° B. 1. For what coefficient of friction will skidding impend for a speed of 60 mph? A. 2. 45° 679.14 m 680. 651.6 m B.23 m D. > 0. 2. Traffic travels at 65 mi/hr around a banked highway curve with a radius of 3000 ft. Find the length of the bar if it makes an angle 45° with the vertical? A.310 . 278. 247. 285. 3. < 0. < 0. 1.4 rad/s B. The seats of a carousel are attached to a vertical rotating shaft by a flexible cable 8 m long.16 m C.4° A. 58.3 m C. 49. 37.4 m B.38 m D.86 m 678.310 B.3 rad/s C. Find the angular velocity of the weight when the cable breaks. What banking angle is necessary such that friction will not be required to resist the centrifugal force? A.9 rad/s B. 681.6 m C. 214. 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. 682. 265.58 m C.26 m D.74 m 677.360 A. 35° D. A concrete highway curve with a radius of 500 feet is banked to give a lateral pressure equivalent to . 540 J B. 7. 6. The block is pushed 2 feet horizontally.56 lb D. The coefficient of friction between all tires and the road is 0. 12 rpm C. A cast-iron governor ball 3 inches in diameter has its center 18 inches from the point of support. 350N-m B. An automobile has a power output of 1 hp.36 lb 688.80. Answer in SI units closest to: A. A 10-kg block is raised vertically 3 meters. What is the change in potential energy. 14 fps D. A 3500 lbf car is towing a 500 lbf trailer.3. 87 mph B. 55 mph 684. 320 J A. When it pulls a cart with a . D. a girl on the swing is 7 feet above the ground. How fast can the car and the trailer travel around an unbanked curve of radius 0.D.360 683. 294 J C. The object will begin to slide off when the platform speed is nearest to: A. 26 mph D. she is 3 feet above the ground. 72 mph C. A force of 200 lbf acts on a block at an angle of 28° with respect to the horizontal. 26 rpm 687. An object is placed 3 feet from the center of a horizontally rotating platform. > 0. Neglecting the weight of the arm itself. 22 rpm At her highest point. 320 J B. The coefficient of friction is 0.36 lb 685.63 lb D. 12 fps C. 480 J C.12 mile without either the car or trailer skidding? 686. and at her lowest point. 10 fps B. 7. C. find the tension in the arm if the angle with the vertical axis is 60°. 7. 16 fps A. What is the work done by this force? A. 350 kg-m2/s2 A. 215 J D. What is her maximum velocity? 689. 17 rpm B. S 75. 6. S 81. 7.52°W C. 0. N 61°20’W.249 m/s B. 423 kph C. S 84. B. .54 mph 696. N 61°20’E. 97. 7. 7. 8. and 40N are in equilibrium. 977 N 691.1326 692.47°W What is the resultant velocity of a point of -component .35 mph C. A.1326 D. A. C.7 N D.37 mph A. relative to the earth’s surface. Find the angle between the 30-N and 40-N forces.37 mph 694. if he can row 12 mph in still water.force of 300 N.7 N D. 8.37 mph 690. What is the effective speed of the boat? B. what is the cart’s velocity? 693. 74. 64. If a wind of 40kph is blowing from the north.42 mph Three forces 20N. 240 kph A.49 m/s A. In what direction and how fast is the man moving. 77. 2. A passenger walks Southeast across the deck at 5 mph. 30N. find the ground speed of the plane. 79.36°W A. 249 m/s C.37 mph D. N 28°40’W. 30°15’25’’ B.9 N C. D.9 m/s A ship moving North at 10 mph. B. what direction should he take to cross the river? A plane is headed due east with air speed of 240 kph.33 mph A.36°W D. 7. 24. 62. C. N 28°40’E. 243 kph A boat has a speed of 8 mph in still water attempts to go directly across a river with a current of 3 mph. 7. 200 kph D. The weight of a mass of 10 kilograms at a location where g=9. and -component at time ? B. A man wishes to cross due west on a river which is flowing due north at the rate of 3 mph. S 14.77m/s2 is: A.1326 B. 63.1326 695. 7° B. 408 m A. 45° 701.6 kN B. 75° 698.5 m high and the other end resting on a horizontal ground. A wooden plank meters long has one end leaning on top of a vertical wall 1. D. The allowable spacing of towers to carry an aluminum cable weighing 0. 3 m D. C. 422 m B. 25. 40° D.80 kg is applied to the weight. the rope will make an angle with the vertical equal to: A. 30° C. Neglecting friction. Neglecting friction. 50 kN 702.25 m? A block of wood is resting on a level surface. 20 kN D. A. 80 kN C.2° D.23 kg B. find the force that causes the block to slide. If a horizontal force of 5. 30.5 kg per horizontal meter in a span of 100 m if the sag is to be limited to 1. A 10-kg weight is suspended by a rope from a ceiling.03 kg per horizontal meter if the maximum tension at the lowest point is not to exceed 1150 kg at sag of 0. 584.B. 60° D. What tension must be applied at the ends of a flexible wire cable supporting a load of 0.96° 700. 423. If the coefficient of friction between the block and the surface is 0.30. 5 m B. 4 m C.42 kg A. find if a force (parallel to the plank) of 100 N is needed to pull a 400 N block up the plank. 248 m B.50 m is: A 100kN block slides down a plane inclined at an angle of 30° with the horizontal.2° C.62 kg C. 390 m C. 16. 6 m A. 623. 33. how much can the plane be inclined without causing the block to slide down? A. 86. 500. 699. 21. 28.3° .97° 697.24 kg D. 0206 m/s2 D. 6. 5205 N 704. a car decelerates at the rate of 500 m/min2 along a straight path.95 B. 793 A.3 Find the required force acting horizontally that will start the block to block up the plane. Find the acceleration of the car in m/s2. 4. 1020 N 707. How far in kilometers from point will it be in 2 minutes after passing point . 4236 N D. From a speed of 75 kph. B. A.0 m/s2. What is the acceleration of the body that increases in velocity from 20 m/s to 40 m/s in 3 seconds? Answer in S.65 2 C. 4. 1160 N C. 5205 N D. 8 m/s C.126 m/s2 A 500-kg block is resting on a 30° inclined plane with a µ=0. 2570 N 705. A. it reaches point .3 Find the required force acting horizontally that will prevent the block from sliding.75 2 A. 3. 0.85 2 B. Howw far in meters. B. A train upon passing point at a speed of 72 kph accelerates at 0. B. 5 m/s 709. 791 C. 0.75 m/s2 for one minute along a straight path then decelerates at 1. 4. A. a car accelerates uniformly.703.42 m/s2 A. 2 D. 10 km . will it travel in 45 sec? A car starting from rest moves with a constant acceleration of 10 km/hr2 for 1 hour. 4. 4236 N 708. B. After 18 minutes. units.I. then decelerates at a constant -5 km/hr2 until it comes to a stop. With a starting speed of 30 kph at a point . 0. 795 A 500-kg block is resting on a 30° inclined plane with a µ=0. 21 km from . 797 D. How far has it travelled? A.0562 m/s2 C. 1160 N C.67 m/s D. 7 m/s 706. B. 20 km 713. 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. 12.48 m A. 2.10 B. 6.25 m B. 1.71 C. 10.28 m C. 2.25 D. 8.63 m D. 2.75 711. 714. A train running at 60 kph decelerated at 8 m/min2 for 14 minutes. Find the distance traveled, in kilometers within this period. 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 A. 12.2 B. -45.2 ft/s2 B. 13.2 C. -33.4 ft/s2 C. 13.8 D. -42.3 ft/s2 D. 12.8 712. 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. 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 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 2 B. 2.39 ft/s B. 113 mm C. 2.12 ft/s2 C. 103 mm 2 D. 2.93 ft/s D. 93 mm 716. A force of 10 Newtons is applied to one end of a 10 inches diameter circular rod. Calculate the stress. safety with respect to the tensile failure? A. 3.15 A. 0.20 kPa B. 3.55 B. 0.05 kPa C. 2.15 C. 0.10 kPa D. 0.15 kPa 717. 718. D. 2.55 What force is required to punch a 20mm diameter hole through a 10-mm thick plate. The ultimate strength of the plate material is 450 MPa. 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. 241 kN A. 88.419 GPa B. 283 kN B. 92.564 GPa C. 386 kN C. 92.658 GPa D. 252 kN D. 95.635 GPa 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. 720. 721. A. 4.56 B. 5.12 A. 3.09 mm C. 4.25 B. 3.56 mm 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 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. 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 B. 54.3 mm 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? C. 35.4 mm D. 45.3 mm 725. A. m/m MPa; B. m/m MPa; C. m/m MPa; D. m/m 723. 724. 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 MPa; 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. B. 240 kN C. 280 kN D. 320 kN A. 3.43 mm A 20-mm diameter steel rod, 250 mm long is subjected to a tensile force of 75 kN. If the Poisson’s ratio µ is 0.30, determine the lateral strain of the rod. Use GPa. B. 2.125 mm A. C. 4.33 mm B. D. 1.985 mm C. Steel bar having a rectangular crosssection 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 726. D. 727. mm/mm mm/mm mm/mm mm/mm 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 A. in kN-m. 101. for a 50-mm diameter steel shaft when the allowable shearing stress is 81. 3. 100.03 B. The rotation of twist in degrees of a shaft.04 C. 5. 100. 20 mm in diameter and shear modulus of 80. 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.81 730. The maximum shearing stress must not exceed 110 MPa. which can be twisted through two complete turns without exceeding a stress of 70 MPa.1 MPa D.0 B. 79. 1. Use GPa. A.0 D. 8.6 MPa B. 3.28 m A. 800 mm long subjected to a torque of 80 N-m.923 MPa B.23 m C. Find the inside diameter and the outside diameter of the shaft that meets these conditions. A.000 MPa is: A hollow steel shaft 2540 mm long must transmit torque of 35 kN-m.0364 mm D. B.C. Determine the length of the shortest 2-mm diameter bronze wire.92 D. The maximum allowable torque. mm mm mm mm Compute the value the shear modulus of steel whose modulus of elasticity is 200 GPa and Poisson’s ratio µ is 0.89 m 732. 2. 4. 76. 2. 100. mm. B.0414 mm 728. 72.0 729.0 D. mm.400 MPa 731. . mm. 6.30. The total angle of twist must not exceed 3 degrees.456 MPa A. 1. 4.698 MPa µ=1/3 and the modulus of elasticity of aluminum be 70 GPa.5 MPa is: A. 110. 100. 6.0303 mm D.56 m B. mm. C.0312 mm C. C. 82. 733. 67 A.5 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds? A. 0.4 N C.002 kg-m2 C. 214. in cm from the uncut longer side.48 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.5 kg-m2 B. A. 10 m long carries a concentrated load of 500 kN at the 739.6 MPa midspan. Determine the value of that will cause a total deflection of 80 mm. 9. 62. is the centroid of the remaining area? B. kN. A simple beam. What is the moment of inertia of a cylinder of radius 5 m and a mass of 5 kg? A. kN-m D. 223. 9.3 N A small square 5 cm by 5 cm is cut out of one corner of a rectangular cardboard 20 cm by 30 cm long.C. A load is supported by two springs arranged in series. kN-m 737. Assume GPa for both springs.56 C.35 D. 735. kN-m kN. 0. 9. 1050 kN-m C.5 MPa 734. 738.8 N A. What is the maximum moment of the beam? D. How far. 0. 80 kg-m2 . 1250 kN-m kN. 1520 kN-m D.0045 kg-m2 B. Determine the maximum shear and moment. B.001 kg-m2 C. 0. The upper spring has 20 turns of 29-mm diameter wire on a mean diameter of 150 mm. B. 228. 736. What is the inertia of a bowling ball (mass = 0. 120. kN-m kN.005 kg-m2 D. 1510 kN-m A. 136. D. The lower spring consist of 15 turns of 10-mm diameter wire on a mean diameter of 130 mm.8 N B. 278. 9. The mass of air in a room which is 3m 5m 20m is known to be 350 kg. assuming that the two fluids mix completely? B. A pressure gage 6 m above the bottom of the tank containing a liquid reads 90 kPa.5 kg-m2 A.8 kPa D. Determine the specific weight of the liquid.20 cu cm/g C. 362 kPa 744. 0. 0. Find its density.63 C. another gage height 4 m reads 103 kPa.86 100 g of water are mixed with 150 g of alcohol ( kg/ cu m). A.88 cu cm/g B. 0. 80 kPa C. 90 kPa D. One hundred (100) grams of water are mixed with 150 grams of alcohol ( kg/ cu m). The pressure 34 meters below the ocean is nearest to: If the pressure at a point in the ocean is 60 kPa. 72. What is the atmospheric pressure on a planet where the absolute pressure is 100kPa and the gage pressure is 10 kPa? D. 256. 0.3 kPa B. 100 kPa D. 1. 1.63 cu cm/g 743.716 kg/m3 741. 185.3 kPa C. 1.5 kN/m3 B. 6. 344 kPa D.C. 10 kPa 745. 3. A. What is the specific volume of the resulting mixtures.82 cu cm/g D. 332.4 kPa 746. 521. 120 kg-m2 B.82 742.5 kN/m3 . 8. What is the specific gravity of the resulting mixtures. assuming that the two fluids mix completely? A. B. 204 kPa D.2 kN/m3 D.96 B. 222 kPa 740. 1. what is the pressure 27 meters below this point? A. 0.1 kN/m3 C. 0.167 kg/m3 C.176 kg/m3 C. A. 5. 0.617 kg/m3 A. 1. Determine the pressure. .92 is floating on salt water of sp. where is in 3 kN/m and is in meters. 30. 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. 186.4 in3 Find the total water pressure on a vertical circular gate. 190 in3 D. 56. 7862 m3 C. The volume of a gas under standard atmospheric pressure 76 cm Hg is 200 in3. 752.48 kN C.3). 753. 78.46 kN A. 138.1 psia D. If the top of the square is An iceberg having specific gravity of 0. 52. 2 meters in diameter. 15 psia 749. 1. 751. 62. gr. 89. with its top 3. 1 meter below the water surface. Of the wood.4 psia D. = 1. 64..5 meters below the water surface. gr.5 kN C.93 kN B. 28. 36. 6325 m3 C. If the volume of ice above the water surface is 1000 cu. Find the weight and sp. The immersion is such that the two edges of the square are horizontal. in kPa. 78. m. 9364 m3 B. 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. 110 in3 750.6 psia C. 107.747.03.5 kPa D. at a depth of 5m. gr. 52. 169. What is the volume when the pressure is 80 cm Hg.9 kN A.54 kPa 748.36 kPa C. what is the total water pressure exerted on the plane surface? A. A two-meter square plane surface is immersed vertically below the water surface.5 kN B.25 kPa D.76 kN B.7 kN B. 43. if the temperature is unchanged? B. what is the total volume of the ice? A. 90 in3 D. The weight density of a mud is given by . 8523 m3 A. this is known as: C. C. 0. characteristic length. 0.9 D. Archimedes’ Principle A. 7. and absolute viscosity B.85 m/s What is the expected head loss per mile of closed circular pipe (17-in inside diameter. 0. and absolute viscosity 755.8 754.5 m/s.98 B. D. elevation head. Water having kinematic viscosity m2/s flows in a 100mm diameter pipe at a velocity of 4.21 m/s A. and the velocity head remains constant. and surface tension m3/s B. 346.96 B. 64 ft 757. velocity.5 m/sec? A. 0.62 and a coefficient of contraction of 0.63 m/s D. 38 ft 759. 3580 ft . mass flow rate per unit area. Bernoulli’s Theorem 756. 5. A.007 ft A. 8. friction factor of 0. Reynolds number may be calculated from: A.150 C. 758. 0. 0. Determine the coefficient of velocity for the orifice. 0. C. m3/s D. 0. Boyle’s Law The theoretical velocity of flow through an orifice 3 m below the surface of water in a tall tank is: C. 9.A. and absolute viscosity m3/s m3/s An orifice has a coefficient of discharge of 0.97 D.6 D.67 m/s 760. density. diameter.7 B. 0.99 The sum of the pressure head. What is the rate of flow of water passing through a pipe with a diameter of 20 mm and speed of 0. C. D. Torrecelli’s Theorem B. diameter. A. the Reynolds number is: B.03) when 3300 gal/min of water flow under pressure? C. velocity.63. diameter. Determine the discharge when the oil level in the tank is 3 m above the exit of the pipe. 0. 576 mm C.0814 Pa-s flows through a cast iron pipe at a velocity of 1 m/s. 12. Find the head lost due to friction.56 feet per mile? Assume .45 m D.25 m 762. 0.8 m 764.B.000179 m3/s A.750 761.450 D. how far apart can they be placed? (Assume ) A. 0. 352 mm 763. The pipe is 50 m long and 150 mm in diameter. 32. 30 m long is used to drain an oil tank.250 C. 19. A.869 and dynamic viscosity of 0.73 m C. A 20-mm diameter commercial steel pipe. 1.000256 m3/s B. 23.2 m C. What commercial size of new cast iron pipe shall be used to carry 4490 gpm with a lost of head of 10. 0. 479 mm D.000113 m3/s B. If each pump produces 685 kPa. 0.68 m D. 625 mm B. 0. D. A. 258. Neglect minor losses and assume . 0. Assume that 57 liters per second of oil ( kg/m3) is pumped through a 300 mm diameter pipeline of cast iron. 387. 298. Oil having specific gravity of 0.000869 m3/s C.6 m MULTIPLE CHOICE QUESTIONS IN .7 m B. .<ENGINEERING ECONOMICS> <DIEGO INOCENCIO TAPANG GILLESANIA> ENCODED BY: BORBON. MARK ADRIAN C. A. compound interest B. straight line method D. SYD method A. sinking fund method C. interest D. The term used to express the series of uniform payments occurring at equal interval of time is: A. investment B. nominal rate The recorded current value of an asset is known as: A. annuity C. SOYD method C. C. salvage value D. sinking fund method 768. declining balance method D. The interest rate at which the present worth of cash flow on a project is zero. A. 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: 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. incremental cost 770. oil. perpetuity D. depreciation 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. present worth 766. book value C. nominal interest C. This refers to the natural resources such as coal. straight line method B. yield 769. depletion C. B. interest rate 767. effective rate 771. B. rate of return B. declining balance method B. and timber in the forest. scrap value D. The lessening of the value of an asset due to the decrease in the quantity available.765. depreciation . inflation D. or the interest earned by an investment. producer goods and services 777. B. perfect competition B. yield 776. A. semi-oligopoly A. necessities C.772. amortization B. utilities As applied to capitalized asset. B. C. principal or present worth 775. earning value C. annuity C. economic return D. utilities The profit derived from a project or business enterprise without consideration of obligations to financial contributors and claims of others based on profit is known as: B. 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. 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. luxuries D. A. A. accumulated amount C. 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. A. capital recovery 774. monopoly C. oligopoly . producer goods and services A. oligopoly Those funds that are required to make the enterprise or project a going concern. B. expected yield 773. banking D. These are product or services that are required to support human life and activities. depreciation D. that will be purchased in somewhat the same quantity even though the price varies considerably. 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. monopoly 778. luxuries D. necessities C. working capital D. perfect competition B. B. D. identical equivalent uniform annual cash flows D.D. evaluation over different periods C. 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. production 782. fair value 780. P1. A. discount B. non-conventional cash flows D. utility C. difference in the magnitude of the projects It is defined to be the capacity of a commodity to satisfy human want.00 . single proprietorship D. different equivalent annual cash flows 786. 784. When using net present worth calculations to compare two projects. face value 783. The worth of a property. different salvage values C. liabilities.00 for 3 years at 11% simple interest.00 C. P1. balance sheet D. What must two investments with the same present worth and unequal lives have? A.875. corporation C. earning value Which of the following is a form of business/company ownership? A. book value D. Find the interest on P6800. and net worth: A. A. book value B. B. break-even point B. use value B. is known as: A. which of the following could invalidate the calculations? C. necessity A form of summary of assets. all of these 785. scrap value A. which is equal to the original cost less depreciation. elastic demand 779. balance method D. mutually exclusive projects A. identical salvage value B. market value C. luxuries 781. partnership B.987. 788. At the end of this time he invests the entire amount (principal plus investment) at 5% compounded annually for 12 years.000. 3% D. P16.350.333. What is the required amount? How long must a P40.700.633.20 D.23 B.00? A.000.500.222. what is the annual rate of interest? D.95% C.00 790.000. How much will he have at the end of the 16year period? C.00 B. P2. 403 days C.200. 12. P13. D.234. D. P13. A.00 from his friend and agrees to pay at the end of 90 days under 8% simple interest rate. B. A man borrowed P10. C.000 for 31 days earns P890.244. 2% C.00 If P16.87 B. Find the rate of interest per annum. P10.00 791.429. 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? C.323. P19. 304 days A. P20.5% A.144.456.000 note bearing 4% simple interest to run to amount to P41. 12. 4% 792.00 A. P2. P10.00 D.97 A. P9.C. P13.000. P11.361. P24. P35.000.00 A time deposit of P110.00 A. P30.00 793. P45. P28.000.00 787.67 A man lends P6000 at 6% simple interest for 4 years. P40. 430 days B.20 D. 340 days B. 1% Annie buys a television set from a merchant who offers P25.20 C.25% . What is the required amount? B.000 earns P480 in 9 months.00 at the end of 60 days.39 on maturity date after deducting the 20% withholding tax on interest income.500.20 789. 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. 11. If paid in 31 days. 5 years 801. 14 years C. A bank charges 12% simple interest on a P300. 4 years A.61 A.456. P15.102.794. Accumulate P5.040.00 D. The tag price of a certain commodity is for 100 days.67 D.14% A. P450. B.000. 16.955.90 D.32% How long will it take P1. B. 12. P14.61 C.20 797. 13 years B.98 C.876. P11.000. D.345. P9. P11.34 C.62 795.00 C.34 B. P10. then the . P8.67 802.00 A.768. P12. P11. P12. 10 years B.20 D.00 for 10 years at 8% compounded semi-annually. What is the simple interest paid? B.25% 796.50 800. P10.455. 11.00 in 2 years is P500. P408. D. 22. P10.867. How long will it take for an investment to double its amount if invested at an interest rate of 6% compounded bimonthly? A.00.233.000. C. 6 years B.000. there is a 3% discount. P551.00 for 10 years at 8% compounded quarterly. 798.000 to amount to P1. Accumulate P5.34 If the compound interest on P3.00 for 10 years at 8% compounded monthly. 6. 3 years Accumulate P5. P10.000.15% C. P415.987.80 D.00 for 10 years at 8% compounded annually. A.876. P13. How much will be repaid if the load is paid back in one lump sum after three years? Accumulate P5.876.75 B.D. 12 years A. P7. P10. C.567.00 loan.346 if invested at 6% compounded quarterly? D.456.87 A.75% 794.00 799. 12 C. 1988 B.000. 7.00 in 4 years is: 806.81% A. P1.800. 1990 D.compound interest on P3. P1. Counting from that date. after how many years will the man receive his will? A.526.180. P171.36 C. A man has a will of P650. P19. 7.00 in a trust fund earning 8% compounded annually.42% D.00 C. If his father deposited an amount of P450. P10. How long will it take for an investment to fivefold its amount if money is worth 14% compounded semiannually? A. P147.000. 805. P162.458.456.1982. 810.000. If you borrowed P10.00 B.55 years B. how much is it worth at present? A. If money is worth 14% compounded quarterly.00 D. P28.77 years C. P11.11 years .000. The salary of Mr. P956.000. P125.000 from a bank with 18% interest per annum. 1991 804. An interest rate of 8% compounded semiannually is how many percent if compounded quarterly? A.083. Cruz is increased by 30% every 2 years beginning January 1. at what year will his salary just exceed twice his original salary? 807.01% D. 8.00 A.00 from his father. 14 803. 4.00 at the end of 7 years.000.00 A.00 C.36 B. 4.85% B. 12.455.00 B. 12. P1. 7.01% B. 1989 C.92% C. 12. 13 D.00 D. 11 B. what is the total amount to be repaid at the end of one year? A man is expecting to receive P450. 12.44 What is the effective rate for an interest rate of 12% compounded continuously? A.89% C.744. 5.125.75% 809.63 D. 69 Mr. P170.77 .343. 5.33 years A. Adam deposited P120.313.77 C.25.000.149. If the interest is subject to a 14% tax.349.77 D. P153. how much will he receive after 5 years? B. P175. D.00 in a bank who offers 8% interest compounded quarterly. P178.