Chemical Engineering Reviewer – Day 3 (General Engineering) Version 1 (June 24, 2016) 1. When a point is observed, the angle formed by the line of sight with the horizontal level where the point being viewed is above the horizontal plane is known as: a. Angle of triangle b. Angle of depression c. Angle of elevation d. None of these 2. The number of real solutions of the equation sin (ex) = 5x + 5 – x is a. 0 b. 1 c. 2 d. Infinitely many 3. The minimum value of the expression sin α + sin β + sin γ, where α, β, γ are the real numbers satisfying α + β + γ = π is
a. Positive b. Zero c. Negative d. – 3 4. A terrorist standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of a river is 60° and when he retreats 40 m away from the tree, the angle of elevation becomes 30°. The breadth of the river is a. 20 m b. 30 m c. 40 m d. 60 m 5. Which of the following statements about the function given by is true? a. The function has no relative extremum. b. The graph of the function has one point of inflection and the function has two relative extrema. c. The graph of the function has two points of inflection and the function has one relative extremum.
d. The graph of the function has two points of inflection and the function has two relative extrema. 6. A curve is described by the parametric equations x = t 3 + 2t and and y = t 2 + t + 1 . An equation of the line tangent to the curve at the point determined by t = -1 is: a. -2x + 3y = 5 b. -3x + 3y = 7 c. -x + 5y = 12 d. x + 5y = 2 7. Determine the area of the inner loop of the polar curve r = 1 - 2sin(θ). a. 0.544 b. 0.585 c. 0.598 d. 0.623 8. (105) Locate the center of curvature of the parabola x2=4y at point (2,2). a. (-2,6) b. (-3,6) c. (-2,4) d. (-3,7) 9. The sum of Patrick’s age and Marko’s age is 58. Eight years ago, Patrick was twice as old as Marko then. How old is Marko? a. 20 b. 22 c. 36 d. 38 10. The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type? a. 0.25 b. 0.40 c. 0.35 d. 0.38 11. Find the area enclosed by f(y) = 2y 2 and g(y) = 4+y2.
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a. 32/3 b. 30/3 c. 18/3 d. 15/2 12. You throw a ball straight up into the air. The position of the ball can be written as s(t) = -5t 2+4t+1. What is the acceleration of the ball at t=0.75 s? a. 9.8 m/s2 b. – 9.8 m/s 2 c. 10 m/s2 d. -10 m/s2 13. Find the distance between the points (-5,5) and (-6,-6) a. √2 b. 2√2 c. √3 d. 2√3 14. In one province, 52% of the voters are supporters of the Liberal Party, and 48% are supporters of the Nacionalista Party. In a second state, 47% of the voters are Liberal Party fans, and 53% are for the Nacionalista Party. Suppose a simple random sample of 100 voters are surveyed from each province. What is the probability that the survey will show a greater percentage of Nacionalista voters in the second province than in the first province? a. 0.04 b. 0.71 c. 0.24 d. 0.76 15. What is the small possible sum of square of two numbers, if their product is -16? a. 18 b. 32 c. 16 d. 8 16. Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m 3 a. 398.2 kg b. 434.3 kg
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c. 367.8 kg d. 411.7 kg Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them. a. 4777.84 cm 3 b. 4522.12 cm 3 c. 5120.03 cm 3 d. 3665.20 cm 3 A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way. a. 32 in2 b. 28 in2 c. 36 in2 d. 54 in2 A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/s, find how fast the lower end is moving when it is 16 ft from the wall. a. 0.9 ft/s b. 1.0 ft/s c. 1.2 ft/s d. 1.5 ft/s A radioactive element follows the law of exponential change and has a half-life of 38 hours. How long will it take for 90% of the radioactivity of the element to be dissipated? a. 211.10 hrs b. 172.32 hrs c. 126.23 hrs d. 104.09 hrs A man in a wharf 6m above the water pulls in a rope to which a boat is tied at the rate of 1.2 m/s. at what rate is the boat approaching the wharf when there is 7.5 m of the rope out? a. 18 m/s b. 17.5 m/s c. 12.5 m/s
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d. 15 m/s What time after 3:00 o'clock will the minute-hand and the hour-hand of the clock be together for the first time? a. 3:15:00.00 b. 3:16:21.82 c. 3:17:12.33 d. 3:16:45.07 Find the equation of the curve for which y” = 12/x 3 if it passes through (1,0) and is tangent to the line 6x+y=6 at that point. a. xy+6x=6 b. 6y+6x=1 c. 6xy+1=6 d. 3xy+2x=1 Find the area enclosed by the cardiod r=a(1-sinx) a. 3πa2 b. 3πa2/2 c. 5πa2/2 d. 2πa2 Two painters work together and take an average of 8 hours to paint standard 12 by 12 rooms. One of the painters, who can do the work alone in 14 hours, is sick today. How long will it take the other painter to complete the job on his own? a. 18.7 hrs b. 15.3 hrs c. 18.0 hrs d. 16.0 hrs One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used? a. 12.00 hrs b. 8.25 hrs c. 11.25 hrs d. 10.75 hrs Identify the conic section that is represented by the equation x2 - 3y2 + 6x + 2y - 5 = 0 a. Circle b. Ellipse
c. Hyperbola d. Parabola
28. (#159) The price of the product in a competitive market is P300. If the cost per unit of producing the product is 160+x where x is the number of units produced per month, how many units should the firm produce and sell to maximize its profit? a. 70 b. 80 c. 60 d. 50 29. (#261) Glycerine is flowing into a conical vessel 18cm deep and 10 cm across the top at the rate of 4 cu cm per min. The depth of glycerine is h cm. If the rate which the surface is rising is 0.1146 cm/min, find the value of h. a. 16 cm b. 12 cm c. 10 cm d. 25 cm 30. (#468) A 600 N block rests on a 30° plane. If the coefficient of static friction is 0.30 and the coefficient of kinetic friction is 0.20, what is the value of P applied horizontally to prevent the block from sliding down the plane. a. 141.85 N b. 183.29 N c. 119.27 N d. 126.59 N 31. A delinquent dropped a stone from the deck of a bridge. The sound of the splash reaches the deck 3 seconds later. If sound travels 342 m/s in still air, how high is the deck of the bridge above the water? a. 40.6 m b. 45.2 m c. 57.3 m d. 33.1 m
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32. A ball is thrown vertically at a speed of 20 m/s from a building 100 m above the ground. Find the velocity and the position of the ball above the ground after 5 seconds. a. 3.34 m, 45.23 m/s b. 4.54 m, 47.68 m/s c. 5.67 m, 56.42 m/s 33. The intercepts of a straight line on the x and y axes are 4 and -6, respectively. Find its equation. a. 3x+2y=12 b. 2x+3y=12 c. 3x-2y=12 d. 2x-3y=12 34. An arch 18 m high has a form of parabola with a vertical axis. The length of the horizontal beam placed across the arch 8 m from the top is 64 m. Find the width of the bottom. a. 96 cm b. 48 cm c. 72 cm d. 64 cm 35. The function f(x) = (x 2 - 4) / (x 3- 2x2- 3x + 10) is discontinuous at x = ____ a. 2 b. -2 c. 0 d. Both 2 and -2 36. Find the diameter of the minimum size of circular cloth that will over a triangular table, 2.5 ft by 2.5 ft by 2.8 ft. a. 2.82 ft b. 3.02 ft c. 0. 3.22 ft d. 0. 3.42 ft 37. A triangle has sides equal to 68 m, 77 m and 75 m respectively. Find the radius of the escribed circle which tangent to the 68 m side. a. 40m b. 44 m c. 50 m d. 55 m
38. Find the sum of an arithmetic progression: 2, 5, 8, where n = 25. a. 900 b. 925 c. 950 d. 975 39. Find the sum of a geometric progression: 2, 3, 4.5, where n = 10. a. 226.7 b. 235.4 c. 242.5 d. 251.8 40. Find the sum of all integers from 300 to 1000 that are exactly divisible by 17. a. 24,548 b. 25,194 c. 25,840 d. 26,486 41. Find the standard deviation for the following data: 2, 5, 3, 4, 7,0, 11, 2, 3, 8. a. 3.1 b. 3.3 c. 3.5 d. 3.7 42. The charge in coulombs that passes through a wire after t seconds is given by the function Q(t) = t3 - 2t2 + 5t + 2. Determine the current at the end of two seconds. a. 6 A b. 8 A c. 9A d. 10 A 43. A bullet from a rifle enters a 50 mm plank with a speed of 600 m/s and leaves with a speed of 24 m/s. Determine the thickness of the plank that can be penetrated by the bullet. a. 55 mm b. 60 mm c. 65 mm d. 70 mm 44. The new vehicle plate number system consists of 3 letters and four numbers. All
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three letters can be repeated. The first of the four numbers cannot be zero (0). The numbers may also be repeated. How many distinct plate numbers can the Land Transportation Office issue? a. 78,624,000 b. 101,088,000 c. 140,400,000 d. 158,184,000 45. What is the accumulated amount of a five year annuity paying P 6,000 at the end of each year, with interest at 15% compounded annually? a. P 40, 454.29 b. P 41, 114.29 c. P 40, 554.29 d. P 41, 454.29 46. The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number of inhabitants. a. 100 years b. 120 years c. 116 years d. 98 years 47. An equipment costs P 10,000 with a salvage value of P 500 at the end of 10 years. Calculate the annual depreciation cost by sinking fund method at 4% interest. a. P 632.21 b. P 845.32 c. P 791.26
d. P 971.12 48. A steel drum manufacturer incurs a yearly fixed operating cost of $ 200,000. Each drum manufactured costs $ 160 to produce, and sells $ 200. What is the manufacturer’s break-even sales volume in drums per year? a. 1000 b. 5000 c. 2500 d. 7500
49. Application of shear strain changes _____? a. Shape b. Area c. Volume d. Velocity
50. An engineer wants to report a privatebased suspicious engineer who performs questionable chemical engineering practices. What organization or institution must the engineer approach to report the suspicious engineer? a. Professional Regulatory Commission b. Philippine Institute of Chemical Engineers c. Office of the Ombudsman d. Sandiganbayan
Sources: 700 Multiple Choice Questions in Engineering Mathematics April 2014 ChE Board Exam Questions General Engineering Reviewer – ChE600 Integration Course
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