Refresher Questions

Algebra: 1. The arithmetic mean and geometric mean of two numbers are 10 and 8, respectively. Find their harmonic mean. a. 6.4 * b. 4.4 c.5.4 d. 3.4 2. Roberto is 25 years younger than his father, However his father will be twice his age in 10 years. Find the ages of Roberto and his father. a. 10, 30 b. 14, 40 c. 15, 50 d. 15, 40 * 3.

The term 5

a.

2x − 7 is equivalent to x3 y

x2 y 4 ( 2x − 7 ) xy

5

b.

5

x ( 2x − 7)

*

2

x

5

y4 ( 2x − 7)

5

x y ( 2x − 7)

c.

d.

x 3

xy

Factor 2 xy + 10 y − 3 x − 15 . A. (2y + 3x)(x + 5) C. (2y – 3)(x + 5) * B. (2y + 3)(x – 5) D. none 5. What number completes the square for x^2 + (2x/3)? a. 1/9 * b. 1/3 c. 4/9 d. 1/6 6. Factor 2 xy + 10 y − 3 x − 15 . A. (2y + 3x)(x + 5) C. (2y – 3)(x + 5) * B. (2y + 3)(x – 5) D. none 7. What number completes the square for x^2 + (2x/3)? a. 1/9 * b. 1/3 c. 4/9 d. 1/6 8. Solve the equation: log (x −1) + log (x +1)=2 log (x +2). a. -5/4 * b. 2/3 c. -3/7 d. -3 9. The sum of Victor’s and Victoria’s ages is 61 five years ago. The ratio of their ages 10 years from now is 4:3. How old is Victor now if he is older? A. 29 C. 35 B. 42 * D. 26 10. If xy = 2 and xy 2 = 8, what is the value of x ? (A) 1/2 * (C) 4 (B) 2 (D) 8 11. Find the value of k in the quadratic equation 4.

( 2k + 2 ) x 2 + ( 4 − 4k ) x + k − 2 = 0 12.

13.

14.

15.

16.

17.

so that the roots are opposite

of each other. a. 4 b. 3 c. 1 * d. 6 Find the value of x from the series of numbers shown. x + 3x + 9x + 27x….729x=3279. a. 3 * b. 5 c. 6 d. 8 John works three times as long as Bill. On a given day John and Bill work together for 4 hours then Bill was called away and John finishes the rest of the job in 2 hours. How long would it take Bill to do the complete job alone? a. 18 hrs. b. 15 hrs. c. 22 hrs. d. 6 hrs. * Spheres of the same radius are piled in the form of a pyramid with a square base until there is just one sphere at the top layer. If there are 4 spheres on each side of the square, find the total number of spheres I the pile. a. 32 spheres c. 30 spheres* b. 25 spheres d. 28 spheres In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? a. 14 * b. 10 c. 12 d. 8 Which number has four significant figures? A. 0.0025 B. 0.02525* B. C. 0.0252 D. 2.4250 What is the solution of the equation 25x2 + 2(x-4)2 = -3, where x is a real-valued variable? A. -6.12 & -3.88 B. -0.52 & 0.700 C. 7.55 D. No Solution*

18. What are the roots of the cubic equation x3 – 6x – 3 = 0? A. x = 1.602, -0.2398, -1.262 C. x = 2.602, -0.3398, -2.262* B. x = 3.602, -0.4398, -3.262 D. x = 4.602, -0.5398, -4.262 19. Solve the following set of simultaneous linear equations for A, B, and C. 2A + 3B – C = -10, -A + 4B + 2C = -4, 2A – 2B + 5C = 30 A. 8.38, -4.81, 4.32 C. 6.38, -9.81, 4.32 B. 1.38, -5.81, 4.32 D. 1.38, -2.81, 4.32 20. What is the value of A satisfies the expression A-5/4 = 0.001? A. 211.19 B. 231.19 C. 251.19* D. 271.19 21. Factor completely the given equation x3 - 5x2 – 48x + 108 = 0 A. (x - 2)(x + 6)(x – 9) = 0* C. ( x + 2)(x – 3)(x – 1) = 0 B. (x + 1)(x – 3)(x – 2) = 0 D. ( x + 4)(x – 4)(x – 2) = 0 22. . Solve for x: Ax – B = Cx + D A. (D + B) / (A – C) * C. (A – B) / (C + D) B. (D + B) / (A + C) D. (D – B) / (A – C) 23. An airplane flies 1,120km with a tail wind and returns, flying into the same wind. The total flying time is 3 hrs and 45 minutes, and the airplanes airspeed is 600 kph. What is the wind speed A. 10 C. 20 B. 30 D. 40* 24. If a = band b = c, then a = c. This illustrates A. reflexive law* C. law of symmetry B. transitive law D. substitution law 25. Given f(x)= (x – 1)/(x3 – 3x2 + 2x), find x when the value of f(x) is undefined. A. 0, -1 and -2 C. 0 and 2 B. 0, 1 and 2 * D. 1 and 2 26. What is the cube root of complex number (8, 90°)? A. (2)(cos(30° + 120°n) + isin(30° + 120°n) * B. (3)(cos(40° +120°n) + isin(30° + 120°n) C. (4)(cos(50° +120°n) + isin(30° + 120°n) D. (5)(cos(60° +120°n) + isin(30° + 120°n) 27. . What is the resultant, R, of the vectors F1, F2, F3? (F1 = 4i + 7j +6k) (F2 = 9i +2j + 11k) (F3 = 5i – 3j – 6k) A. R = 13i + 6j + 11k c. R = 18i + 8j + 11k B. R = 18i – 6j + 11k d. R = 18i + 6j + 11k * 28. Simplify the expression (A x B) C, given A = 3i + 2j B = 2i + 3j + k C = 5i + 2k + 3k A. 13 b. 15 c. 17 d. 19 * 29. What is the exponential form of the complex number 4 + 7i? ° ° A. √𝟔𝟓𝒆𝒊 𝟔𝟎.𝟐𝟔 * c. √45𝑒 𝑖 68.26 ° B. 20𝑒 𝑖34 𝑑𝑒𝑔 d. √25𝑒 𝑖 70.26 30. What is the product of the complex numbers 3 + 5i and 7 – 2i? A. 11 + 29i b. 31 + 22i c. 31 + 29i * d. 31 – 29i 31.What is the lowest common factor of 10 and 32? A. 320 C. 180 B. 2 * D. 90 32.The polynomial x3 + 4x2 -3x + 8 is divided by x-5. What is the remainder? A. 281 C. 218 * B. 812 D. 182 33.Find the quotient of 3x5 – 4x3 + 2x2 + 36x + 48 divided by x3 – 2x2 + 6. A. -3x2 – 4x + 8 C. 3x2 – 4x – 8 B. 3x2 + 4x + 8 D. 3x2 + 6x + 8 * 34.Solve: √(2x-5)- √(x-2)=2. A. 3 C. 9 B. 18 D. 27 * 35.Find the real values of x and y satisfying the given equation: (2x + 3y) + i(3x – 5y) = 8 – i7. A. x = 1, y = -2 C. x = 2, y = 1 B. x = -2, y = -1 D. x = 1, y = 2 * 36.Find the value of k in the quadratic equation (2k + 2) x2 + (4 – 4k) x + k – 2 = 0 so that the roots are reciprocal of each other. A. 4 C. -4 * B. 2 D. -2 37.Solve for x if 8y = 3x – 11 A. (8/3) y + 11 C. (8y - 11)/3 B. (8/3) y – 11 D. (8y + 11)/3 *

38.Rationalize (2+i)/(3-i) A. i/2 C. (1+i)/2 * B. (5+i)/2 D. (1-i)/2 39.Which of the following is equal to √45 A. 5√3 C. √5* B. 9√53 D. 3 40.Find the 5th term of (x2 – 3y)5 without expanding. A. 403x2 y4 C. 404x2 y4 B. 402x2 y4 D. 405x2 y4 * Trigonometry: 41. If 3𝑠𝑖𝑛2 𝑥(𝑐𝑜𝑠 2 𝑥 − 1) = 𝐴 𝑠𝑖𝑛𝐵 𝑥, then find A + B. A. 1* B. 7 C. 5 D. 6 42. Find the radius of a circle of a circle of a sector in it with an angle of 1.2 radians has a perimeter of 48 cm. A. 17 cm B. 16 cm C. 15 cm* D. 14 cm 43. The angle of inclination of ascend of a road having 8.25% grade is ____ degrees? A. 4.72 * B. 4.27 C. 5.12 D. 1.86 44.An observer wishes to determine the height of a tower. He takes sight at the top of the tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The vertical angle at a point A is 30o and at point B is 40o. What is the height of the tower? A. 85.60 ft B. 143.97 ft C. 110.29 ft D. 92.54 ft* 45. A, B and C are points on a circle. AC bisects the circle and AB = BC. The area of triangle ABC is most clearly what percent of the circles area? A. 44 B. 32* C. 36 D. 24 46.A tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50° with the ground and the top of the tree is now 20 ft from its base, how tall was the tree? A. 55 ft* B. 64 ft C. 45 ft D. 36 ft 47.Find the perimeter of an isosceles triangle whose base is 40 cm and whose vertical angle is 40°. A. 127 cm B. 118 cm C. 157 cm* D. 132 cm 48.Which is identically equal to secx/(cotx+tanx)? A. cscx B. sinx * C. cosx D. –secx 49. The angle of elevation of the top of a tower from a point A is 2330' . From another point B, the angle of elevation of the top of the tower is 5530' . The points A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90 degrees. Find the height of the tower. A. 90.6 m* B. 89.5 m C. 86.7 m D. 55.9 m 50.The sum of the sides of a triangle is equal to 100 cm. If the angles of the triangle are in the continued proportions of 1:2:4. Compute the shortest side of the triangle. A. 17.545 B. 18.525 C. 19.806* D. 14.507 51.Two cities 270 mi apart lie on the same meridian. Find their difference in latitude. A. 3/44 rad * C. 4/33 rad B. 3/34 rad D. 4/43 rad 52.In what quadrant will  terminate if sin  and cos  are both negative? A. III* B. II C. II D. I 53.Given and tan x + tan y = 4 and cot x + cot y = 5. Find tan (x+y). A. 4/5 B. 5/4 C. 20 * D. 1/20 54.An airplane is traveling with an airspeed of 320 miles per hour and a heading of 62°. A wind of 42 miles per hour is blowing at a heading of 125°. Find the ground speed and the course of the airplane. A. 340 mph, 68° * C. 430 mph, 86° B. 240 mph, 68° D. 420 mph, 86° 55.In triangle ABC, tangent of angle CAB is 22/7, and the altitude from A divides BC into segments of length 3 and 17. What is the area of triangle ABC? A. 160 B. 185 C. 110 * D. 135

56.The sides of a triangular field which contains an area of 2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle. A. 45.74 B. 95.43 C. 63.62 D. 57.67 * 57.The sum and difference of two angles in a triangle are 90 degrees and 30 degrees, respectively. If the side opposite the smallest angle is 20 cm., find the area of the triangle. A. 346.4* B. 289.6 C. 231.5 D. 268.4 58.Two cities 270 mi apart lie on the same meridian. Find their difference in latitude. A. 3/44 rad * C. 4/33 rad B. 3/34 rad D. 4/43 rad 59.In what quadrant will  terminate if sin  and cos  are both negative? A. III* B. II C. II D. I 60.Given and tan x + tan y = 4 and cot x + cot y = 5. Find tan (x + y). A. 4/5 B. 5/4 C. 20 * D. 1/20 61.The angle of elevation of the top of a tower from a point A is 2330' . From another point B, the angle of elevation of the top of the tower is 5530' . The points A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90 degrees. Find the height of the tower. A. 90.6 m * B. 89.5 m C. 86.7 m D. 55.9 m 62.The sum of the sides of a triangle is equal to 100 cm. If the angles of the triangle are in the continued proportions of 1:2:4. Compute the shortest side of the triangle. A. 17.545 B. 18.525 C. 19.806 * D. 14.507 63.The sides of a triangular field which contains an area of 2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle. A. 45.74 B. 95.43 C. 63.62 D. 57.67 * 64.The sum and difference of two angles in a triangle are 90 degrees and 30 degrees, respectively. If the side opposite the smallest angle is 20 cm., find the area of the triangle. A. 346.4 * B. 289.6 C. 231.5 D. 268.4 65.Two cities 270 mi apart lie on the same meridian. Find their difference in latitude. A. 3/44 rad * C. 4/33 rad B. 3/34 rad D. 4/43 rad 66.A plane with a velocity of 300 mph in still air, is travelling against the wind and travels a distance of 900 miles in 4 hours. Find the headwind velocity. a. 75 mph * c. 150 mph b. 100 mph d. 200 mph 67.A man is standing on a cliff 897 meters. He struck a tree with his axe and the sound 5.2 seconds after. Assuming constant temperature, what is the velocity of sound on that day? a. 340 m/s c. 345 m/s * b. 342 m/s d. 453 m/s 68.A pendulum has a certain frequency in London. What is the effect of this frequency if it is measured with respect to the equator? a. increase c. remains the same b. decrease * d. none of these 69.What is the constant term in the expansion of (2x2 + 1/x)9 ? a. 672 * c. 748 b. 724 d. 860 70.Find the equation of the circle circumscribing a triangle with vertices (-1,-3), (-2, 4), (2, 1). a. x2 + 3x + y2 – 7y – 10 = 0 b. x2 + 3x + y2 + 7y – 10 = 0 c. x2 + 3x + y2 – y – 10 = 0 * d. x2 + 3x + y2 – 7y + 10 = 0 71.Naperian logarithms have a base closest to which number? A. 2.17 c. 3.14 B. 2.72 * d. 10 72.If in a triangle ABC, sin(A) = 1/5, cos(B) = 2/7, then cos(C) = ? A. (√45 - 2√24)/35 * C. (7√24 + 10)/35 B. (√45 + 2√24)/35 D. 0.85

73.The sum of the sides of a triangle is equal to 100 cm. If the angles of the triangle are in the continued proportions of 1:2:4. Compute the shortest side of the triangle. A. 17.545 C. 18.525 B. 19.806 * D. 14.507 74.The sides of the triangular field which contains an area of 2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle. A. 45.74 C. 95.43 B. 63.62 D. 57.67 * 75.In triangle ABC, angle A=80 deg. And point D is inside the triangle. If BD and CD are bisectors of angle B and C, solve for the angle BDC. A. 100 deg. C. 120 deg. B. 130 deg. * D. 140 deg. 76.What is the period of the function f(x) = 3sin2(2x + Pi/4)? A. 3Pi C. Pi/2 * B. 2Pi D. Pi/3 77.In a triangle ABC, angle B has a size of 50o, angle A has a size of 32o and the length of side BC is 150units. The length of side AB is A. 232 C. 260 B. 280 * D. 270 78.The angle of inclination of the road is 32. What is the angle of inclination in mils? A. 456.23 C. 125.36 B. 568.89 * D. 284.44 79.An angle measures x degrees. What is its measure in radians? A. 180° x / π C. 180° π / x B. π x / 180° * D. 180° π x 80.Express 45° in mils. A. 80 mils C. 8000 mils B. 800 mils * D. 80000mils Analytic Geometry and Solid Mensuration: 81.A curve has an equation of x2 = cy + d. the length of latus rectum is 4 and the vertex is at (0, 2). Compute the value of C and d. A. 4, -8 * C. 2, -5 B. 6, -2 D. 3, -7 82.What conic section is 2x2 - 8xy + 4x = 12? A. Parabola C. Hyperbola * B. Ellipse D. Circle 83.What conic section is described by the equation r = 6 / (4 – 3cosӨ)? A. Circle C. Hyperbola B. Ellipse * D. Parabola 84.An ellipse has its center at (0, 0) with its axis horizontal. The distance between the vertices is 8 and its eccentricity is 0.5. Compute the length of the longest focal radius from point (2, 3) on the curve. A. 3 C. 4 B. 5 * D. 6 85.An arc in the form of a parabolic curve is 40 m across the bottom. A flat horizontal beam 26 m long is placed 12 m above the base. Find the height of the arc. A. 20.78 m * C. 25.68 m B. 18.67 m D. 15.87 m 86.Find the coordinates of the focus of the parabola x2=4y-8. A. (0, -3) C. (2, 0) B. (0, 3) * D. (0, -2) 87.An ellipse has an eccentricity of 1/3. Compute the distance between directrices if the distance between foci is 4. A. 18 C. 32 B. 36 * D. 38 88.An ellipse has a length of semi-major axis of 300 m. compute the second eccentricity of the eclipse. A. 1.223 C. 1.333 * B. 1.222 D. 1.233 89.Compute the circumference of an ellipse whose diameters are 14 and 10 meters. A. 28.33 m C. 18.75 m B. 38.22 m * D. 23.14 m

90.Find the eccentricity of a hyperbola having distance between foci equal to 18 and the distance between directrices equal to 2. A. 2 C. 2.8 B. 3 * D. 3.7 91.A cubical container that measure 8m on a side is tightly packed with eight balls and is filled with water. All eight balls are in contact with the walls of the container and the adjacent balls. All of the balls are the same size. What is the volume of the water in the container? A. 213.92 m3 c. 233.92 m3 b. 223.92 m3 d. 243.92 m3 * 92.All three sides of a triangle are initially 6 m in length. One of the triangle’s sides is oriented horizontally. The triangle is scaled down on size without changing any of the angles. What is the new height of the triangle when the area is exactly half of the original triangles are? A. 0.67 m c. 2.67 m b. 1.67 m d. 3.67 m * 93.Find the slope of the line defined by y – 3x + 5. A. 1 b. 2 c. 3 * d. 4 94.Find the equation of a line with slope = 2 and y-intercept = 5. A. y = 2x + 5 * c. y = 4x + 7 B. y = 3x + 6 d. y = 5x + 8 95.A regular pentagon has sides of 20 cm. an inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside the smaller pentagon? A. 430.70 cm2 C. 473.77 cm2 B. 573.26 cm2 d. 516.14 cm2 * 96.Which of the following is perpendicular to the line x/3 + y/4 = 1 A. x – 4y – 8 = 0 C. 3x – 4y – 5 = 0* B. 4x – 3y – 6 = 0 D. 4x + 3y – 11= 0 97.The equation of the line through (1, 2) and parallel to the line 3x – 2y + 4 = 0 is: A. 3x – 2y + 1 = 0* C. 3x + 2y + 1 = 0 B. 3x – 2y – 1 = 0 D. 3x + 2y – 1 = 0 98.If the points (-3, -5), (x, y), and (3, 4) lie on a straight line, which of the following is correct? A. 3x + 2y – 1 = 0 C. 2x + 3y – 1 = 0 B. 2x + 3y + 1 = 0 D. 3x – 2y – 1 = 0* 99.One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is: A. 30° B. 45° * C.60° D.135° 100.What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2 = 0? A. y + x + 4 = 0 C. y - x - 4 = 0* B. y - x + 4 = 0 D. y + x - 4 = 0 101.It is the locus of point which moves equidistant from a fixed point. What is the name of this locus? A. Parabola C. Hyperbola B. Ellipse D. Circle * 102.Compute the angle between the line 2y-9x-18=0 and the x-axis. A. 64.54° C. 77.47° * B. 45° D. 87.65° 103.Find the standard equation of the circle with center (3,5)that is tangent to the line 12x -5y + 2 = 0. A. (x-3)^2 + (y-5)^2 = 1* B. (x-4)^2 + (y-3)^2 = 5 C. (x+3)^2 + (y+4)^2 = 1 D. (x-3)^2 + (y+6)^2 = 2 104.The central circle has 10 cm radius. Six equal smaller circles are to be arranged so that they are externally tangent to the central circle and each tangent to the adjacent small circle. What should be the radius in cm. of each small circle? A. 12 B. 11 C. 10* D. 9

105.A solid gold in the form of a frustum of a pyramid has smaller base area of 20cm2 and a bigger base area of 60 cm2. It has an altitude of 24 cm. If the gold is melted to form 9 spherical balls, find the radius of each ball. A. 3.1 cm C. 3.0 cm B. 2.9 cm* D. 2.8 cm 106.If the points (-3, -5), (x, y), and (3, 4) lie on a straight line, which of the following is correct? A. 3x + 2y – 1 = 0 C. 2x + 3y – 1 = 0 B. 2x + 3y + 1 = 0 D. 3x – 2y – 1 = 0* 107.One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is: A. 30° B. 45°* C.60° D.135° 1078.What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2 = 0? A. y + x + 4 = 0 C. y - x - 4 = 0* B. y - x + 4 = 0 D. y + x - 4 = 0 109.A right circular cone with an altitude of 9m is divided into two segments; one is a smaller circular cone having the same vertex with an altitude of 6m. Find the ratio of the volume of the two cones. A. 19:27 B. 2:3 C. 1:3 D. 8:27* 110.A pipe lining material silicon carbide used in a conveyance of pulverized coal to fuel a boiler, has a thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material with pipe length of 6 meters. A. 45,239 cm^3* C. 42,539 cm^3 B. 49,532 cm^3 D. 43,932 cm^3 111.The line segment drawn from P(x,3) to (4,1) is perpendicular to the segment drawn from (-5,-6) to (4,1). Find the value of x. A. 22/7 C. 2.44* B. 4.5 D. 9/22 112.Find the coordinates of the point which divides the line segment connecting (-1,4) and (2,-3) into two parts which have the ratio 3/2. A. (4/5,- 1/5)* C. (2/5,- 1/5) B. (3/5,- 2/5) D.(6/5,- 3/5) 113.What conic section is defined by the equation 7x2 + 16y2 – 16xy – 60x + 96y + 156 = 0? A. Ellipse* B. circle B. hyperbola D. parabola 114.A chord is 36 cm. long and its mid point is 36 cm. from the midpoint of the longer arc. Find the radius of the circle. A. 20.5 cm C. 21.5 cm B. 22.5 cm* D. 23.5 cm 115.A closed cylindrical tank is 8 feet long and 3 feet in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is the vertical position, the depth of water in the tank is: A. 5.67 m C. 5.82 ft B. 5.82 m D. 5.67 ft* 116.The sum of the coefficient of x and y in Ax + By – 16 = 0 is 14. If the slope of the line is 8, find A and B. A. (7, -1) C. (8, -6) B. (16, -2)* D. (2, -5) 117. Find the focus of the hyperbola 16y2 – 9x2 + 36x + 96y – 36 = 0. A. (2,2) and (2,-7) C. (2,-2) and (2,8) B. (2,1) and (2,8) D. (2,2) and (2, -8) * 118. Find the smallest angle between the lines 2x + y – 8 = 0 and x + 3y + 4 = 0. A. 40o C. 45o * o B. 60 D. 30o

119. A polyhedron of 6 faces, all of which are parallelograms. A. Parallelepiped* B. Cube C. Pyramid D. cone 120. Determine the number of diagonals of a polygon with 15 sides A. 60 C. 120 B. 80 D. 90 * Differential Calculus: 121. The point on the curve where the second derivative of the function is zero. A. Maxima C. point of inflection * B. Minima D. point of deflection 122. An open rectangular box with square ends is to be built to hold 6400 mm3 at the cost of $0.75/mm2 for the base and $0.25/mm2 for the sides. Find the most economical dimensions. A. 10 x 10 x 15 mm C. 30 x 30 x 17 mm B. 20 x 20 x 16 mm* D. 5 x 5 x 14 mm 123. Find y  , given x + xy + y = 2 . A. C.

2(1+𝑦) (1+𝑥)2 (1+𝑥)2

B. −

* D. −

2(1+𝑦)

4𝑥𝑦 (𝑦 2 −𝑥)3

(𝑦 2 −𝑥)3 4𝑥𝑦

124. A balloon leaving the ground 18 from the observer rises 3 m/s. how fast is the angle of elevation of line of sight increasing after 8 seconds. A. 0.12 rad/sec C. 0.08 rad/sec B. 0.03 rad/sec D. 0.06 rad/sec * 125. Evaluate the limit of xx as x approaches to zero. A. 0 C. 1* B. ½ D. 2 126.What is the maximum value of the following function on the interval x ≤ 0? 𝑦 = 2𝑥 3 + 12𝑥 2 − 30𝑥 + 10 a. -210 b. -36 c. -5 d. 210 * 127.Which of the following is not correct derivative? 𝑑 a. 𝑐𝑜𝑠𝑥 = −𝑠𝑖𝑛𝑥 b. c.

𝑑𝑥 𝑑

(1 − 𝑥)^3 = −3(1 − 𝑥)^3

𝑑𝑥 𝑑 1

1

𝑑𝑥 𝑥 𝑑

𝑥

( ) = − ( 2)

d. 𝑐𝑠𝑐𝑥 = −𝑐𝑜𝑡𝑥 * 𝑑𝑥 128.What is dy/dx if y = (2x) x? e. (2x) x (2 + ln2x) f. 2x (1 + ln2x) x g. (2x) x (ln2x2) h. (2x) x (1 + ln2x) * 𝜕𝑓 129.If f(x, y) = x2y3 + xy4 + sinx + cos2x + sin3y, what is ? 𝜕𝑥 i. (2x + y) y3 + 3sin2y cosy j. (4x- 3y2) xy2 + 3sin2y cosy k. (3x + 4y2) xy + 3sin2y cosy l. (2x + y) y3 + (1 – 2sinx) cosx * 130.Evaluate the following limit. lim ( 𝑛→2

𝑥 2 −4 𝑥−2

1

)

m. 0 n. 2 o. 4 * p. ∞ 131.What are the minimum and maximum values, respectively, of the equation f(x) = 5x3 – 2x2 + 1 on the interval ( -2, 2)? q. -47, 33 * r. -4, 4 s. 0.95, 1 t. 0, 0.27 132.What is the first derivative dy/dx, of the following expression? (xy)x = e u. 0

v. –x/y (1-xlnx) w. –y/x (1+ xlnxy) * x. y/x 133.What are the standard from of the equation of the line tangent to a circle centered at the origin with a radius of 5 at the point (3, 4)? y. x = -4/3y – 25/4 z. y = ¾ x + 25/4 aa. y = -3/4 x + 9/4 bb. y = -3/4 x + 25/4 * 134.Evaluate dy/dx for the following expression. y = e-x sin 2x cc. e-x (2cos2x – sin2x) * dd. –e-x (2sin2x + cos2x) ee. e-x (2sin2x + cos2x) ff. –e-x (2cos2x – sin2x) 135.A tank initial contains 200 liters of fresh water. Brine containing 2.5 N/liter of dissolved salt runs into the tank at the rate of 8 liters/min. and the mixture kept uniform by stirring, runs out at the same rate. a. 11* c. 12 b. 13 d. 14 136.Evaluate the following limit. (x in radians) lim ( 𝑥→𝑛

𝑥 2 −𝑛𝑥+𝑠𝑖𝑛𝑥 −𝑠𝑖𝑛𝑥

)

a. 0 b. 1 c. 𝜋 − 1 * d. (2)( 𝜋 − 1) 137.Evaluate the limit of (x^3-2x^2-x+2)/(x^2-4) as x approaches 2. a. infinity b.3/4 c. 2/5 d. 4/7 138.Evaluate the limit of (1-sec^2 (x)/ cos (x)-1 as x approaches 0. a. -2 b. α c. 0 d. 1 139.The function y=(x-4)/(x+2) is discontinuous at x equals? a. -2 b. 0 c. 1 d. 2 140. An elliptical plot of garden has a semi-major axis of 6m and a semi-minor axis of 4.8meters. If these are increased by 0.15m each, find by differential equations the increase in area of the garden in sq.m. a. 0.62π c. 2.62π b. 1.62π d. 2.62π 141. A snowball is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at which the radius is increasing when the snowball is 4 ft in diameter. a. 0.159 ft/min * b. 0.015 ft/min c. 0.259 ft/min d. 0.325 ft/min 142.A stone is dropped into a still pond. Concentric circular ripples spread out, and the radius of the disturbed region increases at the rate of 16 cm/s. At what rate does the area of the disturbed increase when its radius is 4 cm? a. 304.12 cm2/s b. 503.33 cm2/s c. 402.12 cm2/s * d. 413.13 cm2/s 143.A man 1.8 m. tall is walking at the rate of 1.2 m/s away from a lamp post 6.7 m high. At what rate is the tip of his shadow receding from the lamp post? a. 2.16 m/s b. 1.64 m/s * c. 1.83 m/s d. 1.78 m/s 144.A man on a wharf is pulling a rope tied to a raft at a rate of 0.6 m/s. If the hands of the man pulling the rope are 3.66 m above the water, how fast is the raft approaching the wharf when there are 6.1 m of rope out? a. -1.75 m/s b. -0.25 m/s c. -0.75 m/s *

d. -0.54 m/s 145.A man is riding his car at the rate of 30 km/hr toward the foot of a pole 10 m high. At what rate is he approaching the top when he is 40 m from the foot of the pole? a. -5.60 m/s b. -6.78 m/s c. -8.08 m/s * d. -4.86 m/s 145.A boy wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the maximum possible area of his garden. a. 625 ft2 * b. 524 ft2 c. 345 ft2 d. 725 ft2 146.Find the area of the largest rectangle whose base is on the x axis and whose upper two vertices lie on the curve y = 12 – x2. a. 24 b. 32 * c. 16 d. 36 147.Find the radius of the largest right circular cylinder inscribed in a sphere of radius 5. a. 4.08 units * b. 1.25 units c. 5.14 units d. 8.12 units 148.A rectangular box open at the top is to be constructed from a 12x12-inch piece of cardboard by cutting away equal squares from the four corners and folding up the sides. Determine the size of the cutout that maximizes the volume of the box. a. 6 inches b. 1.5 inches c. 2 inches * d. 3 inches 149.Find the number of equal parts into which a given number N must be divided as that their product will be a maximum. a. N/2e b. N/e * c. 2N/e2 d. 2N/e 150.A body moves such that its acceleration as a function of time is a=2+12t, where “a” is in m/s2. If its velocity after 1 s is 11 m/s. find the distance traveled after 5 seconds. a. 256 m b. 340 m c. 290 m * d. 420 m 151.The height of a projectile thrown vertically at any given time is define by the equation h(t) = -16t2 + 256t. What is the maximum height reach by the projectile? a. 1567 ft b. 1920 ft c. 1247 ft d. 1024 ft * 152.It costs 0.05 x2 + 6x + 100 dollars to produce x pounds of soap. Because of quantity discounts, each pound sells for 12 – 0.15x dollars. Calculate the marginal profit when 10 pounds of soap is produced. a. $ 9 b. $ 2 * c. $ 12 d. $ 7 153.A police car is 20 ft away from a long straight wall. Its beacon, rotating 1 revolution per second, shines a beam of light on the wall. How fast is the beam moving when it is nearest to the police car? a. 10pi b. 20pi c. 30pi d. 40pi *

154. A hole of 2 radius is drilled through the axis of a sphere of radius 3. Compute the volume of the remaining part. a. 46.83 * b. 59.23 c. 91.23 d. 62.73 Integral Calculus: 155.The integral of cos x with respect to x is a. sin x + C * b. sec x + C c. –sin x + C d. csc x + C 156.Find the integral of [(e exp x – 1] divided by [e exp x +1] dx a. ln (e exp x – 1) square + x + C b. ln (e exp x + 1) - x + C c. ln (e exp x – 1) + x + C d. ln (e exp x + 1) square - x + C * 157.Evaluate the double integral of r sin u dr du, the limits of r are 0 and cos u and the limits of u are 0 and pi. a. 1 b. 1/2 c. 0 d. 1/3 * 158.Evaluate the integral of (3x^2 + 9y^2) dx dy if the interior limits has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and a lower limit of 0. a. 10 b. 20 c. 30 d. 40 * 159.Evaluate integral of zdz r^2dr sinu du, the limits of z are from 0 to 2, the limits of r are from 0 to 1, and the limits of u are from 0 to π/2. a. 2/3 * b. 4/3 c. 1/3 d. 5/3 160.Evaluate the integral of x(x – 5)^12 dx from 5 to 6. a. 0.456 * b. 0.556 c. 0.656 d. 0.756 161.Evaluate the integral of (xdx) / ((x + 1)^8) from 0 to 1. a. 0.011 b. 0.022 * c. 0.033 d. 0.044 162.Evaluate the integral of (cos3A) dA from 0 to π/6. a. 27π/363 b. 35π/768 * c. 23π/765 d. 12π/81 163.Integrate 1/ (3x + 4) with respect to x and evaluate from x = 0 and x = 2. a. 0.278 b. 0.336 c. 0.252 d. 0.305 * 164.Evaluate the integral of cos^2 ydy. a. y/2 + (sin 2y)/4 + C * b. y + 2cosy + C c. y/4 + (sin 2y)/4 +C 165.Find the area bounded by y2 = 8x and line x = y a. 4.03 b. 6.28 c. 8.37 d. 10.67 * 166.Find the area bounded by the x-axis y2 = x, x =1 and x =16 a. 38 b. 40

c. 42 * d. 44 167. Find the area bounded by y = x2 and y = 2x2 – 3x a. 9/2 * b. 4/5 c. 7/2 d. 5/2 12𝑥 168. Find the area of the region bounded by the curves = 2 , 𝑥 +4 the x-axis, x = 1, and x = 4. a. 4 ln 6 b. ln 24 c. 6 ln 15 d. 6 ln 4 * 169. Find the area of the region bounded by one loop of the curve 𝑥 2 = 𝑦 4 (1 − 𝑦 2 ). a. π sq. units b. (π/2) sq. units c. (π/4) sq. units d. (π/8) sq. units * d. y + sin 2y + C 170. Integrate: (7x^3 + 4x^2) dx. a. (7x^3)/3 + (4x^2)/2 + C b. (7x^4)/4 + (4x^2)/5 + C c. (7x^4)/4 + (4x^3)/3 + C * d. (7x^4) - (4x)/2 + C 178.What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is π/2? a. 0.0203 b. 0.0307 c. 0.0417 * d. 0.0543 179.What is the integral of sin^5 x dx if the lower limit is 0 and the upper limit is π/2? a. 0.233 b. 0.333 c. 0.433 d. 0.533 * 180.Find the integral of 12 sin^5 x cos^5 x dx if the lower limit = 0 and upper limit = π/2. a. 0.2 * b. 0.3 c. 0.4 d. 0.5 191.Evaluate the integral of sin^6 x dx from 0 to π/2. a. π/32 b. 2π/17 c. 3π/32 d. 5π/32 * 192.Evaluate ∫ 𝑒 𝑥 sin 𝑥 𝑑𝑥 . 𝑒𝑥

a. (sin 𝑥 − cos 𝑥) + 𝐶 c. – 𝑒 𝑥 (sin 𝑥 − cos 𝑥) + 𝐶 2 b. – 𝑒 𝑥 (cos 𝑥 + sin 𝑥) + 𝐶 d. 𝑒 𝑥 (cos 𝑥 + sin 𝑥) + 𝐶 2

2𝑦

193.Evaluate ∫1 ∫0 (𝑥 2 + 𝑦 2 )𝑑𝑥𝑑𝑦 . a.35/2 b.19/2 1

2

c.17/2

d.37/2

𝑦

194.Evaluate ∫0 ∫0 ∫0 𝑑𝑥 𝑑𝑦 𝑑𝑧 . a. 1/3 b. 1/4

c. 1/2

d.1/6

195.Evaluate the integral (cos3A)^8 dA from 0 to π/6. a. 27π/363 b.35π/768 c.23π/765 d.12π/81 196.Find the area bounded by the curve y^2=8(x-4), the line y=4, yaxis and x-axis. a.18.67 b.14.67 c.15.67 d.17.67

197.Evaluate ∫(cos 𝑥)(ln sin 𝑥)𝑑𝑥 . a. sin 𝑥 (1 − ln sin 𝑥) + 𝐶 c. sin 𝑥 (1 + ln sin 𝑥) + 𝐶 b. sin 𝑥 (ln sin 𝑥 − 1) + 𝐶 d. ln √sin 𝑥 + 𝐶 198.Evaluate ∫ arctan 𝑥 𝑑𝑥 . a. arctan 𝑥 − ln √1 + 𝑥 2 b. 𝑥 arctan 𝑥 − √1 + 𝑥^2 + 𝐶 b. arctan 𝑥 + 2ln (1 + 𝑥 2 ) d. 𝑥 arctan 𝑥 + ln(1 + 𝑥 2 ) + 𝐶 199.Evaluate the integral of (3𝑥 2 + 9𝑦 2 )𝑑𝑥 𝑑𝑦 if the interior limit has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0. a. 10 b. 40 c. 30 d. 20 200.Evaluate ∫

𝑒 2𝑥

𝑑𝑥 . a. ½ 𝑒 𝑥 + + 1) + 𝐶 c. ln(𝑒 𝑥 + 1) + 𝐶 b. 𝑒 𝑥 − ln(𝑒 𝑥 + 1) + 𝐶 d. 𝑒 𝑥 + ln(𝑒 𝑥 + 1) + 𝐶 𝑒 𝑥 +1 ln(𝑒 𝑥

201.Evaluate ∫ 𝑒 𝑥 sin 𝑥 𝑑𝑥 . 𝑒𝑥

a. (sin 𝑥 − cos 𝑥) + 𝐶 c. – 𝑒 𝑥 (sin 𝑥 − cos 𝑥) + 𝐶 2 b. – 𝑒 𝑥 (cos 𝑥 + sin 𝑥) + 𝐶 d. 𝑒 𝑥 (cos 𝑥 + sin 𝑥) + 𝐶 -202. ∫ 𝑡𝑎𝑛2 𝑥 𝑑𝑥 = ? a. tan x – x + c* b. x - tan x + c c. sec x d. sec x tan x 203. What is the integral of sin^6(φ)cos^4 (φ) dφ if the upper limit is π/2 and lower limit is 0? a.0.0184 b.1.0483 c.0.1398 d.0.9237 204. Evaluate ∫(cos 𝑥)(ln sin 𝑥)𝑑𝑥 . a. sin 𝑥 (1 − ln sin 𝑥) + 𝐶 c. sin 𝑥 (1 + ln sin 𝑥) + 𝐶 b. sin 𝑥 (ln sin 𝑥 − 1) + 𝐶 d. ln √sin 𝑥 + 𝐶 205.Evaluate ∫ arctan 𝑥 𝑑𝑥 . a. arctan 𝑥 − ln √1 + 𝑥 2 b. 𝑥 arctan 𝑥 − √1 + 𝑥^2 + 𝐶 b. arctan 𝑥 + 2ln (1 + 𝑥 2 ) d. 𝑥 arctan 𝑥 + ln(1 + 𝑥 2 ) + 𝐶 206. Evaluate the integral of (3𝑥 2 + 9𝑦 2 )𝑑𝑥 𝑑𝑦 if the interior limit has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0. a. 10 b. 40 c. 30 d. 20 207.Determine the area bounded by y = x2 – 4, the x – axis and the lines x = -1, x = 1. A. 8.87 sq units C. 7.33 sq units * B. 8.07 sq units D. 6.67 sq units 208. A hole of the radius 4 is bored through the center of a sphere of radius 5. Find the volume of the remaining portion of the sphere. A. 28 pi C. 36 pi* B. 30 pi D. 29 pi 209. Evaluate ∫

𝑠𝑖𝑛√𝑥 √𝑥

𝑑𝑥

A. 2cos√𝑥 + C C. -2cos√x + C-2cos√x + C* B. cos√𝑥 + C D. -cos√x + C 210. The integral of sin2 Ɵ dƟ from 0 to pi/2 is: A. pi/2 C. ½ B. pi/4 * D. ¼ 211. Find the volume (in cubic units) generated by rotating a circle x² + y² + 6x + 4y + 12 = 0 about the y-axis A. 39.48 C.59.22* B. 47.23 D. 50.1

Differential Equations: 212. Find the differential equation of the family of line passing through the origin. A. xdy – ydx = 0 C. xdy + ydx = 0 * C. ydy + xdx = 0 D. xdx + dy = 0 213. The rate of population growth of a country is proportional to the number of inhabitants. If the population of a certain country now is 40 million and 50 million in 10 years’ time, what will be its population 20 years from now? A. 62.5 million* C. 56.20 million B. 65.20 million D. 52.6 million 214. What is the equation (DE) of the family of parabolas having their vertices at the origin and their foci n the x – axis. A.2xdy – ydx = 0* C. xdy – 2y2dx = 0 B. 2ydy + x2dx D. y2 dy + 2xydx = 0 215. Determine the degree of the given ordinary D.E y’’’’ – 4(y’’’)² + 3(y’’)³ - y’ = 0 A. 1* C. 3 B. 2 D. 4 216. A thermometer reading 18 deg F is brought into a room where the temperature is 70 deg F; a minute later, the thermometer reading is 31 deg F. determine the temperature reading 5 minutes after the thermometer is first brought into the room. A. 57.68 deg F* C. 30.01 deg F B. 42.4 deg F D. 53.89 deg F 𝜕𝑣 217.What is the partial derivative of the following function? 𝜕𝑦

v = 3x2 + 9xy – y/lnz + cos (-z2 + x) a. 9x – 1/lnz b. 6x + 9x – 1/lnz – sin(z2+x) c. 3x2y + 9xy2/2 – y2/2lnz + sin (z2 + x)/ (z2 +x) d. 9x + 1/lnz * 218.What is the derivative, dy/dt, of y = sin2wt? a. 2wsinwt b. Cos2wt c. 2sinwt coswt d. 2wsinwt coswt * 219.What is the derivative, dy/dx, of the expression x 2y – e2x = siny? a. 2e2x/x2-cosy b.2e2x – 2xy / x2 – cosy * c.2e2x – 2xy d.X2 – cosy 220.A two dimensional function, f (x, y), is defined as f (x, y) = 2x 2 – y2 + 3x – y. What is the gradient vector for this function? a. f (x, y) = (2x2 + 3x) i + (-y2 – y) j e. ∇ f (x, y) = (x3 + 3/2 x2) i + (-1/3 y3 –1/2 y2) j f. ∇ f (x, y) = (4x+3) i + (-2y – 1) j * g. ∇ f (x, y) = (3x + 4) i + (2y + 1) j 221.What is the direction of the line passing through the point (1, 2) that has the maximum slope? h. 4i + 2j i. 7i + 3j * j. 7i + 4j k. 9i – 7j 222.Determine the divergence of the vector function f (x, y, z). f (x, y, z) = xzi + exyj + 7x3yk l. z + ex * m. z + yex + 21x2y n. x + y o. x + yex 223.determine the curl of the vector function f (x, y, z). f (x, y, z) = 3x2i +7exyj p. 7exy q. 7exyi r. 7exyj s. 7exyk *

224.Determine the Laplacian of the scalar function 1/3 x3 – 9y + 5 at the point (3, 2, 7). t. 0 u. 1 v. 6 * w. 18 225.The differential equation y” + x2y’ + y + 2 = 0 is A. Linear homogeneous C. Non linear and homogeneous B. Linear and non homogeneous*D. Non linear and non homogeneous 226.Find the solution to y” + 16y = 0 A. C1cos4t + C2sin4t * C. C1e4t + C2e-4t B. C1e4t + C2te-4t D. (C1 + C2t)cos4t 227.What is the derivative, dy/dt, of y = sin2wt? e. 2wsinwt f. Cos2wt g. 2sinwt coswt h. 2wsinwt coswt * 228.What is the slope of the curve y = 10x2 – 3x – 1 when it crosses the positive part of the x- axis? i. 3/20 j. 1/5 k. 1/3 l. 7 * 229.What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x – axis. a. x(y’)² = a * b. x(y’’) = a c. 2x(y’)² = a d. 3x(y’)³ = a 230.In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour? a. 18.35 kg b. 19.53 kg * c. 15.39 kg d. 13.95 kg 231.A thermometer reading 18 deg F is brought into a room where the temperature is 70 deg F; a minute later, the thermometer reading is 31 deg F. determine the temperature reading 5 minutes after the thermometer is first brought into the room. a. 57.68 deg F * b. 42.4 deg F c. 30.01 deg F d. 53.89 deg F 232.Solve the particular solution of the differential equation dy/dx=2xy if y = 5 when x = 0. m. y=(1/2)e^x5 n. y=(1/5)e^x2 o. y=5e^x2 * p. y=2e^x5 234.Given the differential equation dy/dx =(1 – 2x)/y. The general solution of the given DE is a family of _____. q. ellipses * r. circles s. hyperbolas t. parabolas 235.The population in a certain barangay in Metro Manila increases at a rate numerically equal to the square of the population. If the population 10,000 and time is measured in years, how long will it take for the population to reach 16,000? u. 52 years v. 50 years w. 51 years x. 53 years * 236.A drop of water (spherical form) evaporates at a rate numerically equal to its surface area. If its initial radius is 0.20 cm, how long will it take for the drop to completely evaporate?

y. 0.1 z. 0.3 aa. 0.2 * bb. 0.4 237.If the population of a certain country doubles in 50 years, in how many years will it triple under the assumption that the rate of increase is proportional to the number of inhabitants? cc. 76.34 dd. 77.52 ee. 78.09 ff. 79.26 * 238.A thermometer reading 18 deg F is brought into a room where the temperature is 70 deg F; a minute later, the thermometer reading is 31 deg F. determine the temperature reading 5 minutes after the thermometer is first brought into the room. a. 57.68 deg F * b. 42.4 deg F c. 30.01 deg F d. 53.89 deg F 239.In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour? a. 18.35 kg b. 19.53 kg * c. 15.39 kg d. 13.95 kg 240.Determine the degree of the given ordinary D.E y’’’’ – 4(y’’’)² + 3(y’’)³ - y’ = 0 a. 1 * b. 2 c. 3 d. 4 241.What is the order of the D.E dy/dx = 5y ? a. 1 * b. 3 c. 2 d. 4 242.What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x – axis. a. x(y’)² = a * b. x(y’’) = a c. 2x(y’)² = a d. 3x(y’)³ = a 243.Find the particular solution of the differential dx/dt = x -1 ; x(0) =1 a. X(t) = 1 * b. X(t) = 2 c. X(t) = 3 d. X(t) = 0 244.Which of the following are the solutions to the following y”’ – 3y” + 3y’ –y = 0 I. e^x II. x(e^x) III. e^-x a. I only b. III only c. I and II only * d. II only 245.Find all the values of m for which ; y = e( to power mx ) is a solution of 6y” – y’ – y =0 on (-infinity , + infinity) a. m = -1/2, 2/3 b. m = -1,2,3 c. m= -3,-1/3 d. m= -1/3, ½ *

246.According to Newton’s Law of cooling the temperature of n object changes at a rate proportional to the difference in temperature between the object and the outside medium. If an object whose temperature is 70F is placed in a medium whose temperature is 20⁰ and 40⁰ after 3 minutes, what will its temperature be after 6 minutes? a. 28 deg * b. 38 deg c. 26 deg d. 20 deg 247.At 9am a thermometer reading 70 F is taken outside where the temperature is 15 F. At 9:45 am the thermometer reading is at 45 F. At 9:00 am the thermometer is taken back indoors where the temperature is fixed at 70 F. Find the reading at 9:20. a. 58 F * b. 50 F c. 55 F d. 59 F 248.In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour? a. 18.35 kg b. 19.53 kg* c. 15.39 kg d. 13.95 kg 249.Determine the degree of the given ordinary D.E y’’’’ – 4(y’’’)² + 3(y’’)³ - y’ = 0 C. 1* D. 2 E. 3 F. 4 250.What is the order of the D.E dy/dx = 5y ? a. 1* b. 3 c. 2 d. 4 251.What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x – axis. a. x(y’)² = a* b. x(y’’) = a c. c. 2x(y’)² = a d. 3x(y’)³ = a 252.In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour? a. 18.35 kg b. 19.53 kg* c. 15.39 kg d. 13.95 kg Physics: 253.How do you call the strong bond between the hydrogen atoms ? a. ionic and metallic bonds b. ionic bond c. Covalent bond * d. Metallic bond 254.What are van der waals forces? a.Forces present only on gases b.Primary bond between atoms c.Forces not present in liquids d.Weak secondary bond bonds between atoms * 255.Which of the following is not a viscoelastic material? a. Metal * b. Rubber c. Plastics d. Glass

256.In molecule of the same composition, what are the variation of atomic arrangement known as ? e. isomers * f. monomers g. polymers h. crystal system 257.An amphoteric hydroxide is one which i. has a valence of -2 j. has been carried by bombardment with high energy protons k. reacts violently with water l. may act as either a base or an acid in chemical reactions * 258.How many moles of iron does 25 g of Fe represent? Note: the atomic weight of iron (Fe) is 55.8 g/mol? m. 0.356 mol n. 0.564 mol o. 0.448 mol * p. 0.247 mol 259.How many oxygen atoms are present in 2.00 moles of oxygen molecules considering that it is a diatomic? q. 2.48 x 10^24 atoms* r. 3.43 x 10^25 atoms s. 5.67 x 10^26 atoms t. 1.34 x 10^24 atoms 260.If the atomic mass of copper (Cu) is 63.5 g/mol, compute how many grams does 0.252 mole of copper (Cu) has? u. 16 g* v. 18 g w. 20 g x. 12 g 261.Which of the following elements and compound is unstable in its pure form? y. Hydrochloric acid z. Carbon Dioxide aa. Sodium * bb. Helium 262.What is the actual geometric shape of the methane molecule cc. Tetrahedral * dd. Square planar ee. Pyramidal ff. Linear 263.It is found that a shearing machine requires 300 J of energy to shear a specific gauge of sheet metal. The mean diameter of the flywheel is to be 762 mm. The normal operating speed is 200 rpm, and slows down to 180 rpm during shearing process. The rim width is 304.8 mm and the weight of the cast iron is 7,200 kg/m3. Find the thickness of the rim, assuming that the hub and arms account 10% of the rim weight concentrated on the mean diameter. a. 8.57 mm b. 8.58 mm * c. 8.59 mm d. 9.00 mm 264.A flat belt is to transmit 100 hp to an air compressor. The small sheave is 180 mm in diameter and turns at 1200 rpm, while the larger sheave turns at 450 rpm. The service factor as 2.0, the center distance is equal to two times the diameter of the larger sheave. Determine the length of belt in mm and the arc of contact of small sheave in degrees. a. 2979 mm, 161 deg b. 2980 mm, 160 deg c. 2980 mm, 162 deg d. 2980 mm, 161 deg * 265.A bullet weighing 0.30 N and moving at 660 m/sec, penetrates a 50 N body and emerges with a velocity of 180 m/sec. How far and how long does the body then move? a. 0.734 sec, 1.06 m * b. 0.437 sec, 1.60 m c. 0.347 sec, 6.10 m

d.

0.734 sec, 6.01 m

266.A train weighs 16,000 kN. The train resistance is constant at 96,000 N. If 6000 hp are available to pull this train up a 2% grade, what will be its speed in kph? a. 37.8 kph b. 38.7 kph * c. 38.8 kph d. 37.7 kph 267.A block weighing 500 N is dropped from a height of 1.2 m upon a spring whose modulus is 20 N/mm. What velocity will the block have at the instant the spring is deformed 100 mm? a. 4.56 m/sec b. 4.55 m/sec c. 4.66 m/sec d. 4.65 m/sec * 268.Refer to a particle whose curvilinear motion is represented by the equation s = 20t + 4t2 – 3t3. What is the acceleration of the particle at time t = 0? a. 2 m/s2 b.3 m/s2 c. 5 m/s2 d .8 m/s2 * 269.Refer to a particle whose curvilinear motion is represented by the equation s = 20t + 4t2 – 3t3. What is the maximum speed reached by the particle? a. 21.8 m/s * b. 27.9 m/s c. 34.6 m/s d.48 m/s 270.Choose the equation that best represents a rigid body or particle under constant acceleration. a. a = 9.81 m/s2 + v0/t b. v = v0 + a0t * 𝑡 c. v = v0 + ∫0 𝑎(𝑡)𝑑𝑡 d. a = vt2/r 271.A roller coaster train climbs a hill with a constant gradient. Over a 10 s period, the acceleration is constant at 0.4 m/s2, and the average velocity of the train is 40 km/h. Find the final velocity. a. 9.1 m/s b. 11.1 m/s c. 13.1 m/s * d.15.1 m/s 272.A projectile is fired from a cannon with initial velocity of 1000 m/s and at an angle of 30 degrees from the horizontal. What distance from the cannon will the projectile strike the ground if the point of impact is 1500 m below the point of release? a. 8200 m b. 67,300 m c. 78,200 m d. 90,800 m * 273.A wheel with a radius of 80 cm rolls along a flat surface at 3 m/s. If arc AB on the wheel’s perimeter measures 90 degrees, what is the velocity of point A when point B contacts the ground? a. 3.00 m/s b. 3.39 m/s c. 3.75 m/s d. 4.24 m/s * 274.A 1- kg block is resting on a horizontal circular disk like a turntable at a radius of 0.5 m from the center. The coefficient of friction between the block and disk is 0.20. The disk rotates with a uniform angular velocity. What is the minimum angular velocity of the disk that will cause the block to slip? a. 1.40 rad/s b. 1.98 rad/s * c. 3.92 rad/s

d. 4.43 rad/s 275.A ball is dropped from rest at a point 12 m above the ground into a smooth, frictionless chute. The ball exits the chute 2m above the ground and at an angle 45 degrees from the horizontal. Air resistance is negligible. Approximately how far will the ball travel in horizontal direction before hitting the ground? gg. 12m hh. 20m ii. 22m * jj. 24m 276.A 6kg sphere moving at 3m/s collides with a 10kg sphere travelling 2.5 m/s in the same direction. The 6 kg ball comes to a complete stop after the collision. What s the new velocity of the 10 kg ball immediately after the collision? kk. 0.5 m/s ll. 2.8 m/s mm. 4.3 m/s * nn. 5.5 m/s 278.Refer to a particle whose curvilinear motion is represented by the equation s = 20t + 4t2 – 3t3. What is the particle’s initial velocity? oo. 20 m/s * pp. 25 m/s qq. 30 m/s rr. 32 m/s 278.The elevator in a 12- story building has a mass of 1000 kg. its maximum velocity and maximum acceleration are 2 m/s and 1m/s2, respectively. A passenger with a mass of 75 kg stands on a bathroom scale I the elevator as the elevator ascends at its maximum acceleration. What is the scale reading just as the elevator reaches its maximum acceleration? a. 75 N b. 150 N c. 811 N * d. 886 N

278.A 100 kg block is pulled along a smooth, flat surface, an external 500 N force. If the coefficient of friction between the block and the surface is 0.15, what is the acceleration is experienced by the block due to the external force? a.3.23 m/s2 * b.3.80 m/s2 c.4.3 m/s2 d.5.00 m/s2 279.A 2000 kg car pulls a 500 kg trailer. The car and trailer accelerates from 50 km/h to 75 km/h at a rate of 1 m/s2. What linear impulse does the car impart on the trailer? a. 3470 N.s * b. 8680 N.s c. 12500 N.s d. 17400 N.s 280.The block-spring system shown oscillates once every 3s. There is no friction between the block and the surface. If the spring constant is 6 N/m, what is the approximate mass of the block? a. 1.37 kg * b. 5.47 kg c. 26.3 kg d. 72. 0 kg 281.A hollow cylinder has a mass of 2kg, a height of 1m, an outer diameter of 1m, and an inner diameter of 0.80m. what is the cylinder’s mass moment of inertia about an axis perpendicular to the cylinder’s longitudinal axis and located at the cylinder’s end? a. 0.41 kg.m2 b. 0.79 kg.m2 c. 0.87 kg.m2 * d. 1.49 kg.m2

282.The velocity in m/s of a falling ball is described by the equation v = 32 + t + 6t2. What is the acceleration time t = 2sec? a. 9.8 m/s2 b. 25 m/s2 * c. 32 m/s2 d. 58 m/s2 283.A particle starting from rest experienced an acceleration of 3 m/s2 for 2 s. The particle then returned to rest in an additional distance of 8m. Assuming all accelerations were uniform, what was the total time elapsed for the particle’s motion? a. 2.67 s b. 4.00 s c. 4.67 s * d. 5.33 s 284.The location of a particle moving in the x-y plane is given by the parametric equations x = t2 + 4t and y = (1/4) t4 – 60t, where x and y are in meters and t in seconds. What is the particle’s velocity at t = 4sec? a. 8. 95 m/s b. 11.3 m/s c. 12.6 m/s * d. 16.0 m/s 285.A projectile whose mass is 10 g is fired directly upward from the ground level with in initial velocity of 1000 m/s. Neglecting the effects of air resistance, what will be the speed of the projectile when it impacts the ground? ss. 707 m/s tt. 981 m/s uu. 1000 m/s vv. 1414 m/s 286.A fisherman cuts his boat’s engine as it enters a harbor/ the boat comes to a dead stop with its front end touching the dock. The fisherman’s mass is 80 kg. he moves 5 m from his seat in the back to the front of the boat n 5 s, expecting to be able to reach the dock. If the empty boat has a mass 300 kg, how far will the fisherman have to jump to reach the dock? ww. 1.1 m * xx. 1.3 m yy. 1.9 m zz. 5.0 m 287.An objects acceleration as it starts to fall is: A. equal to g * C. less than B. greater than g D. zero 288. Going against a wind, a domestic plane can travel 5/8 of the distance in one hour that it is going with the wind. If the plane can fly 300mph in calm wind, what is the velocity of the wind? A. 69.3 mph * C. 96.3 mph B. 73.3 mph D. 93.3 mph 289. A bullet is fired from a gun at an angle of 40 0. What is the range if its velocity is 300 m/s? g = 10 m/s. A. 192.9m C. 8863 m* B. 229.8 m D. 12000 m 290. A car accelerates from rest at 2 m/s² for 5 seconds, travels at constant speed for 10 seconds and decelerates to rest at 2 m/s². Calculate the distance traveled by the car. A. 525 m C. 450 m B. 315 m D. 150 m* 291. Two mass collide on a frictionless horizontal floor and perfectly inelastic collision. Mass 1 is 4 times Mass 2; velocity of mass 1 is 10 m/s to the right while mass 2 is 20 m/s to the left. What is the velocity and direction of the resulting combined mass? A. 10 m/s to the right C. 4 m/s to the right* B. 10 m/s to the left D. 1.5 m/s to the left Mechanics: 292. A cable weighing 150 N/m has a span of 150 m and a sag of 36 m. determine the maximum tension in the cable. A. 17, 928 N* C. 19, 728 N B. 20, 123 N D. 15, 267 N

293. The ratio of volume stress to volume strain is called A. Young’s modulus C. Bulk modulus* B. Shear modulus D. Hooke’s Law 294. The valve push rod for an overhead valve engine is ¼ inch in diameter and 14 inches long. Find the diameter and inertia of the rod in inches. A. 1.917 x 10-4* C. 1.917 x 10 -3 -7 B. 1.917 x 10 D. 1.917 x10-1 295. A test specimen is under tension. The load is 20, 000 lb., allowable stress is 10, 00 0 psi, modulus of elasticity is 30 million psi, and original length of specimen is 40 in. what is the required cross section, in sq inches, if the resulting elongation must not be greater than 0.001 inch? A. 2 C. 26.6* B. 10 D. 62.2 296. A circular aluminum tube of length L=400mm is loaded in compression by forces P as shown in the figure. The outside and inside diameters are 60 mm and 50 mm, respectively. If the compressive stress in the bar is intended to be 40 MPa, what should be the load P?

A. 34.6 kN* B. 35.6 kN C. 36.4 kN D. 37.5 kN 297. A motorist drives north for 35.0 minutes at 85.0 km/hr and then stops for 15.0 minutes. He then continues north, traveling 130 km in 2.00 hours. What is his average velocity? A. 57.5 km/hr B. 58.4 km/hr C. 60.6 km/hr D. 63.6 km/hr* 298. An arrow is shot straight up in the air at an initial speed of 15.0 m/s. After how much time is the arrow heading downward at a speed of 8.00 m/s? A. 2.35 s* B. 3.22 s C. 4.28 s D. 5.27 s 299. Determine the bursting steam pressure of a steel shell with diameter of 10 inches and made of ¼ thick steel plate. The joint efficiency is at 70% and the tensile strength is 60 ksi A. 4200 psi * C. 42.8 ksi B. 10.5 ksi D. 8500 psi 300. A drop hammer of 1 ton dead weight capacity is propelled downward by a 12 inch diameter cylinder. At 100 psi air pressure what is the impact velocity if the stroke is 28 inches? A. 47.4 ft/sec C. 15.8 ft/sec B. 31.6 ft/sec * D. 63.2 ft/se 301. Which of the following is the type of stress that differs from compressive stress and it is caused by a contact pressure between separate bodies. A. shearing stress B. bearing stress* C. compressive stress D. tensile stress 302. An electric motor converted 700 W of electrical input into work at 58.186 kg-m/s. The speed was 1750 rpm. Find the kg-m of driven torque. a. 0.183 b. 0.381 c. 0.318* d. 0.138 303. Design the size of solid steel shaft to be used for a 500 hp, 250 rpm application if the allowable torsional deflection is 1  and the allowable stress is 10,000 psi modulus of rigidity is 13 x 106 psi. a. 5” dia. c. 4-7/8” dia. * b. 4-5/8” dia. d. 4-3//4” dia.

304. What modulus of elasticity in tension is required to obtain a unit deformation of 0.00105 m/m from a load producing a unit tensile stress of 44,000 psi? a. 42.300 x 106 psi c. 43.101 x 106 psi b. 41.202 x 106 psi d. 41.905 x 106 psi * 305. If the weight of 6” diameter by 48” long SAE 1030 shafting is 174.5 kg. then what will be the weight of chromium SAE 51416 of same size? a. 305.5 lbs c. 384.6 lbs * b. 426.4 lbs d. 465.1 lbs 306. A lineshaft runs at 360 rpm. An 18” pulley on the same shaft is belt connected to a 12” pulley on the countershaft. From a 15” pulley on the countershaft motion is transmitted to the machine. Compute/check the required of the pulley on the machine to give a spindle speed of 660 rpm. a. 16” c. 101/2” b. 12 1/4” * d. 81/2” 307. A body weighing 40lb starts from rest and slides down a plane at an angle of 30deg with the horizontal for which the coefficient of friction u = 0.30. How far will it move during the third second? A. 19.63 feet B. 19.33 feet * C. 18.33 feet D. 19.99 feet 308. A weight is dropped from a helicopter that is rising vertically with a velocity of 6 m/sec. If the weight reaches the ground in 15 seconds, how high above the ground was the helicopter when the weight was dropped? a. 1100 m b. 1013 m * c. 1580 m d. 1130 m 309. A body weighing 200 kg is being dragged along a rough horizontal plane by a force of 45 kg. If the coefficient of friction is assumed to be 1/12 and the line pull makes an angle of 180 with the horizontal, what is the velocity acquired from rest in the first 3 meters. a. 2.8 m/sec * b. 3.1 m/sec c. 3.5 m/sec d. 4.9 m/sec 310. An iron column of annular cross-section has an outer diameter of 200mm and is subjected to a force of 74kN. Find the thickness of the wall if the allowable compressive stress is 10MPa. a. 12.75mm b. 12.57mm * c. 17.75mm d. 15.75mm 311. A force of 10N is applied to one end of a 10inches diameter circular rod. Calculate the stress. a. 0.20kPa b. 0.15kPa c. 0.05kPa * d. 0.10kPa 312. A cable is suspended between two supports at the same elevation and 200 m apart. The load is 100 N/m and the sag is 12 m. What is the tension at the support? A. 31.54 kN C. 36.47 kN B. 41.67 kN D. 42.85 kN * 313. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. If the efficiency of the winch is 60%, calculate the energy consumed in kwh. A. 179 kwh C. 821 kwh B. 281 kwh D. 182 kwh *

314. A 16 ft horizontal beam is subjected to a load of 500 lbs located at its center. The dimension of the beam is 3 x 5 inches respectively and its unit weight is 100 lb/ft. Find the flexural stress in psi. A. 2992 psi C. 4992 psi B. 3255 psi D. 5982 psi * 315. Compute for the torsional deflection in degrees of a 100 mm diameter, 1.75 meter long shaft subjected to a twist moment of 5.5 x 106 N-mm. The torsional modulus of elasticity is 85000 N/mm2. A. 0.22 deg C. 0.33 deg B. 0.55 deg D. 0.66 deg * 316. Find the polar section modulus of a hollow shaft with an outside diameter of 5 inches and inside diameter of 3 inches. A. 51.36 in3 C. 41.36 in3 B. 31.36 in3 D. 21.36 in3 * 317. A projectile leaves a velocity of 50m/s at an angle of 30deg with the horizontal. Find the maximum height that it could reach. A. 31.86m* B. 31.28m C. 30.62m D. 30.12m 318. What force is necessary to accelerate a 30,000 pounds railway electric car at the rate of 1.25ft/sec^2, if the force required to overcome frictional resistance is 400 pounds? A. 1565 pounds* B. 1585 pounds C. 1595 pounds D. 1575 pounds 319. A body weighing 40lb starts from rest and slides down a plane at an angle of 30deg with the horizontal for which the coefficient of friction u = 0.30. How far will it move during the third second? A. 19.63 feet B. 19.33 feet* C. 18.33 feet D. 19.99 feet 320. A cylindrical tank with 10inches inside diameter contains oxygen gas at 2,500psi. Calculate the required thickness in mm under a stress of 28,000 psi. a. 11.44 b. 11.34 * c. 10.60 d. 10.30 321. A 250 lb. block is initially at rest on a flat surface that is inclined at 30deg. If the coefficient of kinetic friction is 0.30 and the coefficient of static friction is 0.40, find the force required to start the block moving up the plane. a. 190lb b. 212lb * c. 125lb d. 75lb 322. A body weighing 40lb starts from rest and slides down a plane at an angle of 30deg with the horizontal for which the coefficient of friction u = 0.30. How far will it move during the third second? E. 19.63 feet F. 19.33 feet * G. 18.33 feet H. 19.99 feet 323. A weight is dropped from a helicopter that is rising vertically with a velocity of 6 m/sec. If the weight reaches the ground in 15 seconds, how high above the ground was the helicopter when the weight was dropped? a. 1100 m b. 1013 m * c. 1580 m d. 1130 m

324. A body weighing 200 kg is being dragged along a rough horizontal plane by a force of 45 kg. If the coefficient of friction is assumed to be 1/12 and the line pull makes an angle of 180 with the horizontal, what is the velocity acquired from rest in the first 3 meters. a. 2.8 m/sec * b. 3.1 m/sec c. 3.5 m/sec d. 4.9 m/sec 325. An iron column of annular cross-section has an outer diameter of 200mm and is subjected to a force of 74kN. Find the thickness of the wall if the allowable compressive stress is 10MPa. a. 12.75mm b. 12.57mm * c. 17.75mm d. 15.75mm 326. A force of 10N is applied to one end of a 10inches diameter circular rod. Calculate the stress. a. 0.20kPa b. 0.15kPa c. 0.05kPa * d. 0.10kPa 327. A steel tie rod on bridge must be made to withstand a pull of 5000lbs. Find the diameter of the rod assuming a factor of safety of 5 and ultimate stress of 64,000 psi. a. 0.75 b. 0.71 * c. 0.84 d. 0.79 328. A hollow shaft has an inner diameter of 0.035m and an outer diameter of 0.06m. Compute for the torque in N-m, if the stress is not to exceed 120MPa. a. 4500 b. 4100 c. 4300 * d. 4150 329. A hollow shaft has an inner diameter of 0.035m and an outer diameter of 0.06m. Determine the polar moment of inertia of the hollow shaft. a. 1.512x10^-6 m^4 * b. 1.215x10^-6 m^4 c. 1.152x10^-6 m^4 d. 1.125x10^-6 m^4 330. What power would a spindle 55mm in diameter transmit at 480rpm. Stress allowed for short shaft is 59N/mm^2 a. 42.12kW b. 50.61kW c. 96.88kW * d. 39.21kW 331. A 30-m long aluminum bar is subjected to a tensile stress of 172MPa. Find the elongation if E=69,116MPa. a. 0.746m b. 0.007m c. 6.270mm d. 7.46cm * 332. The muzzle velocity of a projectile is 1500fps and the distance of the target is 10 miles. The angle of elevation of the gun must be: a. 21o59’ b. 22o41’ c. 24o43’ * d. 25o18’ 333. A projectile is fired with a muzzle velocity of 300m/s from a gun aimed upward at an angle of 20deg with the horizontal, from the top of a building 30m high above a level ground. With what velocity will it hit the ground in m/s? a. 298 m/s b. 299 m/s c. 300 m/s d. 301 m/s *

334. The flywheel of a puncher is to be brought to a complete stop in 8 seconds from a speed of 60 revolutions per minute. Compute the number of turns the flywheel will still make if its deceleration is uniform. a. 5 turns b. 3 turns c. 4 turns * d. 6 turns 335. A boy tied a 80grams stone to a string which he rotated to form a circular motion with a diameter of 1000mm. compute for the pull exerted on the string by the stone if it got loose leaving at a velocity of 25m/sec. a. 120N b. 100N * c. 150N d. 135N 336. A man keeps a 1kg toy airplane flying horizontally in a circle by holding onto a 1.5m long string attached to its wing tip. The string is always in the plane of the circular path. If the plane flies at 10m/sec, find the tension in the string. a. 28N b. 15N c. 67N * d. 18N 337. The stress in a 90-cm diameter pipe having a wall thickness of 9.5cm and under a static head of 70m of water is a. 325kPa b. 32.5kPa c. 32.5MPa d. 3.25Mpa * 338. A solid shaft 48.2cm long is used for a transmission of a mechanical power at a rate of 37kW running at 1760rpm. The stress is 8.13MPa. Calculate the diameter. a. 30mm b. 35mm c. 40mm d. 50mm * 339. What is the modulus of elasticity if the stress is 44,000 psi and unit strain of 0.00105? a. 41.905x10^6 * b. 42.300x10^6 c. 41.202x10^6 d. 43.101x10^6 340. Compute the nominal shear stress at the surface in MPa for a 40mm diameter shaft that transmits 750kW at 1500rpm. Axial and bending loads are assumed negligible. a. 218 b. 312 c. 232 d. 380 * 341. A hollow shaft has an inner diameter of 0.035m and an outer diameter of 0.06m. Determine the polar moment of inertia of the hollow shaft. a. 1.512x10^-6 m^4 * b. 1.215x10^-6 m^4 c. 1.152x10^-6 m^4 d. 1.125x10^-6 m^4 342. A hi-way curve has a super elevation of 7degrees. What is the radius of the curve such that there will be no lateral pressure between the tires and the roadway at a speed of 40mph? a. 265.71m * b. 438.34m c. 345.34m d. 330.78m 343. The inclination of ascend of a road having an 8.25% grade is _______. a. 4.72 deg * b.4.27 deg c. 5.12 deg d. 1.86 deg

344. A concrete hi-way curve with a radius of 500ft is banked to give lateral pressure equivalent to f= 0.16. For what coefficient of friction will skidding impend for a speed of 60mph? a. u>0.360 b. u<0.310 * c. u>0.310 d. u<0.360 345. A car weighing 40 tons is switched to a 2 percent upgrade with a velocity of 30mph. if the train resistance is 10lb/ton, how far up the grade will it go? a. 1124 ft on slope b. 2024 ft on slope c. 1204 ft on slope * d. 1402 ft on slope 346. An elevator weighing 2,000 lb attains an upward velocity of 16fps in 4seconds with uniform acceleration. What is the tension in the supporting cables? a. 2,150 lb b. 2,495 lb c. 1,950 lb d. 2,250lb * 347. If the ultimate shear strength of a steel plate is 42,000 psi, what force is necessary to punch a 0.75inch diameter hole in a 0.625inch thick plate? a. 63,000 b. 68,080 c. 61, 850 * d. 66,800 348. A single bolt is used to lap joint two steel bars together. Tensile force on the bar is 20000N. Determine the diameter of the bolt required if the allowable shearing stress is 70MPa? a. 17mm b. 18mm c. 19mm * d. 20mm 349. What is the stress in a thin-walled spherical shell of diameter D and a wall thickness t when subjected to internal pressure p? a. S = D/pt b. S = 4D/pt c. S = pD/4t * d. S = pD/t 350. Compute the safe wall thickness of a 76.2cm diameter steel tank. The tank is subjected to 7.33MPa pressure and the steel material has a yield stress of 215.4 MPa. The factor of safety to use is 3. a. 1 ½ inches * b. 3.69 inches c. 4.09 inches d. 3.95 inches 351. A cylindrical water tank is 8m in diameter and 12m high. If the tank is to be completely filled, determine the minimum thickness of the tank plating if the stress is limited to 40MPa. a. 11.77mm * b. 13.18mm c. 10.25mm d. 12.6mm 352. Determine the maximum shearing stress in a helical steel spring composed of 20 turns of 20-mm diameter wire on a mean radius of 80 mm when the spring is supporting a load of 2 kN. a. 110.6 MPa b. 101.1 MPa c. 120.6 MPa * d. 136.5 MPa 353. What is the inertia of a bowling ball (mass = 0.5 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds? a. 0.0045 kg-m2 * b. 0.001 kg-m2 c. 0.005 kg-m2

d. 0.002 kg-m2 354. A simple beam, 10 m long carries a concentrated load of 500 kN at the midspan. What is the maximum moment of the beam? a. 1250 kN-m * b. 1050 kN-m c. 1520 kN-m d. 1510 kN-m 355. What is the moment of inertia of a cylinder of radius 5 m and mass of 5 kg? a. 62.5 kg-m2 * b. 80 kg-m2 c. 72.5 kg-m2 d. 120 kg-m2 356. A cylindrical tank with 10inches inside diameter contains oxygen gas at 2,500psi. Calculate the required thickness in mm under a stress of 28,000 psi. a. 11.44 b. 11.34 * c. 10.60 d. 10.30 357. A 250 lb. block is initially at rest on a flat surface that is inclined at 30deg. If the coefficient of kinetic friction is 0.30 and the coefficient of static friction is 0.40, find the force required to start the block moving up the plane. a. 190lb b. 212lb * c. 125lb d. 75lb 358. A ball is thrown vertically upward from the ground and a student gazing out of the window sees it moving upward pass him at 5m/sec. The window is 10m above the ground. How high does the ball go above the ground? A. 15.25m B. 14.87m C. 9.97m D. 11.30m*

359. A projectile leaves a velocity of 50m/s at an angle of 30deg with the horizontal. Find the maximum height that it could reach. A. 31.86m* B. 31.28m C. 30.62m D. 30.12m 360. What force is necessary to accelerate a 30,000 pounds railway electric car at the rate of 1.25ft/sec^2, if the force required to overcome frictional resistance is 400 pounds? A. 1565 pounds* B. 1585 pounds C. 1595 pounds D. 1575 pounds 361. A body weighing 40lb starts from rest and slides down a plane at an angle of 30deg with the horizontal for which the coefficient of friction u = 0.30. How far will it move during the third second? A. 19.63 feet B. 19.33 feet* C. 18.33 feet D. 19.99 feet

Probability & Statistics: 362. The probability that an examinee passes the board examination is 0.8. Find the probability that the examinee will pass the examination on the fourth try. A. 3/625 B. 4/625 * C. 8/625 D. 9/625 363. In a gambling game, you are paid Php 100 if you draw a jack or a queen and Php300 if you draw a king or an ace from an ordinary deck of 52 playing cards. If you draw any other card, you lose. How much should you pay to play if the game is fair? A. 78.99 B. 31.77 C. 88.89 D. 61.54 * 364. A dart is thrown at a 13 – inch square board containing a circle of radius 5 inches. Assuming that the dart hits the board, and that it is equally likely to land on any point on the board, what is the probability that the dart hits the circle? A. 0.338 B. 0.191 C. 0.781 D. 0.464 * 365. Allen picked 10 differently colored beads. How many different bracelets can he make if he is going to use only 6 of the 10 beads per bracelet? A. 12200 B. 12500 C. 12600 * D. 12700 366. The odds that A can solve a given problem are 5 to 7, and the odds that B can solve it are 3 to 6. Find the probability that either A or B can solve the problem. A. 3/4 * B. 17/14 C. 11/18 D. 17/36 367. A certain department contains 10 civil engineers and 15 electrical engineers. How many ways are there to form a committee with six members if it must have the same number of civil and electrical engineers? A. 65400 B. 54600 * C. 45600 D. 406504 368. Ten students are given two identical speakers to listen to for differences, if any. Suppose that these people answered by guessing only. Find the probability that four people claim to have heard a difference between the two speakers. A. 0.205 * B. 0.206 C. 0.207 D. 0.203 369. According to the Fairhaven City Police Department, the need for money to buy drugs is stated as the reason for 65% of all thefts .Find the probability that among the next 4 theft cases reported in this city, at most 2 resulted from the need for money to buy drugs. A. 0.734 B. 0.347 C. 0.473 D. 0.437 * 370. According to a survey by the Department of Labor and Employment, one-half of Philippine companies give employees 2 weeks of vacation after they have been with the company for 20 years. Find the probability that among 6 companies surveyed at random, the number that give employees 2 weeks of vacation after20 years of employment is anywhere from 1 to 4. A. 5/8 B. 3/8 C. 7/8 * D. 1/8 371. A jar contains 3 green balls, 2 blue balls, and4 red balls. In a random sample: of 5 balls, find the probability that both blue balls and at least 1 red ball are selected. A. 12/63 B. 17/63 * C. 19/63 D. 11/63 372. What is the probability that a poker hand contains full house, that is, three of one kind and two of another kind? a. A. 7/4165 B. 3/4165 C. 6/4165 * D. 1/4165 373. A set N is described as N = {-0,1,2, 3….}. We can therefore say that N is a set of _________. a. A. positive integers C. natural numbers * b. B. negative integers D. integers 374. A sequence of 9 bits is randomly generated. What is the probability that at least one of these bits is 1? A. 0.998 * B. 0.889 C. 0.989 D. 0.988 375. What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 2 or 5? A. 4/5 B. 3/5 * C. 2/5 D. 1/5

376. In a standard poker game, determine the probability that someone will have a hand that does not contain the queen of hearts? A. 45/52 B. 41/52 C. 47/52 * D. 43/52 377. Samples of aluminum-alloy channels were tested for stiffness. The following frequency distribution was obtained. The distribution is assumed to be normal. Stiffness Frequency 2480

23

2440

35

2400

40

2360

33

2320

21

What is the approximate standard deviation of the population from which the samples were taken? a. 19 b. 23 c. 37 d. 51 * 378. Samples of aluminum-alloy channels were tested for stiffness. The following frequency distribution was obtained. The distribution is assumed to be normal. Stiffness Frequency 2480

23

2440

35

2400

40

2360

33

2320

21

What is the approximate probability that stiffness would be less than 2350 for any given channel section? a. 0.08 b. 0.16* c. 0.23 d. 0.36 379. For the probability density function shown, what is the probability of the random variable x being less than 1/3? a. 0.11 b. 0.22* c. 0.25 d. 0.33 380. Two people are selected randomly from a group of 4 men and 4 women. The probability that a man and a woman are selected is A. 4/7 * B. 2/7 C. 1/4 D. 3/7 381. Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is A. 0.5 * B. 0.25 C. 0.167 D. 0.125 382. 100 random samples were taken from a large population. A particular numerical characteristics of sampled items was measured. The results of the measurements were as follows: 45 measurements were between 0.859 and 0.900.0.901 was observed once 0.902 was observed three times 0.903 was observed twice 0.904 was observed four times 45 measurements were between 0.905 and 0.958.The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170, except those noted, no measurements occurred more than twice. What is the mode of the measurements? a. 0.902 b. 0.903 c. 0.904 * d.0.909

383. Samples of aluminum-alloy channels were tested for stiffness. The following frequency distribution was obtained. The distribution is assumed to be normal. Stiffness Frequency 2480 23 2440 35 2400 40 2360 33 2320 21 What is the approximate mean of the population from which the samples were taken? a. 2367 b. 2398 c. 2402 * d. 2419 384. The required probability that a two-stage rocket will perform successfully is 0.97. The reliability for the first stage is 0.99. The reliabilities of the two stages are independent. What must be the reliability for the second stage? a. 0.90 b. 0.95 c. 0.97 d. 0.98* 385. What is the sample variance of the following data? 0.50, 0.80, 0.75, 0.52, 0.60 a. 0.0146 b. 0.0183* c. 0.1128 d. 0.1209 386. When it is operating properly, a chemical plant has a daily production rate that is normally distributed with a mean of 880 tons/day and a standard deviation of 21 tons/day. During an analysis period, the output is measured with random sampling on 50 consecutive days, and the mean output is found to be 871 tons/day. With a 95 percent confidence level, determine if the plant is operating properly. a. There is at least 5 percent probability that the plant is operating properly b. There is at least 95 percent probability that the plant is operating properly c. There is at least 5 percent probability that the plant is not operating properly d. There is at least 95 percent probability that the plant is not operating properly* 387. A bag contains 100 balls numbered 1 to 100. One ball is drawn from the bag. What is the probability that the number on the ball selected will be odd or greater than 80? a. 0.10 b. 0.50 c. 0.60 * d. 0.70 388. 100 random samples were taken from a large population. A particular numerical characteristics of sampled items was measured. The results of the measurements were as follows: 45 measurements were between 0.859 and 0.900. 0.901 was observed once 0.902 was observed three times 0.903 was observed twice 0.904 was observed four times 45 measurements were between 0.905 and 0.95 The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170, except those noted, no measurements occurred more than twice. What is the mean of the measurements? a. 0.9029 b. 0.9050 c. 0.9055 d. 0.9117 *

389. 100 random samples were taken from a large population. A particular numerical characteristics of sampled items was measured. The results of the measurements were as follows: 45 measurements were between 0.859 and 0.900. 0.901 was observed once 0.902 was observed three times 0.903 was observed twice 0.904 was observed four times 45 measurements were between 0.905 and 0.958 The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170, except those noted, no measurements occurred more than twice. What is the median of the measurements? a. 0.901 b. 0.902 c. 0.9025 d. 0.903 * 390. For the probability density function shown, what is the probability of the random variable x being less than 1/3? a. 0.11 b. 0.22* c. 0.25 d. 0.33 391. If seven fair cones are simultaneously tossed in the air, what is the probability that at least one will land heads up? a. 0.144 b. 0.286 c. 0.971 d. 0.992* 392. What is the probability of picking an orange ball and a white ball out of a bag containing seven orange balls, eight green balls, and two white balls? a. 0.071 b. 0.10 * c. 0.36 d. 0.53 393. A cat has a litter of seven kittens. If the probability is 0.52 that a kitten will be female, what is the probability that exactly two of the seven will be male? a. 0.07 b. 0.18 * c. 0.23 d. 0.29 394. What is the approximate probability that no two people in a group of seven have the same birthday? a. 0.056 b. 0.43 c. 0.92 d. 0.94 * 395. What is the approximate probability of exactly two people in a group of seven having a birthday on April 15? a. 1.2 x 10-18 b. 2.4 x 10-17 c. 7.4 x 10-6 d. 1.6 x 10-18 * 396. What is the approximate probability of exactly two people in a group of seven having the same birthday? a. 0.00016 b. 0.026 c. 0.055 * d. 0.12

397.In a ME 600 final examination, the probability that the examinee will pass each of the three subjects is 0.60. what is the probability that the examinee will pass at most three subjects? A. 0.064 C. 0.784 B. 0.216 * D. 0.936 398. In a single throw of a pair of ice, what is the probability of having a sum of 7 or 11? A. 2/9 * C. 1/6 B. 7/36 D. 1/3 399. The mode of the set {2,2,8,20,33} is A. 2* C. 8 B. 13 D. 18 400. A bag contains 4 white, 3 blacks ball and another bag contains 3 white and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black? A. 38/63* C. 24/63 B. 35/63 D. 45/63 401. Given a set 25 elements with ∑ 𝑥 = 75 and ∑ 𝑥 2 = 350, find the standard deviation. A. 5.12 C. 3 B. 5 D. 2.24* Engineering Economy 402. A company needs P60, 000 in five years to buy a new equipment in order to accumulate this sum, a sinking fund consisting of three annual payments is established now. For tax purposes, no further payments will be made after three years. What payments are necessary if money is worth 18% per annum? A. 12, 620 C. 12, 220 B. 12, 062 * D. 12, 602 403. A man borrowed the amount of P20,000 with an interest of 30%. How much is the interest is he going to pay at the end of 22 months? A. 32, 353 C. 31, 533 B. 12, 353 * D. 32, 296 404. What is the present worth of a $100 annuity starting at the end of the third year and continuing to the end of the fourth year, if the annual interest rate is 8%? A. $122* C. $160 B. $153 D. $162 405. An item is purchased for P5,000,000 annual cost are P900,000. Using 8%, what is the capitalized cost of perpetual service? A. P16,250,000.00* C. P16,890,000.00 B. P18,345,243.00 D. P17,435,000.00 406. You borrowed the amount of P10, 000 in a bank with an interest rate of 30% compounded monthly. How much would you have to pay after 2 years? A. P18, 807 * C. P17, 987 B. P17, 032 D. P17, 825 407. A man invests 10,000 today to be repaid in 5 years in 1 lump sum at 12 % compounded annually. If the rate of inflation is 3 % compounded annually, how much profit in present day pesos, is realized over the five years? A. P320 C. P5202* B. P5628 D. P 7623 408. An investment of x dollar is made at the end of each year for three years, at an interest rate of 9% per year compounded annually. What will the dollar value of the total investment be upon the deposit of the third payment? A. 0.727x C. 3.278x* B. 1.295x D. 3x 409. A mining company invested 25,000,000 to develop an oil well which is estimated to contain 1,000,000 barrels of oil. During a certain year, 200,000 barrels were produced from this well. Compute the depletion charge during the year. A. 10M C. 8M B. 5M* D. 1M

410. A machine has a first cost of ₱60,000 and has an expected salvage value after 10 years of ₱6,000. Find the book value after 5 years using declining balance method. A.₱10,028.34 B. ₱15,071.32* C. ₱20,083.45 D. ₱25,083.45 411. If the nominal interest rate is 3%, how much worth in 10 years in a continuously compounded account? A.$3180 C. $5420 B.$4490 D. $6750 * 412. An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain in a 30-year home loan for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150. What is the maximum amount she can pay for a house if her disposable monthly income is $2000? A. $80, 000 B.$83, 100 * C.$85, 200 D.$90, 500 413. The designer of the penstock for a small hydroelectric cogeneration station has the option of using steel pipe, which costs $150,000 installed and requires $5,000 yearly for painting and leak-checking maintenance, or DSR4.3 (heavyduty plastic) pipe, which costs $180,000 installed and requires $1,200 yearly for leak-checking maintenance. Both options have an expected life of 25 years. If the interest rate is 8%, which choices has the lower present equivalent cost and how much lower is it? a. DSR4.3 cost less by $10,600 * b. Steel pipe cost less by $10,600 c. DSR4.3 cost less by $65,000 d. Steel pipe cost less by $65,000 414. If the interest rate on the account is 11.5% compounded yearly, approximately how many years will it take to triple the amount? a. 8 b. 9 c. 10 * d. 11 415. Fifteen years ago $1,000 was deposited in a bank account, and today it is worth $2,370. The bank pays interest semiannually. What was the nominal annual interest rate paid on this account? a. 2.9% b. 4.4% c. 5.0% d. 5.8% * 416. A deposit of $1,000 is made in the bank account that pays 8% interest compounded annually. Approximately how much money will be in the account after 10 years? a. $1890 b. $2000 c. $2160 * d. $2240 417. A deposit of $1,000 is made in the bank account that pays 24% interest per year compounded quarterly. Approximately how much money will be in the account after 10 years? a. $7000 b. $7200 c. $8600 d. $10,000 * 418. A machine costs $20,000 today and has an estimated scrap cash value of $2,000 after eight years. Inflation is 8% per year. The effective annual interest rate earned on money invested is 8%. How much money needs to be set aside each year to replace the machine with an identical model eight years from now? a. $2970 b. $3000 c. $3290* d. $3510

419. At what rate of annual interest will an investment quadruple itself in 12 years? a. 10.1% b. 11.2% c. 12.2% * d. 13.1% 420. A machine has an initial cost of $50,000 and a salvage value of $10,000 after 10 years. What is the straight-line depreciation rate as a percentage of the initial cost? a. 4% b. 8% * c. 10% d. 12% 421. Mr. Jones plans to deposit $500 at the end of each month for 10 years at 12% annual interest, compounded monthly. The amount that will be available in two years is a. $13000 b. $13500 * c. $14000 d. $14500 422. The purchase price of a car is $25,000. Mr. Smith makes a down payment of $5000 and borrows the balance from a bank at 6% interest for five years. Calculate the nearest value of the required monthly payments to pay off the loan. a. $350 b. $400 * c. $450 d. $500 423. A piece of machinery can be bought for $10,000 cash or for $2,000 down and payments of $750 per year for 15 years. What is the annual interest rate for the time payments? a. 1.51% b. 4.61% * c. 7.71% d. 12.0% 424. You have borrowed $5,000 and must pay it off in five equal annual payments. Your annual interest rate is 10%. How much interest rate will you pay in the first two years? a. $855 b. $868 c. $875 d. $918 * 425. A company puts $25,000 down and will pay $5,000 every year for the life of a machine (10 years). If the salvage value is zero and the interest rate is 10% compounded annually, what is the present value of the machine? a. $55,700* b. $61,400 c. $75,500 d. $82,500 426. A machine has an initial cost of $50,000 and a salvage value of $10,000 after 10 years. What is the book value after five years using straight-line depreciation? a. $12,500 b. $16,400 c. $22,300 d. $30,000 * 427. A machine that costs $20,000 has a 10-year life and a $2,000 salvage value. If straight-line depreciation is used, what is the book value of the machine at the end of the second year? a. $14,000 b. $14,400 c. $15,600 d. $16,400 * 428. A man makes a series of ten annual deposits starting at 2000 at the end of first year and increasing the amount deposited by 10% every year thereafter. Find the total amount at the end of ten years if the rate of interest on all sum’s of deposit is 8 %

a. 34,384.56* c. 28,784.77 b. 43,481.74 d. 47,845.26 429. In comparing alternatives the economical choice would be base from the economic study supported with mathematical calculation to justify its feasibility. a. True* c. False b. Not necessarily d. Not sure 430. The cost of a certain asset is 10,000 its life is 10 years and the scrap value is 500. find the total depreciation at the end of the fifth year. a. 4500 c. 4750 * b. 5000 d. 5250 431. You borrow $3,500 for one year from a friend at an interest rate of 1.5% per month instead of taking a loan from a bank at a rate of 18% per year. Compare how much money you will save or lose on the transactions. a. You will pay $55 more than if you borrow from the bank * b. You will pay $630 more than if you borrow from the bank c. You will pay $685 more than if you borrow from the bank d. You will save $55 by borrowing from your friend 432. If you invest $25,000 at 8% interest compounded annually, approximately how much money will be in the account at the end of 10 years? a. $31,000 b. $46,000 c. $54,000 * d. $75,000 433. A college student borrows $10,000 today at 10% interest compounded annually. Four years later, the student makes the first repayment of $3,000. Approximately how much money will the student still owe on the loan after the first payment? a. $7700 b. $8300 c. $11000 d. $11700 * 434. A 40-year-old consulting engineer wants to set up a retirement fund to be used starting at the age of 65. $20,000 is invested now at 6% compounded annually. Approximately how much money will be in the fund at retirement? a. $84 000 b. $86 000 * c. $88 000 d. $92 000 435. The maintenance cost for a car this year is expected to be $500. The cost will increase $50 each for the subsequent 9 years. The interest is 8% compounded annually. What is the approximate present worth of the maintenance for the car over the full 10 years? a. $4 300 b. $4 700 * c. $5 300 d. $5 500 436. ₱10,000 is invested at the beginning of a year in a 15% security and held for 5 yr. During that time, the average annual inflation is 8%. Approximately how much, in terms of year zero dollars will be in the account at maturity? a. ₱13,689* b. ₱13,789 c.₱13,889 d. ₱13,989 437. An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain a 30 year home load for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150. What is the maximum amount she can pay for a house if her disposable monthly income is $2500?

a.$109,521* b. $119,521 c. $129,521 d. $139,521 438. A machine has a maintenance of ₱40,000 in 2nd year, ₱60,000 in the 6th year and ₱80,000 in the 8th year. If interest is 10% compounded annually, find the equivalent equal annual maintenance of the machine for a period of 10 years. a.₱14,973.45 b. ₱12,084.02 c. ₱16,965.70* d. ₱18,028.89 439. A member of congress wants to know the capitalized cost of maintaining a proposed national park. The annual maintenance cost is expected to be ₱20,000. At an interest rate of 6% per year, the capitalized cost of the maintenance would be closest to: a. ₱1,500 b. ₱25,000 c. ₱333,333* d. ₱416,667 440. A machine has a first cost of ₱100,000 and salvage value of ₱10,000 after 10 years. The annual maintenance of the machine is ₱4,000. If interest rate is 10%. Find the annual cost of the machine. a. ₱17,009.34 b. ₱19,647.08* c. ₱21,083.56 d. ₱32,074.56 441. A house is expected to have a maintenance cost of $1000 the first year. It is believed that the maintenance cost will increase $500 per year. The interest rate is 6% compounded annually. Over a 10-year period, what will be approximate affective annual maintenance cost? a. $1 900 b. $3 000 * c. $3 500 d. $3 800 442. You deposited $10,000 in a savings account five years ago. The account has earned 5.25% interest compounded continuously since then. How much money is in the account today? a. $12 800 b. $12 900 c. $13 000 * d. $13 600 443. A young engineer wants to surprise husband with a European vacation for their tenth anniversary, which is five years away. She determines that the trip will cost $5,000. Assuming an interest rate of 5.50% compounded daily, approximately how much money does she need to deposit today for the trip? a. $3790 b. $3800 * c. $3880 d. $3930 444. A young woman plans to retire in 30 years. She intends to contribute the same amount of money each year to her retirement fund. The fund earns 10% compounded annually. She would like to withdraw $100,000 each year for 20 years, starting 1 year after the last contribution is made. Approximately how much money should she contribute to her retirement fund each year? a. $490 b. $570 c. $5200 * d. $11000 445. A piece of machinery has a first cost of $35,000 with monthly operating cost of $12,000. If the company wants to recover its investment in five years at an interest rate of 1% per month, the monthly income must be closed to: a. $5,498 b. $6,386 c. $8,295 d. $12,779* 446. A man applied for a loan with 12% compounded semi-annually. He promised to pay an amount ₱20,000 semi-annually starting 4 years from now for 10 years. Find the amount stated in the loan. a. ₱122,563 b. ₱132,563 c. ₱142, 563 d. 152, 563* 447. A series of bank deposits of ₱2000 quarterly from 5th year to 11th year. If interest rate is 16% compounded quarterly, find the total amount at the 15th year.

₱177,177 b. ₱146,401.97 * c. ₱197,177 d. ₱207,177 448. A series of deposits of ₱1000 bi-monthly starting today up to the 10th year. Find the amount at the 12th year if interest rate is 8% compounded bi-monthly. a. ₱98,106 b. ₱107,976.16 * c.₱138,106 d. ₱178,106 449. Kathy buys a television set from a merchant who asks ₱1,250.00 at the end of 60 days (cash in 60 days). Kathy wishes to pay immediately and the merchant offers to compute the cash price on the assumption that money is worth 8% simple interest. What is the cash price today? ₱1233.55* b. ₱1324.45 c. ₱2195.60 d. ₱2135.50 450. An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain a 30 year home load for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150. What is the maximum amount she can pay for a house if her disposable monthly income is $2500? a. $109,521* b. $119,521c. $129,521 d. $139,521 451.. What is the book value of equipment purchased 3 yr ago for ₱15,000 if it is depreciated using the sum of the year’s digits (SOYD) method? The expected life is 5 years. a. ₱3,000* b. ₱4000 c. ₱6,000 c. ₱9000 452. What annuity over a 10 year period at 8% interest is most nearly equivalent to a present worth of $7000? a. ₱104.32* b. ₱114.32 c. ₱124.32 d. ₱134.32 453. ₱10,000 is invested at the beginning of a year in a 15% security and held for 5 yr. During that time, the average annual inflation is 8%. Approximately how much, in terms of year zero dollars will be in the account at maturity? a. ₱13,689* b. ₱13,789 c. ₱13,889 d. ₱13,989 454. An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain a 30 year home load for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150. What is the maximum amount she can pay for a house if her disposable monthly income is $2500? a. $109,521* b. $119,521 c.$129,521 d. $139,521 455. A machine has a maintenance of ₱40,000 in 2nd year, ₱60,000 in the 6th year and ₱80,000 in the 8th year. If interest is 10% compounded annually, find the equivalent equal annual maintenance of the machine for a period of 10 years. a. ₱14,973.45 b. ₱12,084.02 c. ₱16,965.70* d. ₱18,028.89 456. How many years will ₱100,000 earned a compound interest of ₱50,000 if the interest rate is 9% compounded quarterly? a. 3.25 b. 4.55* c. 5.86 d. 2.11 457. Fifteen years ago ₱1,000.00 was deposited in a bank account, and today it is worth ₱2,370.00. The bank pays interest semiannually. What was the interest rate paid? a. 4.9% b. 5.8%* c. 5.0% d. 3.8% 458. ₱200,000 was deposited on Jan. 1, 1988 at an interest rate of 24% compounded semi-annually. How much would the sum be on Jan. 1, 1993? a. ₱421,170 b. ₱521,170 c. ₱401,170 d. ₱621,170* a.

459. Mr. W borrowed ₱2,000.00 from Mr. Y on June 1, 1928 and ₱500 on June 1, 1930, agreeing that money is worth 5% compounded annually. Mr. W paid ₱500 on June 1, 1931, ₱400 on June 1, 1932 and ₱700 on June 1, 1933. What additional sum should Mr. W pay on June 1, 1936 to discharge all remaining liability? a. ₱1780.29 b. ₱1690.28* c. ₱1754.53 d. ₱1896.77 460. Consider a deposit of ₱600, to be paid back in 1 yr by ₱700. What are the conditions on the rate of interest, I, in %/yr compounded annually, such that the net present worth of the investment is positive? Assume i ≥ 0%. a. 12.5% ≤ i ≤ 14.3% c. 0% ≤ i < 16.7%* b. 0% ≤ i < 14.3% d. 16.7% ≤ i < 100% 461. An item purchased for ₱150,000. Annual cost is ₱10,000. Using 10%, what is the capitalized cost of perpetual service? a. ₱352,000 b. ₱250,000* b. ₱532,000 d. ₱325,000 462. An asset is purchased for P10,000. Its estimated life is 10 years after which it will be sold for P1,000. Find the book value during the first year if sum-of-the-years digit (SOYD) depreciation is used. a. ₱8,363.64* b. ₱6,500.00 c. ₱7,545.00 d. ₱6,000.00 463. A machine has a first cost of ₱60,000 and has an expected salvage value after 10 years of ₱6,000. Find the book value after 5 years using declining balance method. a. ₱10,028.34 b. ₱15,071.32* c. ₱20,083.45 d. ₱25,083.45 464. A machine has a first cost of ₱50,000 with interest rate of 10% annually. Expected salvage value after 10 years is ₱5,000. Find the book value after 5 years using sinking fund method. a. ₱12,039 b. ₱22,084 c. ₱42,084 d. ₱32,762* 465. Mr. Richardson borrowed ₱16,000 two years ago. The repayment terms of the loan are 12% interest for 10 years and uniform annual payments. He just made his second payment. How much principal, most nearly, does he still owe? a. ₱14,069* b. ₱15021 c. ₱14801d. ₱13100 Thermodynamics 1: 466. Find the enthalpy of the helium if its internal energy is 200KJ/Kg. a. 144 kJ/kg b. 223.42 kJ/kg c. 333.42 kJ/kg * d. 168 kJ/kg 467. Steam at 2Mpa and 250deg C in a rigid cylinder is cooled until the quality is 30%. Find the heat rejected from the cylinder. a. -432.23 b. -926.26 c. -1265.02 * d. 1082.34 468. In an adiabatic, isentropic process, p1 = 200 psia, p2 = 300 psia, and T1 = 700 °R. Find T2, using γ= 1.4. a. 576 °R b. 590 °R c. 680 °R d. 786 °R* 469. Determine the specific gravity of carbon dioxide gas (molecular weight = 44) at 150degF and 20 psia. a. 1.67* b. 1.45 c. 1.87 d. 1.30

470. Gas is enclosed in a cylinder with a weighted piston as the top boundary. The gas is heated and expands from a volume 0.04 m3 to 0.1 m3. The pressure varies such that PV = C, and the initial pressure is 200 kPa. Calculate the work done by the system. a. 6.8 kJ b. 7.33 kJ* c. 9.59 kJ 471. 200g of water are heated from 5C to 100C and vaporized at a constant pressure. The heat of vaporization of water at 100C is 539.2 cal/g. Determine the total change in entropy. a. 248.2 cal/K b. 298.2 cal/K c. 348.0 cal/K * d. 398.2 cal/K 472. Steam at 1000 lbf/ft2 pressure and 300°R has a specific volume of 6.5 ft3/lbm and a specific enthalpy of 9800 lbfft/lbm. Find the internal energy per pound mass of steam. a. 2500 lbf-ft/lbm b. 3300 lbf-ft/lbm * c. 5400 lbf-ft/lbm d. 6900 lbf-ft/lbm 473. One kilogram of water (cv = 4.2 kJ/kg-K) is heated by 300 BTU of energy. What is the change in temperature, in K? a. 17.9 K * b. 71.4 K c. 73.8 K d. 75.4 K 474. Shaft work of -15 BTU/lb and heat transfer of -10 BTU/lb change enthalpy of a system by: a. -25 BTU/lb b. -15 BTU/lb c. -10 BTU/lb d. +5 BTU/lb * 475. A mixture at 14.7 psia and 68F that is 30% weight CO2 (m wt=44) and 7% wt. N2 (m wt=28) has a partial pressure of CO2 in psia that is nearest to: a. 2.14 b. 3.15 * c. 6.83 d. 1.43 d. 12.0 kJ 476. 200 mL of oxygen are collected over water at 23C and a pressure of 1 atmosphere. What volume would the oxygen occupy dry at 273K and 1 atmosphere? a. 179.3 ml * b. 184.4 ml c. 190.0 ml d. 194.5 ml 477. Steam turbine is receiving 1014 lbm/hr of steam, determine the horsepower output of the turbine if the work done by steam is 251 btu/lbm. a. 100 HP * b. 462.7 HP c. 200 HP d. 6002.7 HP 478. A cylinder and a piston arrangement contains saturated water vapor at 110 °C. The vapor is compressed in a reversible adiabatic process until the pressure is 1.6 MPa. Determine the work done by the system per kilogram of water. a. -637 kJ/kg b. -509 kJ/kg c. -432 kJ/kg * d. -330 kJ/kg 479. A gas has a density of 0.094 lb/ft3 at 100degF and 2 atm. What pressure is needed to change the density to 0.270 lb/ft3 at 250 deg F? a. 7.28 atm * b. 6.32 atm c.3.45 atm d. 5.25 atm

480. Water (specific heat cv = 4.2 kJ/kg-K) is being heated by a 1500W heater. What is the rate of change in temperature of 1 kg of the water? a. 0.043 K/s b. 0.719 K/s c. 0.357 K/s * d. 1.50 K/s 481. A reversed Carnot cycle absorbs heat at the rate of 1 kW from cold chamber maintained at 250 K and discharges it to the atmosphere at 300 K. Find the work required for the cycle. a. 1 kWc. C.0.2 kW * b. 1.5 kW d. 0.5 kW 482. The isentropic compression of 1 m3 of air, cp /cv = 1.4, from 20 kPa to a pressure of 100 kPa gives a final volume of a. 0.16 m3 c. 0.32 m3 * b. 0.20 m3 d. 0.40 m3 483. If the initial volume of an ideal gas is allowed to expand to twice its original volume and lower its temperature by half, the pressure a. doubles c. remains b. is reduced to one fourth * d. is indeterminat 484. The temperature at which oil will vaporize and burn continuously a. Cloud point c. Critical point b. Dropping point d. Fire point * 485. States that the external pressure applied to a confined fluid increases the pressure of every point in the fluid by an amount equal to the external pressure. a. Archimedes principle c. Bernoulli’s principle b. Pascal’s law * d. Dalton’slaw 486. If air is at pressure, p, of 3200 lbf/ft2, and at a temperature, T, of 800R, what is the specific volume, v? a. 14.2 cu.ft/lbm c. 11.2 cu.ft/lbm b. 13.3 cu.ft/lbm* d. 9.8 cu.ft/lbm 487. The mass of air in the room 3m x 5m x 20m is known to be 350 kg. find its density. a. 1.617 kg/m^3 b. 1.716 kg/m^3 c. 1.167 kg/m^3* d. 1.176 kg/m^3 488. Which process where work done is zero? a. Isentropic b. polytropic c. isometric* d. isobaric 489. If an initial volume of an ideal gas is compressed to one-half its original volume and twice its original temperature, the pressure: a. Doubles b. quadruples* c. remains constant d. halves 490. What is the change in internal energy of air cooled from 1000F to 200F? a. 180 Btu/lbm b. 800 Btu/lbm c. 700 Btu/lbm d. 140 Btu/lbm* 491. If the vapor occupies 3.45% by volume, what is the partial pressure of the air if the atmospheric pressure is 99.97 kPa? a. 76.5 kPa b. 86.5 kPa c. 96.5 kPa* d. 99.9 kPa 492. A bicycle tire has a volume of 600 cu. cm. it is inflated with carbon dioxide to pressure of 80 psi at 20C. how many grams of carbon dioxide are contained in the tire? a. 5.98 g* b. 6.43 g c. 4.63 g d. 3.83 g 493. In the process, neglecting KE and PE changes, ∫ −𝑉𝑑𝑃 represents which item below? a. Enthalpy change b. flow energy c. shaft work* d. heat transfer 494. In a constant temperature, closed system process, 100 Btu of heat is transferred to the working fluid at 100F. what is the change in entropy of the working fluid? a. 0.18 kJ/K b. 0.57 kJ/K c. 0.25 kJ/K d. 0.34 kJ/K*

495. An elastic sphere containing gas at 140 kPa has a diameter of 1.1m . heating sphere causes it to expand to a diameter of 1.3 m. during the process the pressure is proportional to the sphere diameter, calculate the work done by the gas in kJ. a. 51.8 b. 59.6 c. 55.6 d. 69.6* 496. A reversible thermodynamic process is made to follow the Carnot cycle between the temperature limits of 650o F and 150oF. 300 Btu of heat are supplied per cycle to the system. What is the change in entropy during the heat addition? A. 0.27 Btu/R* C. 0.16 Btu/R B. 1.30 Btu/R D. 0.75 Btu/R 497. A reverse carnot cycle requires 3 Hp and extracts energy from Taal lake to heat a house. If the house is kept at 21C and requires 2100 Btu per minute, what is the temperature of the lake? A.38.18F* B. 36.29F C. 34.25F D. 28.75F 498. 150 grams of water at 75C is heated at constant pressure, the water is completely vaporized. Find the heat added: A.543.52 kJ B. 816.66 kJ C. 354.25 kJ* D. 1135.66 kJ 499. The isentropic compressor of 1 m3 of air, cp/cv = 1.4, from 20 kPa to a pressure of 100 kPa gives a final volume of A.0.16 m3 b. 0.20 m3 c. 0.32 m3* d. 0.40 m3 500. If 6 liters of a gas at a pressure of 100 kPa are compressed reversibly according to pV2=constant until the volume becomes 2 liters, find the final pressure. A. 845 kPa C. 756 kPa B. 900 kPa* D. 700 kPa .501. Air is compressed adiabatically from 30oC to 100oC. If mass of air being compressed is 5 kg. Find the change in entropy. A. 1.039 kJ/kg B. 0.746 kJ/kg C. 0 * D. 1.245 kJ/kg 502. A perfect gas has a value of R = 58.8 ft-lb/lb-oR and k = 1.26. if 20 BTU are added to 10 lbs of the gas at constant volume when initial temperature is 90o F. Find the final temperature. A. 97oF * B. 104oF C. 154oF D. 185oF 503. Air enters a nozzle steadily at 1.71 kg/m3 and 35 m/s. what is the mass flow rate through the nozzle if the inlet area of the nozzle is 80 cm2? A. 0.479 kg/s* B. 3.57 kg/s C. 4.79 kg/s D. 0.53 kg/s 504. A carnot cycle has a maximum temperature of 580F and minimum temperature of 150F. if the heat added is 4200 BTU/min, find the horsepower output of the engine. A. 33.53 B. 40.94* C. 44.69 D. 75.40 505. Steam turbine is receiving 1000 lbm/hr of steam, determine the horsepower output of the turbine if the work done by steam is 250 Btu/lbm. A. 98.23 Hp* B. 362.7 Hp C. 280 Hp D. 6072.7 Hp Thermodynamics 2: 506. Determine th air – standard efficiency of an engine operating on the diesel cycle with clearance of 6% when the suction pressure is 99.97 kPa and the fuel is injected for 7% of the stroke. Assume k = 1.4 A. 62.11% * B. 51.20% C. 73.58% D. 60.02%

507. A 2000 kW Diesel engine unit uses 1 bbl oil per 525 kWh produced. Oil is 25°API. Efficiency of generator 93%, mechanical efficiency of engine 80%. What is the thermal of engine based on indicated power (%)? A.39.3% B. 39.4% C. 39.5% D.39.6% * 508. An air-standard Brayton cycle has a pressure ratio of 8. The air properties at the start of compression are 100 kPa and 25°C. The maximum allowable temperature is 1100°C. Determine the net work. A. 373.23 kJ/kg B. 373.24 kJ/kg * C. 373.25 kJ/kg D. 373.26 kJ/kg 509. Steam leaves an industrial boiler at 827.4 kPa and 171.6C. A portion of the steam is passed through a throttling calorimeter and is exhausted to the atmosphere when the calorimeter pressure is 101.4 kPa. How much moisture does the steam leaving the boiler contain if the temperature of the steam at the calorimeter is 115.6C? At 827.4 kPa (171.6C): hf = 727.25 kJ/kg, hfg = 2043.2kJ/kg From table 3: at 101.4 kPA and 115.6C: h2 = 20707.6 kJ/kg A. 3.78% B. 3.08%* C. 4.56% D. 2.34% 510. A turbine has an available enthalpy of 3300 kJ/kg in a Rankine cycle. The pump work has also 25 kJ/kg. For flow of 3 kg/s, find the system output. A.5960 kW B. 6080 kW C. 6343 kW D. 9825 kW* 511. An Otto cycle with air as the working fluid has a compression ratio of 8.2. Under cold air standard conditions, the thermal efficiency of this cycle is A. 24% B. 43% C.52% D. 57%* 512. For specified limits for the maximum and minimum temperatures, the ideal cycle with the lowest thermal efficiency is A. Carnot B. Stirling C. Ericsson D. Otto * 513. Air in an ideal Diesel cycle is compressed from 3 L to 0.15 L, and then it expands during the constant pressure heat addition process to 0.30 L. Under cold air standard conditions, the thermal efficiency of this cycle is A, 35% B. 44% C. 65% * D. 70% 514. An ideal Brayton cycle has a net work output of 150 kJ/kg and a backwork ratio of 0.4. If both the turbine and the compressor had an isentropic efficiency of 85%, the net work output of the cycle would be a. 74 kJ/kg C. 109 kJ/kg b. 95 kJ/kg * D. 177 kJ/kg 515. Water at a pressure of 10 MPa and temperature of 230 oC is throttled to a pressure of 1 MPa in an adiabatic process. What is the quality after throttling? Note: at 10 MPa and 230oC, h= 991.7 kJ/kg; at 1 MPa, hf= 762.81 kJ/kg. hfg = 2015.3 kJ/kg. A. 11.36%* C. 12.33% B. 13.45 % D. 14.1 % 516. A vessel with a volume of 1 m3 contains liquid water and vapor in equilibrium at 600 kPa. The liquid water has a mass of 1 kg. Using steam tables, calculate the mass of the water vapor. At 600 kPa: vf = 0.001101 m3/kg, vg = 0.3157 m3/kg a. 0.99 kg b. 1.57 kg c. 2.54 kg d. 3.16 kg* 517. Steam with a specific volume of 0.09596 m3/kg undergoes constant pressure process at 1.70 Mpa until its specific volume 0.13796 m3/kg. what is the work done? a. 71.4 kJ/kg* b. 67.1 kJ/kg c. 82.78 kJ/kg d. 97.23 kJ/kg 518. One kg of steam at 121C and 10% moisture undergoes a constant volume until the pressure becomes 0.28 Mpa. Determine the final temperature. a. 200.4C b. 374.5C c. 206.5C* d. 873.4C

519. Air in an ideal Diesel cycle is compressed from 3 L to 0.15 L, and then it expands during the constant pressure heat addition process to 0.30 L. Under cold air standard conditions, the thermal efficiency of this cycle is a. 35% b. 44% c. 65% * d. 70% 520. In an ideal Brayton cycle, air is compressed from 95 kPa and 25°C to 800 kPa. Under cold air standard conditions, the thermal efficiency of this cycle is a. 46% * b. 54% c. 57% d. 39% 521. A rankine cycle has a turbine work of 600 kJ/kg and efficiency of 88%, pump work is 3 kJ/kg and efficiency of 75%. If the cycle efficiency is 26%, find the heat added to the cycle. a. 2577.60 kJ/kg b. 2345.19 kJ/kg c. 2015.38 kJ/kg* d. 1852.40 kJ/kg 522. In a rankine cycle steam enters the turbine at 3 Mpa and condenser of 60 kPa, what is the thermal efficiency of the cycle? At 3 Mpa: hg = 2804.2 sg = 6.1869 At 60 kPa: hf = 359.86 hfg = 2293.6 sf= 1.1457 vf = 0.0010331 a. 25.55%* b. 45.23% c. 34.23% d. 12.34% 523. The available enthalpy of the at the exit of boiler in a rankine cycle is 2900 kJ/kg and enthalpy at the entrance of the turbine is 2870 kj/kg. if the mass of steam is 3.5 kg/s, find the heat loss between the boiler exit and turbine entrance. a. 105 kW* b. 30 kW c. 20 kW d. 50 kW 524. A turbine has an available enthalpy of 3300 kJ/kg in a Rankine cycle. The pump work has also 25 kJ/kg. For flow of 3 kg/s, find the system output. a. 5960 kW b. 6080 kW c. 6343 kW d. 9825 kW* 525. An ideal Brayton cycle has a net work output of 150 kJ/kg and a backwork ratio of 0.4. If both the turbine and the compressor had an isentropic efficiency of 85%, the net work output of the cycle would be a. 74 kJ/kg b. 95 kJ/kg * c. 109 kJ/kg d. 128 kJ/kg 526. An OTTO engine has a clearance volume of 7%. It produces 300 kW power. What is the amount of heat rejected in kW? a. 170 b. 160 c. 152* d. 145 527. In an air standard OTTO cycle, the clearance volume is 18% of the displacement volume. Find the thermal efficiency. a. 0.52 b. 0.55 c. 0.53* d. 0.60 528. The compression ratio of an ideal OTTO cycle is 6:1. Initial conditions are 101.3 kPa and 20C. Find the pressure and temperature at the end of adiabatic compression. a. 1244.5 kPa, 599.96 K* b. 1244.5 kPa, 60C c. 1224.5 kPa, 60C d. 1232.3 kPa, 155K 529. The condition at the beginning of compression in an OTTO engine operating on hot-air standard with k= 1.35 are 101.325 kPa, 0.05 cubic meter and 32C. The clearance is 8% and 15 kJ are added per cycle. Determine the mean effective pressure. a. 323.97 kPa* b. 423.97 kPa c. 223.97 kPa d. 523.97 kPa 530. In a rankine cycle, the system turbine inlet has a condition of 3126 kJ/kg enthalpy and entropy of 6.68 kJ/kg-K. The quality after expansion is 82% and enthalpy of 2103 kJ/kg with hf = 233 kJ/kg. Find the efficiency of the cycle. a. 23.45% b. 35.40%* c. 30.34% d. 38.44%

531. Steam at 2 Mpa and 250C in a rigid cylinder is cooled until the quality is 30%. Find the haet rejected from the cylinder. At 2 Mpa and 250C: v = 0.11144 m3/kg u = 2679.6 kJ/kg At 2 Mpa, (saturated): vf = 0.0011767 m3/kg, vg = 0.09963 uf = 906.44, ug = 1693.8 a.-432.23 kJ/kg b. -926.26 kJ/kg c. -1,265.02 kJ/kg* d. 1082.34 kJ/kg 532. An OTTO engine has a clearance volume of 7%. It produces 300 kW power. What is the amount of heat rejected in kW? a.170 b. 160 c. 152* d. 145 533. The compression ratio of an ideal OTTO cycle is 6:1. Initial conditions are 101.3 kPa and 20C. Find the pressure and temperature at the end of adiabatic compression. a.1244.5 kPa, 599.96 K* b. 1244.5 kPa, 60C c. 1224.5 kPa, 60C d. 1232.3 kPa, 155K 534. Determine the air-standard efficiency of an engine operating on the Diesel cycle when the suction pressure is 99.97 kPa and the fuel is injecting for 6% of the stroke, the clearance volume is 8% of the stroke. Assume k = 1.4. a.60.07%* b. 65.01% c. 67.01% d. 64.02% 535. In an ideal Rankine cycle, the steam throttle condition is 4.10 MPa and 440°C. If turbine exhaust is 0.105 MPa, determine the thermal efficiency of the cycle. (Ans: 27.55%) a. 27.54% b.27.55% * c. 27.56% d.27.57% 536. How many degree Celsius is 80 degrees Fahrenheit? a. 26.67* b. 86.4 c. 33.33 d. 16.33 537. How many horsepower is 746 kW? a. 1 HP b. 100 HP c. 74.6 HP d. 1000 HP * 538. How many grams is 8 ounce? a. 226.79 rams * b. 262.79 rams c. 622.79 rams d. 626.79 rams 539. How many cubic meters is 100 gallons of liquid? a. 0.1638 cu. meters b. 1.638 cu. meters c. 0.3785 cu. meters * d. 1.430 cu. Meters 540. A pressure reading of 35 psi in kPa abs is: a. 427.3 b. 724 c. 273.4 d. 342.72 * 541. A carnot engine requires 35 kJ/s from the hot source. The engine produces 15 kW power and the temperature of the sink is 26C. What is the temperature of the hot source in C? a.245.57 b. 210.10 c. 250.18* d. 260.68 542. How many pascals in 60 mmhg? a. 7999.34 pascals * b. 8000.34 pascals c. 8001.34 pascals d. 8002.34 pascals 543. What is the final temperature after compression of a Diesel cycle if the initial temperature is 32C and the clearance is 8%. a.863.84 K* b. 763.84 K c. 963.84 K d. 663.84 K 544. A diesel engine is operating on a 4-stroke cycle, has a heat rate of 11,315.6 kJ/kW-hr brake. The compression ratio is 13. The cut-off ratio is 2. Using k = 1.32 what is the brake engine efficiency? a.65.5 % b. 51.2 % c. 63. 4 % * d. 45.3 %

545. A carnot engine receives 130 BTU of heat from a hot reservoir at 700F and rejects 49 Btu of heat. Calculate the temperature of the cold reservoir. a.-21.9 F b. -24.2 F c. -20.8 F d. -22.7 F* Fluid Mechanics: 546. A substance temperature was 620OR. What is the temperature in OC? a. 50.7 b. 45.54 c. 71.11* d. 94.44 547. The specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid cm3/g? a. 0.5321 cm3/g b. 0.6748 cm3/g c. 0.9504 cm3/g d. 1.0675 cm3/g* 548. The equivalent weight of mass 10 kg at a location where the acceleration of gravity is 9.77 m/sec2 a. 97.7 N* b. 79.7 N c. 77.9 N d. 977 N 549. Air enters a nozzle steadily at 2.21 kg/m^3 and 30 m/s . What is the mass flow rate through the nozzle if the inlet area of the nozzle is 80 cm^2? a. 0.35 kg/s b. 3.5 kg/s c. 5.3 kg/s d. 0.53 kg/s* 550. Determine the submerged depth of a cube of steel 0.3 m on each side floating in mercury. The specific gravities of steel and mercury are 7.8 and 13.6 respectively. a. 0.155 m b. 0.165 m c. 0.134 m d. 0.172 m * 551. The pressure drop across a turbine is 200 kPa. The flow rate is 0.25 m3/min. What is most nearly the power output of the turbine? a. 0.41 kW b. 0.83 kW* c. 0.95 kW d. 1.3 kW 552. Water is pumped at 1m3/s to an elevation of 5 m through a flexible hose using a 100% efficient pump rated at 100 kW. Using the same length of hose, what size motor is needed to pump 1m3/s of water to a tank with no elevation gain? Both ends of the hose are at atmospheric pressure. Neglect kinetic energy effects. a. 18 kW b. 22 kW c. 37 kW d. 51 kW * 553. Calculate the Reynolds number for water at 20° C flowing in an open channel. The water is flowing at a volumetric rate of 0.8 m3js. The channel has a height of 1.2 m and a width of 2.5 m. At this temperature, water has a kinematic viscosity of 1.02 x 106 m2js. a. 6.5 X 105 * b. 8.5 x 105 c. 9.2 x 105 d. 1.2 x 106 554. The Reynolds number of a sphere falling in air is 1 x 106 • If the sphere's radius is 0.5 m, what is most nearly its velocity? (Pair = 1.225 kg/m3, air = 1.789 x 10-5 Pa•s) a. 2.5 m/s b. 5.2 m/s c. 11 m/s d. 15 m/s* 555. A circular cylinder 4 m long and 3 m in diameter is in an air stream. The flow velocity is 5 m/s perpendicular to the longitudinal axis of the cylinder. Given that the coefficient of drag on the cylinder is 1.3, and the density of air is 1.225 kg/m3 , what is most nearly the drag force on the cylinder? a. 0.090 kN b. 0.11 kN c. 0.24 kN * d. 0.91 kN

556. Estimate the height to which the water will rise in a capillary tube of diameter 5 mm if the surface tension is 0.0728 N/m and the contact angle is 0°? a. 5.94 mm * b. 5.95 mm c. 5.96 mm d. 5.97 mm 557. A sonar transmitter operates at 2 impulses per second. If the device is held to the surface of fresh water (EB = 2.04 × 109 Pa) and the echo is received midway between impulses, how deep is the water? a. 178.4 m b. 178.5 m * c. 178.6 m d. 178.7 m 558. A cylindrical tank having a diameter of 1.5 m and a height of 4 m is open at one end and closed at the other end. It is placed below the water surface with its open end down. How deep below the water surface should the tank be placed if the depth of the water inside the tank is 1.8 m? a. 6.23 m b. 6.20 m c. 6.25 m* d. 6.26 m 559. Assuming normal barometric pressure, how deep in the ocean is the point where an air bubble, upon reaching the surface, has five times its volume than it had at the bottom? a. 40.05 m b. 40.08 m c. 4.20 m d. 40.11 m * 560. A vertical rectangular gate 1.5 m wide and 3 m high is submerged in water with its top edge 2 m below the water surface, find the total pressure acting on one side of the gate and its location from the bottom. a. 1.286 m * b. 1.682 m c. 1.248 m d. 1.284 m 561. What is the resultant hydrostatic force on one side of a 25cm diameter vertical circular plate standing at the bottom of a 3 m pool of water? a. 1.38 KN * b. 1.63 KN c. 1.91 KN d. 2.72 KN 562. A closed tank with the dimensions shown contains water. If the pressure of the air in the tank is 700 kpa, what is the pressure at point P, which is located halfway up the inclined wall? a. 922 kpa * b. 7.22 Mpa c. 7.56 Mpa d. 8.13 Mpa 563. A 300 mm long rigid metal cylindrical container with a diameter of 200 mm is closed at one end. The container is held vertically, barely submerged, and closed – end-up in water, as shown. The atmospheric pressure is 101.3 kpa. The water rises 75 mm inside the container under these conditions. What is the approximate total pressure of the air inside the container? a. 101.3 kpa b. 102.1 kpa c. 103.5 kpa * d. 110.4 kpa 564. An open cylindrical vessel 1.2 m in diameter and 2.1 m high is 2/3 full of water. Compute the amount of water in liters that will be spilled out if the vessel is rotated about its vertical axis at a constant angular speed of 90 rpm. a. 125 liters b. 130 liters * c. 135 liters d. 140 liters 565. Find the approximate flow rate at which water will flow in a conduit shaped in the form of an equilateral triangle if the head lost is 5 m per kilometer length. The cross-sectional area of the duct is 0.075 m2. Assume f = 0.0155. a. 94.2 li/sec b. 92.4 li/sec * c. 89.9 li/sec d. 89.8 li/sec 566. Archimedes established his principle while investigating a suspecting fraud in the construction of a crown. The crown was made from an alloy of gold and silver instead of from pure gold. Assume that the volume of the alloy was combined volumes of

the components (the density of gold is 19.3 g/cm3, density of silver is 10.5 g/cm3. If the crown had a weight of 1000 g in air and 940 g in pure water, what percentage of gold (by weight) is it? a. 53.1 % b. 67.4 % c. 81.2 %* d. 91.3 % 567. What is the depth of the center of pressure on the vertical plate if the upper edge is 1.5m below the water surface? a. 2.12m b. 2.32m c. 2.50m d. 2.63m * 568. What height of mercury column is equivalent to a pressure of 700 kpa? The density of mercury is 13,500 kg/m3. a. 0.75m b. 1.5m c. 3.4m d. 5.3m * 569. A fluid with a vapour pressure of 0.2 Pa and a specific gravity of 12 is used in a barometer. If the fluid’s column height is 1m, what is the atmospheric pressure? a. 9.80 kpa b. 11.8 kpa c. 101 kpa d. 118 kpa * 570. One leg of a mercury U-tube manometer is connected to a pipe containing water under a gage pressure of 100 kpa. The mercury in this leg stands 750 mm below the water. What is the height of mercury in the other leg, which is open to the air? The specific gravity of mercury is 13.5. a. 0.2m b. 0.5m c. 0.8m * d. 1m 571. The film width in a surface tension experiment is 10 cm. If mercury is the fluid (surface tension = 0.52 N/m), what is the maximum force that can be applied without breaking the membrane? Neglect gravitational force. a. 0.1 N * b. 1.0 N c. 2.0 N d. 3.4 N 572. Oil with a specific gravity of 0.72 is used as the indicating fluid in a manometer. If the differential pressure across the ends of the manometer is 7 kpa, what will be the difference in oil levels in the manometer? a. 0.23 m b.0.44 m c.0.53 m d.1.0 m * 573. A pressure of 35 kpa is measured 4m below the surface of an unknown liquid. What is the specific gravity of the liquid? a. 0.09 b. 0.89* c. 0.93 d. 1.85 574. A dimensional analysis of a ship model is being performed using a total of four different dimensional quantities: mass, length, time, and temperature. Six different variables (density, surface tension, viscosity, gravity, power, and mass) have been identified as potentially affecting the velocity of the boat. Use the Buckingham pi theorem to predict how many pi-groups will be needed? a. 1 b. 2 * c. 10 d. 24 575. The average specific gravity of seawater is 1.15. what is the absolute pressure at the bottom of 3000 m of sea? a. 2.1 kpa

b. 2.5 Mpa c. 28 Mpa d. 34 Mpa * 576. A vessel is initially connected to a reservoir open to the atmosphere. The connecting valve is then closed, and a vacuum of 65.5 kpa is applied to the vessel. What is the absolute pressure in the vessel? Assume standard atmospheric pressure. a. 36 kpa * b. 66 kpa c. 86 kpa d. 110 kpa 577. At a particular temperature, the surface tension of water is 0.073 N/m. under ideal conditions, the contact angle between glass and water is zero. A student in a laboratory observes water in a glass capillary tube with a diameter of 0.10 mm. what is the theoretical height of the capillary rise? a. 0.00020 m b. 0.013 m c. 0.045 m d. 0.30 m * 578. What is the atmospheric pressure on a planet if the absolute pressure is 100 kpa and the gage pressure is 10 kpa? a. 10 kpa b. 80 kpa c. 90 kpa * d. 100 kpa 579. 100 g of water are mixed with 150 g of another fluid (w = 790 kg/m3). What is the specific volume of the resulting mixture, assuming that the volumes are additive and the mixture is homogenous? a. 0.63 cm3/g b. 0.82 cm3/g c. 0.88 cm3/g d. 1.20 cm3/g * 580. 100 g of water are mixed with 150 g of another fluid (w = 790 kg/m3). What is the specific gravity of the resulting mixture, assuming that the volumes are additive and the mixture is homogenous? a. 0.63 b. 0.82 c. 0.86 * d. 0.95 581.Water, density = 62.4 lbf/ft3, is flowing through a pipe. A pitot static gage registers 3.0 inches of mercury. What is the velocity of water in the pipe? Note: densityhg = 848.6 lbf/ft3. A. 14.24 ft/s * C. 8.24 ft/s B. 11.24 ft/s D. 7.45 ft/s 582. A cylindrical 1 ft diameter tank, 4 ft high contains 3 ft of water. What rotational speed is required to spin the water out the top? A. 22.7 rad/s * C. 23.7 rad/s B. 21.4 rad/s D. 18.90 rad/s 583. A 1 m x 1.5 m cylindrical tank is full of oil with SG = 0.92. Find the force acting at the bottom of the tank in dynes. A. 106.33 x 107 dynes B. 106.33 x 104 dynes C. 106.33 x 105 dynes D. 106.33 x 106 dynes* 584. Find the pressure at the 100 fathom depth of water in kPag. A. 1,793.96 kPag* B. 1,893.96 kPag C. 1,983.96 kPag D. 1,693.96 kPag

585. A large mining company was provided with a 3 m3 of compressed air tank. Air pressure in the tank drops from 700 kPa to 150 kPa while the temperature remains constant at 28oC. What percentage has the mass of air in the tank been reduced? A. 74.00 B. 72.45 C. 78.56 D. 78.57 * Heat Transfer: 586. A 5 cm diameter spherical ball whose surface is maintained at a temperature of 70 deg. C is suspended in the middle of a room at 20 deg. C. if the convection heat transfer coefficient is 15 W/m^2-C and the emissivity of the surface is 0.8, determine the total heat transfer from the ball. A. 23.56 watts B. 32.77 watts* C. 9.22 watts D. 43.45 watts 587. For heat transfer purposes, a standing man can be modeled as a 30 cm diameter, 170 cm long vertical cylinder with bottom both the top and bottom surfaces insulated and with the side surface at an average temperature of 34 deg C. For a convection heat transfer coefficient is 15 W/m2-C, determine the rate of the heat loss from this man by convection in an environment at 20 deg C. A. 316.46 watts C. 336.46 watts * B. 326.46 watts D. 346.46 watts 588. Consider a person standing in a breezy room at 20 deg C. Determine the total rate transfer from this person of the exposed surface area and the average outer surface temperature of the person are 1.6m2 and 29 deg C, respectively, and the convection heat transfer coefficient is 6 W/m2 with emissivity of 0.95. A. 86.40 watts C. 198.1 watts B. 81.70 watts D. 168.1 watts * 589. A tank contains liquid nitrogen at -190 c0 is suspected in a vacuum shell by three stainless steel rods 0.80 cm in diameter and 3 meters long with a thermal conductivity of 16.3 W/m2-C0. If the ambient air outside the vacuum shell is 15 C0, calculate the magnitude of the conductive heat flow in watts along the support rods. A. 0.168 * B. 0.176 C. 0.182 D. 0.0587 590. How many watts will be radiated from a spherical black body 15 cm in diameter at a temperature of 800 degC? A. 5.34 KW* B. 4.34 KW C. 6.34 KW D. 3.34 KW 591. Heat is lost at a rate of 275 W per m2 area of a 15-cm-thick wall with a thermal conductivity of k=1.1 W/m⋅ºC.The temperature drop across the wall is A. 37.5ºC* B. 27.5ºC C. 16.0ºC D.8.0ºC 592. Consider a wall that consists of two layers, A and B, with the following values: kA = 0.8 W/m⋅ºC, LA= 8 cm, kB= 0.2 W/m⋅ºC, LB = 5 cm. If the temperature drop across the wall is 18ºC, the rate of heat transfer through the wall per unit area of the wall is A.180 W/m2 B. 153 W/m2 C. 89.6 W/m2 D.51.4 W/m2* 593. A plane furnace surface at 150°C covered with 1-cm-thick insulation is exposed to air at 30°C, and the combined heat transfer coefficient is 25 W/m2⋅°C. The thermal conductivity of insulation is 0.04 W/m⋅°C. The rate of heat loss from the surface per unit surface area is A. 35 W B. 414 W* C. 300 W D. 480 W

594. A 10-m-long, 5-cm-outer-radius cylindrical steam pipe is covered with 3-cm thick cylindrical insulation with a thermal conductivity of 0.05 W/m.°C. If the rate of heat loss from the pipe is 1000 W, the temperature drop across the insulation is A. 163°C B. 600°C C. 48°C D. 150°C* 595. Consider a surface at -5ºC in an environment at 25ºC. The maximum rate of heat that can be emitted from this surface by radiation is 2

A.0 W/m

B. 155 W/m 2*

2 2

C. 293 W/m D. 354 W/m 596. A surface temperature of the hot side of the furnace was is 1200C. It is desired to maintain the outside of the wall at 38C. A 152 mm of refractory silica is used adjacent to the combustion chamber and 10 mm of steel covers the outside. What thickness of insulating bricks is necessary between refractory silica and steel, if the heat loss should be kept at 788 W/m2? Use k =13.84 W/m-K for refractory silica; 0.15 for insulating brick, and 45 for steel. A.220 mm* b. 240 mm c. 260 mm d. 280 mm 597. An insulated steam pipe located where the ambient temperature is 32C, has an inside diameter of 50 mm with 10 mm thick wall. The outside diameter of the corrugated asbestos insulation is 125 mm and the surface coefficient of still air, ho = 12 W/m2-K. inside the pipe is steam having a temperature of 150C with film coefficient hi = 6000 W/m2-K. Thermal conductivity of pipe and asbestos insulation are 45 and 0.12 W/m-K respectively. Determine the heat loss per unit length of pipe. a. 110W b. 120W* c. 130W d. 140W 598. Two walls of a storage plant composed of insulating material (k=0.25 kJ/hr-m-C) with 15 cm thick and concrete (k=3.2382 kJ/hr-m-C) with 10 cm thick. The surface temperature in hot side is 35C and cold side is -10C. if the area is 8 m2, find the temperature between walls. Note: Insulating materials is in cold side. a. 28.24C b. 34.12C c. 32.79C* d. -7.78C 599. Determine the thermal conductivity of a material that is used a 4 m2 test panel, 25 mm thick with a temperature difference of 20F between surfaces. During the 4 hrs of test period, the heat transmitted is 500 kJ. a. 0.0432 W/m-Cb. 0.0723 W/m-C c. 0.0321 W/m-C d. 0.0195 W/m-C* 600. A steam initially is saturated at 250C passed through a 12 cm steel pipe for a total distance of 200 m. the steam line is insulated with material having k = 10 W/m2-K and thickness of 6 cm. the ambient temperature of 25C. Determine the surface film conductance of air if the moisture at the discharge end is 10% and steam rate is 0.13 kg/s. a. 0.124 W/m2-C b. 0.872 W/m2-C c. 0.661 W/m2-C* d. 0.452 W/m2-C 601. A surface temperature of the hot side of the furnace was is 1200C. It is desired to maintain the outside of the wall at 38C. A 152 mm of refractory silica is used adjacent to the combustion chamber and 10 mm of steel covers the outside. What thickness of insulating bricks is necessary between refractory silica and steel, if the heat loss should be kept at 788 W/m2? Use k =13.84 W/m-K for refractory silica; 0.15 for insulating brick, and 45 for steel. a. 220 mm* b. 240 mm c. 260 mm d. 280 mm 602. An insulated steam pipe located where the ambient temperature is 32C, has an inside diameter of 50 mm with 10 mm thick wall. The outside diameter of the corrugated asbestos insulation is 125 mm and the surface coefficient of still air, ho = 12 W/m2-K. inside the pipe is steam having a temperature of 150C with film coefficient hi = 6000 W/m2-K. Thermal conductivity of pipe and

asbestos insulation are 45 and 0.12 W/m-K respectively. Determine the heat loss per unit length of pipe. b. 110W b. 120W* c. 130W d. 140W 603. The surface transfer coefficients of the inside wall is 3.1 W/m2-K while that of the outside wall is 2.5 W/m2-K. Take the internal ambient temperature as 10C and the external temperature is 27C. Determine the heat loss through such wall 6 m high and 10 m long. a. 330.10 W b. 230.10 W c. 430.10 W d. 530.10 W 604. A counterflow heat exchanger is designed to heat fuel oil from 45C to 100C while heating fluid enters at 150C and leaves at 115C. Calculate the arithmetic mean temperature difference. a. 40C b. 50C c. 60C d. 70C 605. Water is flowing in a pipe with radius of 25.4 cm at a velocity of 5 m/s at the temperature in the pipe. The density and viscosity of the water are follows: density = 997.9 kg/m3 and viscosity of 1.131 Pa-s. what is the Reynolds no. for this situation. a. 2241* b. 96.2 c. 3100 d. 1140 606. A composite furnace is to be constructed. The inside wall temperature is 1300C while the outside wall temperature is 40C. three types of bricks are available with the following properties: Brick Thermal Conductivity Thickness Maximumallowable temperature (W/m-K) (meters) (C) A 1.50 .12 2000 B0.2 0.070 1000 C0.7 0.10 500 The heat loss must not exceed 800 W/m2. Calculate the minimum wall thickness in meters. a. 0.76 b. 0.88* c. 0.82 d. 0.77 607. A cold soda initially at 2C gains 18 kJ of heat in a room at 20C during a 15-minute period. What is the average rate of heat transfer during the process? a. 20W* b. 18W c. 12W d. 10W 608. The air contained in a room loses heat to the surroundings at a rate of 50 kJ/min while work is supplied to the room by computer. TV, and lights at a rate of 1.2 kW. what is the net amount of energy change in kJ of air in the room during a 30minute period? a. 0.36 b. 70 c. 660* d. 1100 609. Sea water for cooling enters a condenser at 25C and leaves at 40C. The condenser temperature is 45C, what is the log mean temperature difference? a. 16.34C b. 10.82C* c. 23.34 d. 12.34

610. Hot gases at 280 degC flow on one side of a metal plate of 10mm thickness and air at 35 degC flows the other side. The heat transfer coefficient of the gases is 31.5 W/m^2-k and that of the air is 32 W/m^2-K. calculate the over all transfer coefficient. a. 15.82 W/m^2-K* b. 16.82 W/m^2-K c. 14.82 W/m^2-K d. 17.82 W/m^2-K 611. Water (specific heat cv = 4.2 kJ/kg-K) is being heated by a 1500W heater. What is the rate of change in temperature of 1 kg of the water? a. 0.043 K/s b. 0.719 K/s c. 0.357 K/s* d. 1.50 K/s 612. One kilogram of water (cv = 4.2 kJ/kg-K) is heated by 300 BTU of energy. What is the change in temperature, in K? a. 17.9 K b. 71.4 K c. 73.8 K d. 75.4 K* 613. The surface of household radiator has an emissivity of 0.55 and an area of 1.5 m2. At what rate is the radiation absorbed emitted by the radiator when its temperature is 50 deg. C.? a. 308 W b. 509 W* c. 108 W d. 409 W 614. A plate type solar energy collector with absorbing surface covered by a glass plate is to receive an incident Radiation of 800 W/m^2. The glass plate has a reflectivity of 0.12 and a transitivity of 0.85. The absorbing surface has an absorptivity of 0.90. The area of the collector is 5 m^2. How much solar energy in watts is absorbed by the collector? a. 2500 b. 2880 c. 3510 d. 3060* 615. 55,000 gallons of water passes through a heat exchanger and absorbs 28,000,000 BTU’s. The exit temperature is 110F. The entrance water temperature in F is nearest to: a. 49* b. 56 c. 68 d. 73 616. What is the log mean temperature difference in C of a double-pipe counterflow heat exchanger where a fluid enters at 90C and exits at 50C. inside the inner pipe another fluid enters at 20C and exits at 60C. a.0 b. 30* c. 75 d. 35 617. Sea water for cooling enters a condenser at 25C and leaves at 40C. The condenser temperature is 45C, what is the log mean temperature difference? a.16.34C b. 10.82C* c. 23.34 d. 12.34 618. A counterflow heat exchanger is designed to heat fuel oil from 45C to 100C while heating fluid enters at 150C and leaves at 115C. Calculate the arithmetic mean temperature difference. a.40C b. 50C c. 60C* d. 70C 619. Water is boiling in a pan on a stove at sea level. During 10 minutes of boiling, it is observed that 200 grams of water has evaporated. Then the rate of heat transfer to the water is: a.0.84 KJ/min b.45.1 KJ/min* c.41.8 KJ/min d.53.5 KJ/min 620. For a heat transfer purposes, a standing man can be modeled as a 30 cm diameter, 170 cm long vertical cylinder with both the top and bottom surfaces insulated and with the side surface at an average temperature of 34 deg. C. for convection heat transfer coefficient of 15 W/m^2-C, determine the rate of heat loss from this man by convection in an environment at 20 deg. C.

a. 316.46 watts b. 326.46 watts c. 336.46 watts* d. 346.46 watts 621. Water is flowing in a pipe with radius of 25.4 cm at a velocity of 5 m/s at the temperature in the pipe. The density and viscosity of the water are follows: density = 997.9 kg/m3 and viscosity of 1.131 Pa-s. What is the Reynolds no. for this situation? a.2241* b. 96.2 c. 3100 d. 1140 622. A cold soda initially at 2 deg. C gains 18 kJ of heat in a room at 20 deg. C during a 15-minute period. What is the average rate of heat transfer during the process? a.20W* b. 18W c. 12W d. 10W 623. A counter flow heat exchanger is designed to cool 0.65 kg/sec oil with specific heat Cp = 3.4 kJ/kg-K from 150C to 70C. water cooling, Cp = 4.18 kJ/kg-K is available at 20C and flow rate of 0.6 kg/s. Calculate the length of a 3.5 cm in inside diameter tubing in meters. The overall coefficient of heat transfer is 90 W/m2-K. a.337* b. 427 c. 296 d. 543 624. Calculate the heat transfer per hour through a solid bricks wall 6m long, 2.9m high, and 225 mm thick, when the outer surface is at 5 degC and the inner surface 17 degC, the coefficient of thermal conductivity o the bricks being 0.6 W/m-K. a. 2,004.48 kJ* b. 3,004.48 kJ c. 2,400.48 kJ d. 3,400.48 kJ 625. Consider a person standing in a breezy room at 20oC. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.6 m2 and 29oC, respectively, and the convection heat transfer coefficient is 6 W/m2 with emissivity factor of 0.95. a. 86.40 watts b. 61.70 watts c. 198.1 watts d. 168.1 watts* Combustion: 626. The compression ratio of an ideal OTTO cycle is 6:1. Initial combustions are 101.3 kPa and 20°C. Find the pressure at the end of adiabatic compression. a.1244.5 kPa* b. 1246.5 kPa c. 1265.5 kPa d. 1269.5 kPa 627. The compression ratio of an OTTO cycle is 9. If the initial pressure is 150 kPa, determine the final pressure at the end of adiabatic compression process. a.1251.10 kPa b.4251.10 kPa c. 2251.10 kPa d. 3251.10 kPa* 628. In combustion process, the mixture of fuel and air is known as a.Fuel additives b.Oxidizers c.Reactants* d.Catalysts 629. Which of the following is an inert gas during the combustion process? a.Oxygen b.Nitrogen* c.Hydrogen d.Carbon monoxide 630. The apparatus commonly used to determine the volumetric percentage of the constituents of the flue gases is a.Orsat apparatus* b.Junker calorimeter c.Bomb calorimeter d.Viscosimeter

631. Which Hydrocarbon has a chemical formula of C2H5OH? a. Ethanol* b. Methane c. Octane d. Ehtane 632. Which Hydrocarbon has a chemical formula of C8H18? a. Ethanol b. Methane c. Octane* d. Ehtane 633. Which Hydrocarbon has a chemical formula of CH4? a. Ethanol b. Methane* c. Octane d. Ehtane 634. Which Hydrocarbon has a chemical formula of C2H6? a. Ethanol b. Ethane* c. Octane d. Methanol 635. For something to burn, you need fuel and air. Which part of air is needed to sustain a fire? a. Nitrogen b. Phlogiston c. Carbon Dioxide d. Oxygen* 636. Which of the following groups of chemical elements of solid fuels is included in determining the heating value using Dulong’s empirical formula? a. Carbon, freehydrogen, and nitrogen b. Carbon, free hydrogen, and sulfur* c. Carbon, free hydrogen, and oxygen d. Carbon, oxygen, and sulfur 637. The coal which is most widely distributed and used more extensively in steam power generation is a. Bituminous coal* b. Anthracite coal c. Semi-bituminous coal d. Lignite coal 638. Which of the following manufactured fuels does not belong to the group? a. Producer gas b. Coke* c. Coke-oven gas d. Blast-furnace gas 639. Octane gasoline is the most common liquid fuel used in car industry. The chemical formula for octane gasoline is a. C2H6 b. C4H10 c. C8H18* d. C3H8 640. Which of the following statements is false? a.Water has a free point of 0°C. b.The atomic weight of carbon is 12. c.Methane is one of the chief constituents of natural gas. d.Anthracite is considered a soft coal.* 641. Calculate the higher heating value of liquid dodecane fuel. The chemical formula of dodecane is C12H26. a. 48445.04 kJ/kg b. 48255.04 kJ/kg* b. c. 43850.04 kJ/kg d. 44850.04 kJ/kg 642. Calculate the minimum volume of day tank of 28°API fuel having a fuel consumption of 1 kg/s. a. 97.41 m3 * b. 96.41 m3 c. 95.41 m3 d. 95.86 m3 643. An unknown hydrocarbon fuel, CXHY, is burned with excess air containing 23.3% oxygen by mass. The volumetric analysis of the dry products of combustion is as follows: 11.94% CO2, 0.41% CO, 2.26% O2, AND 85.39% N2. Find the value of x and y, respectively. a.14.35, 44.22 b. 12.35, 33.22* c. 10.35, 32.33 d. 14.35, 32.33

644. A diesel engine takes in air at 105 kPa and 26°C subjected to a compression ratio of 19. What is the operating clearance in percent? a.5.56%* b. 6.66% c. 4.56% d. 7.56% 645. The compression ratio in a Diesel engine is 13 to 1 and the ratio of expansion is 6.5 to 1. (Use constant properties of air). a.54.04% b. 56.04% c. 58.04%* d. 52.04% 646. The ultimate analysis of coal is given below: C = 68.5% S = 1.5% Ash = 12.0% H = 2.5% O = 3.5% Calculate the higher heating value of coal. a. 25, 280 kJ/kg b. 28, 280 kJ/kg c. 27, 280 kJ/kg d. 26, 280 kJ/kg* 647. Fuel oil in a day tank for use of an industrial boiler is tested with hydrometer. The hydrometer reading indicates a S.G. = 0.924 when the temperature of the oil in the tank is 35°C. Calculate the higher heating value of the fuel. a. 43,852.13 kJ/kg* b. 53,852.13 kJ/kg c. 58,852.13 kJ/kg d. 48,852.13 kJ/kg 648. If the theoretical air-fuel ratio is 15, what is the approximate higher heating value in kJ/kgfuel? a. 46,755 kJ/kg* b. 56,755 kJ/kg c.45,765 kJ/kg d.55,765 kJ/kg 649. Calculate the calorific value of coal, which has the following analysis: Carbon 81%, Hydrogen 5%, Oxygen 5.6%, Sulfur 1% and the remainder is ash content. a. 12,456.34 kJ/kg b. 32,457.45 kJ/kg c. 33,688.35 kJ/kg* d.32,135.45 kJ/kg 650. A petrol has the following analysis 85.5% Carbon, 14.4% Hydrogen, and 0.10% Sulfur. Calculate the volume of air at 1.0 bar and 15°C required for perfect combustion of 1 kg of the fuel. Note: Rair = 0.287 kJ/kg-K. a. 13.45 m3air/kgfuel b. 12.24 m3air/kgfuel* c. 15.54 m3air/kgfuel d. 14.57 3 m air/kgfuel 651. Calculate the minimum volume of day tank of 28°API fuel having a fuel consumption of 1 kg/s. a. 97.41 m3 * b. 96.41 m3 c. 95.41 m3 d. 95.86 m3 652. A gaseous mixture has the following molal analysis: H2=14% N2=50.9% CO2=4.5% O2=0.6% CH4=3% CO=27% Determine the Air-Fuel ratio for complete combustion on molal basis. 𝑚𝑜𝑙𝑒𝑠 𝑎𝑖𝑟 𝑚𝑜𝑙𝑒𝑠 𝑎𝑖𝑟 a. 1.233 * b. 1.533 c. 1.033

𝑚𝑜𝑙𝑒𝑠 𝑓𝑢𝑒𝑙 𝑚𝑜𝑙𝑒𝑠 𝑎𝑖𝑟

𝑚𝑜𝑙𝑒𝑠 𝑓𝑢𝑒𝑙

d. 1.933

𝑚𝑜𝑙𝑒𝑠 𝑓𝑢𝑒𝑙 𝑚𝑜𝑙𝑒𝑠 𝑎𝑖𝑟 𝑚𝑜𝑙𝑒𝑠 𝑓𝑢𝑒𝑙

653. A bituminous coal has the following composition: C = 71.5% O = 7% S = 3.6% W = 3.4 H = 5% N = 1.3% ASH = 8.2% Calculate for complete combustion the theoretical weight 𝑘𝑔 𝑎𝑖𝑟 of air required in . 𝑘𝑔 𝑐𝑜𝑎𝑙

a. 6.8 b. 7.8 c. 8.8 d. 9.8* 654. An unknown hydrocarbon fuel, CXHY, is burned with excess air containing 23.3% oxygen by mass. The volumetric analysis of the dry products of combustion is as follows: 11.94% CO2, 0.41% CO, 2.26% O2, AND 85.39% N2. Find the value of x and y, respectively. a. 14.35, 44.22 b. 12.35, 33.22* c. 10.35, 32.33 d. 14.35, 32.33 655. A typical industrial fuel oil, C16H32 with 20% excess air by weight. Assuming complete oxidation of the fuel, calculate the actual air-fuel ratio by weight. a. 17.56 kgair/kgfuel b. 15.76 kgair/kgfuel c. 16.75 kgair/kgfuelf d. 17.65 kgair/kgfuel* 641. A diesel power plant consumed 1 m3 of fuel with 30 API at 27C in 20 hrs. calculate the fuel rate in kg/hr. a.36.21 b. 26.25 c. 29.34 d. 43.45*

656. The heating value of fuel supplied in a boiler is 43,000 kJ/kg. If the factor of evaporation is 1.10 and the actual specific evaporation is 10, what is the efficiency of the boiler? a. 62.07% b. 53.08%c. 78.05% d. 57.77%* 657. The density of fuel having 28 Baume is: a. 0.886* b. 0.871 c. 0.893 d . 0.654 658. Find the density of fuel at 50C if fuel used is 27 API. a. 763.556 kg/m3 b. 834.56 kg/m3 c. 853.45 kg/m3 d. 871.30 kg/m3* 659. A diesel power plant uses fuel that has a density of 887.14 kg/m3 at 15.66C. find the heating value. a. 44,680 kJ/kg b. 19,361 Btu/lb* c. 43,000 kJ/kg d. 45,178.8 kJ/kg 660.A gaseous fuel mixture has a molar analysis: H2 = 14% CH4 = 3% CO = 27% O2 = 0.6% CO2 = 4.5% N2 = 50.9% Determine the air – fuel ratio for complete combustion on molar basis. A. 2.130 B. 3.230 C. 1.233* D. 1.130 661. A bituminous coal has the following composition: C = 71.5% H = 5.0% O = 7.0% N = 1.3% S = 3% Ash = 7.6% W = 3.4% Determine the theoretical weight of Nitrogen in lb/lb of coal. A. 2.870 B. 7.526 * C. 2.274 D. 6.233 662. A diesel power plant uses fuel with heating vlue of 43,000 kJ/kg. What is the density of the fuel at 25C? A. 840 kg/m3 B. 873 kg/m3 C. 970 kg/m3* D. 940 kg/m3 663. The heating value of fuel supplied in a boiler is 43,000 kJ/kg. If the factor of evaporation is 1.10 and the actual specific evaporation is 10, what is the efficiency of the boiler? A. 62.07% B. 53.08% C. 78.05% D. 57.77%* 664.. Find the density of fuel at 50C if fuel used is 27 API. A. 763.556 kg/m3 B. 834.56 kg/m3 C. 853.45 kg/m3 D. 871.30 kg/m3* ME Laws: 665. The Mechanical Engineering Law is also known as A. RA 8459 * C. RA 5984 B. RA 3449 D. RA 6561 666. The Article V of the the Mechanical Engineering Law A. TITLE, STATEMENT OF POLICY, AND DEFINITION OF TERMS B. PENAL AND CONCLUDING PROVISIONS* C. PRACTICE OF THE PROFESSION D. CONCLUSION 667. Article V, Sec. 43 talks about A. Implementing Rules and Regulations* B. Penalties C. Transitory Provisions D. Funding Provisions 668. The Article I, Sec. 1 of the Mechanical Engineering Law A. statement of policy C. Title * B. Definition of terms D. Creation and Composition of the Board 669. According to Sec 42, t any person who violates any of the provisions of this Act and its rules and regulations shall, upon conviction be penalized by a fine of not less than A. P 50, 000 * C. P40, 000 B. 30, 000 D. P100, 000

670. To comply with the requirement of the Mechanical Engineering Law on the minimum complement of mechanical engineers, a mechanical plant with a combine prime movers rating of 373 KW must have in its employ the following. A. 1 PME, 1 RME, and 1 CPM C. 1 RME, 2 CPM B. 1 PME, 2 RME*D. 1 RME is charge of every shift 671. Mechanical Plant Engineer (MPE) may be allowed to take the licensure examination for PME if A. He has 4 years practice as a MPE* B. If he graduated with a BMSE degree and has a 4 years of practice as a RME C. If he has a BSME degree, passed the examinations for RME and has 4 years practice as RME. D. None of these 672. The only country that recognizes the mechanical engineering licensure of Filipinos issued by the Professional Regulation Commission and allowed to use the practice as RME. A. America B. Canada C. Japan D. none of these* 673. The ratio between the average load and total available capacity A. load factor B. power factor C. demand factor D. capacity factor* 674. In Roman numerals, the bar written above with the letter indicates that the number equivalent to the letter is to be multiplied by A. 100 B. 1,000 C. 10,000* D. 100,000 675. The reciprocating machine part within a cylinder is called a. ram b. plunger c. slide mandrel d. all of the above * 676. Fixed-mounted or movable hood guards covering the length of run of power chains. a. coupling guards b. chain guards * c. belt guards d. hood guards 677. A boom type mobile crane mounted on endless tracks or thread belts. a. gantry crane b. jib crane c. locomotive crane d. crawler crane * 678. A mechanical contrivance for raising or lowering a load. a. crane b. hoist * c. rope d. chain 679. A horizontal arm for supporting a trolley or fall blocks which does not change its inclination with the horizontal. a. clevis b. boom c. hood d. jib * 680. On existing installation boiler, the lowest factor of safety permissible shall be a. 7 b. 6 c. 5 d. 4.5 *

681. The age limit of a horizontal return tubular flue or cylinder boiler having a longitude lap joint and operating at a pressure in excess of 0.345 MPa or 3.45 bar gage shall be: a. 18 years b. 35 years c. 30 years * d. 20 years 682. All proposed installation, additions and alterations involving machinery, mechanical equipment or process shall be covered by plans and specifications prepared by or under the supervision of a: a. Mechanical Plant Engineer (MPE) b. Professional Mechanical Engineer (PME)* c. Registered Mechanical Engineer (RME) d. Certified Plant Mechanic(CPM) 683. Minimum grade of Mechanical Engineer required to supervise operation of a 500 kW diesel engine. a. RME * b. PME c. CPM d. MPE 684. Following the ASA code for the pressure piping, which pipe is used in power plants for small control lines, condenser tubes and for tubular water heater? a. copper alloy b. cast iron c. carbon steel * d. wrought iron 685. On existing installation boiler, the lowest factor of safety permissible shall be a. 7 b. 6 c. 5 d. 4.5 * 686. The age limit of a horizontal return tubular flue or cylinder boiler having a longitude lap joint and operating at a pressure in excess of 0.345 MPa or 3.45 bar gage shall be: a. 18 years b. 35 years c. 30 years * d. 20 years 687. All proposed installation, additions and alterations involving machinery, mechanical equipment or process shall be covered by plans and specifications prepared by or under the supervision of a: a. Mechanical Plant Engineer (MPE) b. Professional Mechanical Engineer (PME)* c. Registered Mechanical Engineer (RME) d. Certified Plant Mechanic(CPM) 688. Minimum grade of Mechanical Engineer required to supervise operation of a 500 kW diesel engine. a. RME * b. PME c. CPM d. MPE 689. Following the ASA code for the pressure piping, which pipe is used in power plants for small control lines, condenser tubes and for tubular water heater? a. copper alloy b. cast iron c. carbon steel * d. wrought iron 690. Which of the following common wealth act is known as the oldest Mechanical Engineering law? a. Commonwealth Act 394 b. Commonwealth Act 594 c. Commonwealth Act 294 * d. Commonwealth Act 8394 691. Prior to Republic Act 8495, what law governs the practice of mechanical engineering the Philippines? a. Republic Act No. 5124 b. Commonwealth Act No. 294 * c. Commonwealth Act No. 293 d. Republic Act No. 2934

692. One best known practices in industrial plant is: a. To provide alert security guards b. To provide machines with appropriate guards* c. To maintain a fire brigade d. To train delivery personnel 693. Which of the four does not belong to the group? a. Class D Fire – fire caused by LPG * b. Class B Fire – fire caused by oil and other hydrocarbons c. Class C Fire – electrical fire d. Class A Fire – fire caused by light combustible materials like paper and wood 694. All heavy machinery should be supported on solid foundations of sufficient mass and base area to prevent or minimize transmission of a. objectionable vibration to the building and occupied space * b. objectionable vibration of forces from nearby machine c. better control of the drainage system d. objectionable sound coming from the exhaust 695. The reciprocating machine part within a cylinder is called a. ram b. plunger c. slide mandrel d. all of the above * 696. Fixed-mounted or movable hood guards covering the length of run of power chains. a. coupling guards b. chain guards * c. belt guards d. hood guards 697. A boom type mobile crane mounted on endless tracks or thread belts. a. gantry crane b. jib crane c. locomotive crane d. crawler crane * 698. A mechanical contrivance for raising or lowering a load. a. crane b. hoist * c. rope d. chain 699. A horizontal arm for supporting a trolley or fall blocks which does not change its inclination with the horizontal. a. clevis b. boom c. hood d. jib * Basic Electronics 700. An ideal voltage source has a. Zero internal resistance* b. Infinite internal resistance c. A load-dependent voltage d. A load-dependent current 701. An ideal current source has a. Zero internal resistance b. Infinite internal resistance* c. A load-dependent voltage d. A load-dependent current 702. The net charge of a neutral copper atom is a. 0* b. +1 c. -1 d. +4 703. The valence electron of a copper atom experiences what kind of attraction toward the nucleus? a. None b. Weak* c. Strong d. Impossible to say

704. If you wanted to produce a p-type semiconductor, which of these would you use? a. Acceptor atoms* b. Donor atoms c. Pentavalent impurity d. Silicon 705. A zener diode a. Is a battery b. Has a constant voltage in the breakdown region* c. Has a barrier potential of 1 V d. Is forward-biased

714.Ignoring the bulk resistance of the collector diode, the collector-emitter saturation voltage is a. 0* b. A few tenths of a volt C. 1 V d. Supply voltage 715. A semiconductor has how many types of flow? a. 1 b. 2* c. 3 d. 4

706. A germanium diode is connected to a load resistance of 1.5 kΩ and is supplied with 12-V such that the diode will be forward biased. What is the voltage across the diode? a. approximately 12 V b. approximately 0.7 V c. approximately 0.3 V* d. lack of data and can’t be solved

716. The flow of valence electrons to the left means that holes are flowing to the a. Left b. Right* c. Either way d. None of the above

707. What is the drop across the diode when it is connected in series to a resistor of 1.8 kΩ and a supply voltage of 50 V. The supply voltage causes the diode to be reverse-biased. a. 50 V* b. 0.7 V c. 0.3 V d. can not be solve, lack of data 708. __________is the procedure by which an atom is given a net charge by adding or taking away electron. a. Polarization b. Irradiation c. Ionization * d. Doping 709. What is the peak load voltage out of a bridge rectifier for a secondary voltage of 15 V rms? (Use second approximation.) a. 9.2 V b. 15 V c. 19.8 V * d. 24.3 V For numbers 96-99 refer to the network below

717. If you wanted to produce a p-type semiconductor, which of these would you use? a. Acceptor atoms* b. Donor atoms c. Pentavalent impurity d. Silicon d. Impossible to say 718. What is the drop across the diode when it is connected in series to a resistor of 1.8 kΩ and a supply voltage of 50 V. The supply voltage causes the diode to be reverse-biased. a. 50 V* b. 0.7 V c. 0.3 V d. can not be solve, lack of data 719. __________is the procedure by which an atom is given a net charge by adding or taking away electron. a. Polarization b. Irradiation c. Ionization * d. Doping 720. How many protons , neutrons, and electrons are in the carbon isotope C-14? a. 6 protons, 6 electrons and 8 neutrons* b. 8 protons, 6 electrons and 8 neutrons c. 6 protons, 6 electrons and 10 neutrons d. 6 protons, 8 electrons and 8 neutrons 721. A certain reaction is first order in A. The specific rate constant is 3E-3/s. The half life is. A. 2.1E-3 s b. 100 s c. 231 s* d. 768 s 722. A radioactive material has a half-life of 68.3 min. What percentage of the original sample will remain at the end of 3 hr? a.16.2 %* b. 12.7 % c. 21.4 % d. 0

710.Output current is a. 3.11mA c. 3.2mA* b. 6.04 mA d. none of the these 711.Current gain is a. 10.1 A c. 80* b. 90 d. none of the these 712. Rc is a. 1.5kΩ b. 282kΩ

c. 1.875kΩ* d. none of the these

713.Vce is a. 0.7V b. 2.7V

c. 6V* d. none of the these

723. Determine the frequency of light having a wavelength of 1 angstrom. a.3.0 E 18 Hz b. 3.0 E 17 Hz c. 3.0 E 16 Hz d. 0 724. If the infrared radiation has a wavelength of 3.5 microns, what will be the wave number in 𝑐𝑚−1 ? a.3,000 b. 2,500 c. 2,900* d. 2,700 725. A 50-microfarad capacitor discharges through a 100 kilo ohms resistor. What is the time constant of a circuit? A. 5 sec* C. 0.5 sec B. 0.05 sec D. 5 ms 726. The region in an electronic transistor that is very lightly doped and very thin is referred to the ___. a.Collector B. emitter C. Base* D. collector-base

727. The output electrode of a bipolar transistor is usually the A. gate B. base C. source D. collector* 728. In a rectifier diode, current flows for approximately how much of the ac cycle A. 90 degrees B. 180 degrees* C. 270 degrees D. 360 degrees 729. A device that can deliver high voltage AC from a low voltage DC source. A. transformer B. inverter* C. converter D. power supply 730. The purpose of the ballast in a fluorescent lamp assembly is A. To regulate the voltage across the lamp B. To improve the overall power factor C. To limit the current through the lamp* D. To regulate the lumens output 731. If N1/N2 = 2, and the primary voltage is 120 V, what is the secondary voltage? A. 0 V B. 36 V C. 60 V * D. 240 V 732.A transformer has a turns ratio of 4: 1. What is the peak secondary voltage if 115 V rms is applied to the primary winding? A. 40.7 V * B. 64.6 V C. 163 V D. 650 V 733.Line voltage may be from 105 V rms to 125 rms in a halfwave rectifier. With a 5:1 step-down transformer, the maximum peak load voltage of an ideal approximation is closest to A. 21 V B 25 V C. 29.6 V D. 35.4 V* 734..What is the peak load voltage out of a bridge rectifier for a secondary voltage of 15 V rms? (Use second approximation.) A. 9.2 V B. 15 V C. 19.8 V * D. 24.3 V AC/DC 735. An ideal step-up transformer with 100 turns in the primary and 2500 turns in the secondary carries a load of 2A in the secondary windings. What is the current in the primary side? A. 50A* C. 25A B. 0.08A D. 1,250A 736.Gearmotors are selected based on which of the following? A. Speed requirement C. both A and B* B. Torque reuirement D. neither A or B 737. If N1/N2 = 2, and the primary voltage is 120 V, what is the secondary voltage? A. 0 V C. 60 V * B. 36 V D. 240 V 738.A transformer has a turns ratio of 4: 1. What is the peak secondary voltage if 115 V rms is applied to the primary winding? A. 40.7 V * C. 163 V B. 64.6 V D. 650 V 739. Line voltage may be from 105 V rms to 125 rms in a halfwave rectifier. With a 5:1 step-down transformer, the maximum peak load voltage of an ideal approximation is closest to A. 21 V C. 29.6 V B. 25 V D. 35.4 V * 740. Which law(s) find application in electrolysis? A. Ohm’s law C. Faraday’s law* B. Coulomb’s law D. Gauss’s law 741. For a constant current source supplying two branch parallel resistors whose resistances are R and 2R respectively, what current will flow the R ohms resistor A. ½ that of the other C. twice that of the other* B. two thirds of the other D. one third of the other

742. A 15 ohm resistor is connected in series with the parallel combination of 6 and 4 ohms resistor respectively. Calculate the total conductance of the circuit? A. 0.0575* C. 0.0757 B. 0.0686 D. 0.0868 743. The current in the conductor changes uniformly from zero to 2 A in 3 sec. Remain steady at 2 A for 6 sec, and then drops uniformly to 1.5 A in 8 sec. Calculate the total amount of charge for the total elapsed time of 17 sec. A. 30 C C.29 C* B. 24 C D. 35 C 744. Six cells are connected in parallel and the group is connected to an external resistance of 0.69 ohm. If the emf of each cell is 1.4 volts and internal of each is 0.06 ohm, the total current is A. 1.69 A C. 2 A* B. 2.8 A D. 2.2 A 745. If line frequency is 60 Hz, the output frequency of a bridge rectifier is a. 30 Hz c. 120 Hz * b. 60 Hz d. 240 Hz 746. If N1/N2 = 2, and the primary voltage is 120 V, what is the secondary voltage? a. 0 V c. 60 V * b. 36 V d. 240 V 747. A transformer has a turns ratio of 4: 1. What is the peak secondary voltage if 115 V rms is applied to the primary winding? a. 40.7 V * c. 163 V b. 64.6 V d. 650V 748. Line voltage may be from 105 V rms to 125 rms in a halfwave rectifier. With a 5:1 step-down transformer, the maximum peak load voltage of an ideal approximation is closest to a. 21 V c. 29.6 V b. 25 V d. 35.4 V * 749. If the base current is 100 mA and the current gain is 30, the collector current is a. 300 mA c. 3.33 A b. 3 A * d. 10 A 750. Frequency f of monochromatic yellow light which as a wavelength £ of 589 nm (nanometers) in vacuum is nearest to: a. 295, 000 Ghz b. 510, 000 Ghz * c. 589, 000 Ghz d. 1, 020, 000 Ghz 751. The audible sound frequency is in the range of which of the following a. Above 20,000 Hz b. below 20 Hz c. between 100 and 1000 Hz d. 10 to 20,000 Hz * 752. Two resistances of 8 and 10 ohms respectively are connected in parallel and take a total current of 9A. What is the current flowing in the 8 – ohm resistance? a. 5 A * c. 2 A b. 4 A d. 3 A 753. An electric iron takes 3.5A. If the heating element has a resistance of 40 ohms, what is its power consumption? a. 0.44 kW c. 0.53 kW b. 0.49 kW * d. 0.52 kW 754. Find the amperage of a 5 kVA load on a 220V, three-phase branch circuit? a. 13 A * c. 12.7 A b. 8.66 A d. 25 A 755. What is the equivalent capacitance of two series capacitors rated 4 and 6 µF respectively? a. 2.4 * c. 0.416 b. 10 d. 0.9

756. Three resistorsR_1, R_2 and R_3 are connected in series across a 100-V source. If R_2 opens, the a. Voltage across R_2 is 100V * c. voltage across R_1 is 100V b.Total resistance decreases d. voltage across R_2 is zero

757. What is 50 gradients equal to in degrees? a. 100 deg c. 20 deg b. 45 deg d. 90 deg 758. When one metal bar is heated. The other part gradually becomes heated, that is, energy will flow from hot part to cold part. What is the mode of heat transfer? a. radiation c. conduction * b. convection d. fusion 759. What is the power required to transfer 97,000 coulumbs of charge through a potential rise of 50 volts in one hour? a. 0.55 kW c. 0.9 kW b. 1.3 kW * d. 2.8 kW 760. Frequency f of monochromatic yellow light which as a wavelength £ of 589 nm (nanometers) in vacuum is nearest to: a. 295, 000 Ghz b. 510, 000 Ghz * c. 589, 000 Ghz d. 1, 020, 000 Ghz 761. The audible sound frequency is in the range of which of the following a. Above 20,000 Hz b. below 20 Hz c. between 100 and 1000 Hz d. 10 to 20,000 Hz * 762. Two resistances of 8 and 10 ohms respectively are connected in parallel and take a total current of 9A. What is the current flowing in the 8 – ohm resistance? a. 5 A * c. 2 A b. 4 A d. 3 A 763. An electric iron takes 3.5A. If the heating element has a resistance of 40 ohms, what is its power consumption? a. 0.44 kW c. 0.53 kW b. 0.49 kW * d. 0.52 kW 764. Find the amperage of a 5 kVA load on a 220V, three-phase branch circuit? a. 13 A * c. 12.7 A b. 8.66 A d. 25 A 765. What is the index of refraction of a material if the speed of light through the material is 2.37 x 108 m/s? a. 1.10 c. 1.27 * b. 1.19 d. 1.34 766. To produce a large forward current in a silicon diode, the applied voltage must be greater than a. 0 c. 0.7 V * b. 0.3 V d. 1 V 767. How is a nonconducting diode biased? a. Forward c. Poorly b. Inverse d. Reverse * 768. What is the drop across the diode when it is connected in series to a resistor of 1.8 kΩ and a supply voltage of 50 V. The supply voltage causes the diode to be reverse-biased. a. 50 V * c. 0.3 V b. 0.7 V d. cannot be solve, lack of data 769. What is the peak load voltage out of a bridge rectifier for a secondary voltage of 15 V rms? (Use second approximation.) a. 9.2 V c. 19.8 V * b. 15 V d. 24.3 V

770. A semiconductor has how many types of flow? a. 1 c. 3 b. 2 * d. 4 771. The net charge of a neutral copper atom is a. 0 * c. -1 b. +1 d. +4 772. The valence electron of a copper atom experiences what kind of attraction toward the nucleus? a. None c. Strong b. Weak * d. Impossible to say

773. An ideal voltage source has a. Zero internal resistance c. A load-dependent voltage b. Infinite internal resistance *d. A load-dependent current 774. If you wanted to produce a p-type semiconductor, which of these would you use? a. Acceptor atoms * c.Pentavalent impurity b. Donor atoms d. Silicon