Civil Engineering Exams (Civil Math) – Page 3

#40. A spherical sector is cut from a sphere whose radius if 12 cm. Find its volume it its central angle is \(30^o\).
A 133.3 cu. cm
B 132.3 cu. cm
C 150.3 cu. cm
D 123.3 cu. cm
Answer: 123.3 cu. cm
#41. If arc Sin (3x -4y ) = 1.571 and arc Cos(x-y) = 1.047 find x.
A 1
B positive infinity
C -1
D None of the above
Answer: 1
#42. A circle having a radius of 9cm. circumscribes a right triangle whose area is 43.23sq.cm. If one of the sides if 18cm long., another side is_____
A 15cm
B 5cm
C 10cm
D 4cm
Answer: 5cm
#43. Given the data: find Y.
Lines LAT DEP DMD 2A
AB 445.56 30.371 30.3731 1372.324
BC Y 75.451 X 2158.023
CD -58.328 ---- 148.621 -8668.766
DA -2.090 -42.439 ----- Z
A 15.762
B 65.24
C -78.8
D 34.2
Answer: 15.762
#44. Given the data: find Z.
Lines LAT DEP DMD 2A
AB 445.56 30.371 30.3731 1372.324
BC Y 75.451 X 2158.023
CD -58.328 ---- 148.621 -8668.766
DA -2.090 -42.439 ----- Z
A -95.3
B 136.913
C 15.762
D -88.698
Answer: -88.698
#45. A boat makes 25 mph in still water. It is headed N 45 E in a 7.5 mph water current flowing east. Find the direction of the course of the boat.
A N 45E
B N 20.5 E
C N 9.93 E
D N 54.93 E
Answer: N 54.93 E
#46. Find the equation of the plane that contains the point(2, -4, 1) and is perpendicular to the vector equal to 2i-3j+4k.
A 2x -3y +4z = 20
B 3x -2y +4z = 20
C 3x -4y +2z = 20
D 4x -3y +2z = 20
Answer: 2x -3y +4z = 20
#47. Find the acute angle in radians between the plane 2x - 4y – x + 5 = 0 and 3x + 4y + 5z + 6 = 0.
A 1.09 rad
B 62.4 \(\pi\) rad
C 117.6 rad
D 2.1 rad
Answer: 1.09 rad
#48. Find the vector that is perpendicular to the plane passing through the points A(1, 2, 6), B(4, 4, 1) and C (2, 3, 7).
A 7i -8j -k
B 7i -8j +k
C 8i -7j -k
D 7i +8j +k
Answer: 7i -8j +k
#49. What is the absolute value of 5-3i?
A \(\sqrt {24}\)
B \(\sqrt {15}\)
C \(\sqrt {34}\)
D \(\sqrt {8}\)
Answer: \(\sqrt {34}\)
#50. What is the value of \( \frac{3-2i}{2-i}\)?
A \( \frac{8i}{5}\)
B \( \frac{8-3i}{5}\)
C \( \frac{8+i}{5}\)
D \( \frac{8-i}{5}\)
Answer: \( \frac{8-i}{5}\)
#51. Evaluate \( \int _{0}^{\frac{\pi}{2}} cos^6x sin^7x dx \)
A 5.3
B Undefine
C 0.0053
D 0.035
Answer: 0.0053
#52. Evaluate \(\int_{1}^{2} \frac{lnx}{x} dx\)
A 0.24
B 0.12
C 0.25
D 0.36
Answer: 0.24
#53. Solve for x if 2ix -5 +3i = (2-i)x + i
A \(\frac{-16-11i}{13}\)
B \(\frac{16+11i}{13}\)
C \(\frac{11+16i}{13}\)
D \(\frac{-11-16i}{13}\)
Answer: \(\frac{-16-11i}{13}\)
#54. Evaluate \(\int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} csc x cot x dx\)
A 1
B 2
C 0.0
D infinite
Answer: 0.0
#55. A machine costing P 1, 000, 000 is expected to produce 10, 000 units of steel pipe during its entire life before being replaced. At the end of its life it will have a scrap value of P50, 000. The cost of housing the machine is P25, 000 a year. The power consumption per unit is P9 and the maintenance of the machine per unit will be P7. If depreciation if the Sinking Fund Method at 12% and the annual production is 2, 500 units. What is the fixed cost per unit produced?
A P50
B P51
C P52
D P53
Answer: P51
#56. A machine costing P 1, 000, 000 is expected to produce 10, 000 units of steel pipe during its entire life before being replaced. At the end of its life it will have a scrap value of P50, 000. The cost of housing the machine is P25, 000 a year. The power consumption per unit is P9 and the maintenance of the machine per unit will be P7. If depreciation if the Sinking Fund Method at 12% and the annual production is 2, 500 units. What is variable cost per unit?
A 89.51
B 51.89
C 69.51
D 61.51
Answer: 89.51
#57. A machine costing P 1, 000, 000 is expected to produce 10, 000 units of steel pipe during its entire life before being replaced. At the end of its life it will have a scrap value of P50, 000. The cost of housing the machine is P25, 000 a year. The power consumption per unit is P9 and the maintenance of the machine per unit will be P7. If depreciation if the Sinking Fund Method at 12% and the annual production is 2, 500 units. What it the total production cost per unit?
A 89.51
B 150.51
C 151.51
D 140.51
Answer: 140.51
#58. Object A approaches object B which is stationary. Velocity of object A is V = 25i + 4j -5k in m/s. Mass of A = 10kg, and that of B = 4 kg. After impact, the two objects sticks together. Compute the x component of the velocity after impact.
A 18.36i
B 19.55i
C 17.863i
D 12.25i
Answer: 17.86i
#59. Object A approaches object B which is stationary. Velocity of object A is V = 25i + 4j -5k in m/s. Mass of A = 10kg, and that of B = 4 kg. After impact, the two objects sticks together. Compute the y component of the velocity after impact.
A 4.2j
B 3.27j
C 2.45j
D 2.86j
Answer: 2.86j