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MARCH 2005
DEPARTMENT OF ELECTRICAL ENGINEERING
Wednesday, Mar 29, 2006 8:00-12:00 NN
ELECTRICAL ENGINEERING SET A SEAT NO.____
INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
1. What is the force on a +5x10
-11
C charge that is 5 cm from each of two +2x10
-9
C charges that are separated by 8 cm?
A. 0.8906 µ N C. O. 4314 µ N
B. 0. 6927 µ N D. 0. 7924 µ N
2. A 0 –10 ampere ammeter with internal resistance of 0.01 ohm. What shunt resistance do the ammeter be connected to have a
range of 0-100 ammeter?
A. 1.11 x 10
-3
C. 0.111
B. 1.0 x 10
-3
D. 0.1
3. A 10 kw, 250 v shunt generator, having an armature resistance of 0.1 Ω and a field resistance of 250 Ω, delivers full-load at
rated voltage and 800 rpm. The machine is now running as a motor while taking 10 KW at 250 V. What is the speed of the
motor? Neglect brush contact drop.
A. 896 RPM C. 650 RPM
B. 774.8 RPM D. 980 RPM
4. A 240 v motor requiring 2000 W is located 1 km from a power source. What minimum copper wire diameter is to be used if the
power loss is to be kept less than 5% of the motor power?
A. 0.217 in C. 0.424 in
B. 0.325 in D. 0.675 in
5. A 2,400 volt, 100 KVA transformer has an equivalent impedance of 0.708 + j 0.92 ohms. Determine the equivalent IZ voltage
at one - half rated current.
COMPREHENSIVE EXAM Page 1 of 5
March 27-29, 2006

2. A. 12. 12 v C. 43. 49 v
B. 32. 45 v D. 24.24 v
6. A 200 microfarad capacitor is connected in series with a 10 ohm resistors. The circuit is connected to a 24v battery. What is
the initial current on putting the switches on?
A. 2.4 amperes C. 0.025 ampere
B. 1.2 ampere D. 0.26 ampere
7. A 3-phase alternator generates an open-circuit phase voltage of 4000 V when exciting current is 50 A; the short circuit current
for the same excitation being 800 A. The synchronous reactance per phase is ____.
A. 80Ω B. 5Ω C. 15Ω D 46.2 Ω
8. A 5 km long, three-phase line has a horizontal configuration of 4 ft spacing. The conductor is 336.4 MCM ACSR with GMR of
0.0244 ft and a resistance of 0.306 ohms per mile. What is the impedance?
A. 2.22 cis 65 C. 1.19 cis 46
B. 6.66 cis 65 D. 3.57 cis 46
9. A 55,000 kW thermal plant delivers an annual output of 238,000,000 kW-hr with peak load of 44 MW. What is the capacity
factor?
A. 49.4% B. 42.4% C. 48.2% D. 44.6%
10. A classroom 15ft. x 10ft height , having 2ft. ceiling cavity and 3f. floor cavity. What is the height of the room cavity of the said
classroom?
A. 300 ft C. 5 ft
B. 3000 ft. D. 3 ft
11. A DC series motor is running at rated speed, voltage, and current when the load torque increases by 25%. Determine the
effects of this change (power drop), assuming that the line voltage remains the same.
A. 5% B. 1% C. 15% D. 10%
12. A diesel plant as has an overall efficiency of 30%, the heating value of diesel is 18,000 btu per lb. If diesel cost of P6.00 per
liter. What is the fuel cost of production in peso per kwh. Take density of diesel to be 900 grams per litter.
A. 1.91 kwh C. 1.12 kwh
B. 1.85 kwh D. 2.45 kwh
13. A farm is supplied with 30kW at 0.8 pf and 415 V from two small hydro-electric plants A and B. Station A has an alternator and
is at the end of a 3 phase line of impedance 0.6 + j0.8 Ω per phase. Station B at the middle if this line has an induction
generator supplying 15 kW at power factor 0.09. Find the power supplied by the alternator.
A. 19.4 KW C. 9.8 KW
B. 12.5 KW D. 29.3 KW
14. A germanium diode which has an offset voltage of 0.2 V and an incremental resistance of 20 ohms, is connected in series with
a 10, 000 ohm resistor across a 100 V DC source. What is the current?
A. 9.98 mA C. 9.78 mA
B. 10 mA D. 9.96 mA
15. A manufacturing firm operates a 10 MW power plants, the voltage is 480 volts, 3-phase and rated power factor is 85%. The
monthly generation is 5,000,000 Kw-hr at 90% power factor. What is the average plant load factor?
A. 69.4% C. 76.66%
B. 90% D. 85%
16. A piece of conductor 10 cm long moves across a magnetic field of 10,000 grams at a velocity of 120 cm. sec. What voltage
appears across the conductor?
A. 0.24 V C. 0.12 V
B. 60 V D. 120 V
COMPREHENSIVE EXAM Page 2 of 5
March 27-29, 2006

3. 17. A piezoelectric transducer is
A. an Italian C. a ceramic disk to produce sound
B. a device used as a receiver D. a device used as a transmitter
18. A plant has a total generating capacity of 800 kilowatts. The coal consumption is 1900 lbs per hours. Heating value of coal is
9,500 BTU per lb. What APROXIMATE percent of the heat in the coal is converted into useful energy?
A. 12.3 C. 15.0
B. 8.7 D. 17.5
19. A separately excited motor runs at 1045 rpm, with a constant field current, while taking an armature current of 50 A at 120 V.
The armature resistance is 0.1 ohms. If the load on a motor changes such that it now takes 95 A at 120 V , determined the
speed at this load
A. 1004 rpm B. 1020 rpm C. 1110 rpm D. 975 rpm
20. A series RC circuit consist of R = 2 M ohms and a uncharged capacitors C = 5 µF. The circuit voltage E of 100 volts is applied
across the series circuit at t = 0 and the initial current i900 = 5a. The applicable differential equation is : R (di/dt) + i/c=0.
Solve the differential equation and determine the resulting current I(t) at t = 0.01 seconds
A. 3.34 A C. 3.67 A
B. 2.78 A D. 3.03 A
21. A synchronous motor
A. will have a low power factor when run below rated speed
B. may have its speed varied by inserting a rheostat in the D.C. field circuit
C. will slow down with an increase in load within the limits of its pull-out torque
D. will take minimum line current at any load when operating at unity power factor
22. An impedance draws a current i = 10 cos (wt – 30
o
) from a voltage v = 220 sin wt. What is the maximum power?
A. 2200 watts C. 1100 watts
B. 190.5 watts D. 1320 watts
23. An operational amplifier has a gain-bandwidth product of 2π x 10
7
rad/s. The amplifier is used as an inverting mode with a
feedback resistance of 25, 000 ohms and an input resistance of 5, 000 ohms. The gain of the circuit is
A. -10 B. -5 C. 0 D. 10
24. An unbalanced wye connected system
Ia = 10 cis (-32
o
) Vna = 132 cis 0
o
Ib = 13 cis (212
o
) Vnb = 130 cis 235
o
Ic = 14 cis 86
o
Vnc = 133 cis 117
o
A. 2820 C. 4271
B. 4325 D. 3650
25. At a certain location an electric system, the available faults MVA is 400 MVA. A 15 MVA, 34.5 kV/6.24 kV, 25% impedance,
wye-wye grounded transformer is installed at the location. Determine the short circuit MVA at the secondary side of the
transformer
A. 195 MVA B. 150 MVA C. 90 MVA D. 240 MVA
26. For ac transmission, whether overhead or underground, the most unsuitable system is the
A. three phase, three wire
B. three phase, four wire
C. single phase
D. two phase, three wire
27. In a short circuit study, the positive , negative and the zero sequence impedance are 0.25 p.u. and 0.25 p.u and 0.3 p.u
respectively. The base MVA is 100. Determine the fault current for a three-phase fault at 155 kV level.
COMPREHENSIVE EXAM Page 3 of 5
March 27-29, 2006

4. A. 3000 A C. 2000 A
B. 2500 A D. 3500 A
28. Interior and exterior wiring, including power, lighting, control and signal circuit wiring together with associated hardware,
fittings, and wiring devices, both temporarily and permanently installed is called _____________ wiring.
A. Premises C. Branch circuit
B. Feeder D. General circuit
29. Of the various methods of utilizing the heat from the sun, one appears to be the most efficient so far. Which one is this?
A. Self-contained collector C. Mirror and tracking system
B. Direct application of lenses D. Flat plate collector
30. Range of carrier frequencies for commercial FM broadcasting.
A. 535 Khz - 1605 Khz C. 88 Ghz - 108 Ghz
B. 88 Mhz - 108 Mhz D. 0.88 Khz - 1.08 Khz
31. Solenoid has magnetic reluctance of 2.2x10 raised to the (-3). It has 300 turns when the current flowing is ½ ampere. What is
the total flux?
A. 9.12 X 10
4
maxwell C. 8.57 X 10
4
maxwell
B. 9.82 X 10
4
maxwell D. 9.52 X 10
4
maxwell
32. The amount of kinetic energy by which an electron increases when it falls through a potential of 1 V and is equal to 1.6 x 10
-19
J
is
A. 1.0 eV C. 1.1 Ev
B. 1.6 eV D. 0.67 eV
33. The connected electrical load of an office building is 300 KVA. The main circuit breaker to be installed is 1, 600 A, 2 poles, 250
volts. The distribution transformer is rated 20, 000/230 volts. It is to serve this load with a rated connected load of 500 KVA,
single phase, 60 Hz, 3% volts. What interrupting rating should be required of the main circuit breaker ?
A. 50, 000 A B. 15, 000 A C. 100, 000 A D. 75, 000 A
34. The differential equation of a series RC circuit with DC applied voltage is : Ri +1/C ƒidt = E, if R = 50 ohms , C = 0.0001 farad,
e = 100 volts and I(o) = 2.0 amperes, determine the Laplace transform expression for I(s).
A. 1 (s) = 2 / s + 200 C. 1 (s) = 2 / s (s + 2)
B. 1 (s) = 2 / s + 50 D. 1 (s) = 2 / s + 2
35. The distribution system is 34.5 kv grounded, which arrester shall be installed to protect a distribution transformer.
A. 34.5 KV B. 27KV C. 38 KV D. 30 KV
36. The electric energy required to raise the temperature of a water in a pool is 1000 kWh. If the heat losses are 25%, the heating
energy required will be________
A. 1111 kWh C. 1266 kWh
B. 1750 kWh D. 1333 kWh
37. The flux density emanating from a pole of generator is 20000 gauss. A conductor 1 meter long cuts the flux perpendicularly at
a speed of 40 m per second. What voltage is developed?
A. 80 volts C. 230 volts
B. 800 volts D. 8 volts
38. The function of moderator in nuclear reaction is
A. to accelerate the reaction C. to control the reaction
B. to absorb excessive neutrons D. to liberate excessive neutrons
39. The illumination of a room being designed. The illumination intensity required is 50 FC. The maintenance factor is 70% and
coefficient of utilization is 0.6. If is the room is 20 ft. by 15 ft. What is the total required lumen output of the lamp?
A. 10,500 lumens C. 6,300 lumens
COMPREHENSIVE EXAM Page 4 of 5
March 27-29, 2006

5. B. 12,800 lumens D. 35,000 lumens
40. The main difference between the circuits of the AM and FM receivers lies in the
A. Mixer circuit B. Oscillator circuit
C. Demodulator circuit D. power amplifier circuit
41. The maximum instantaneous voltage and current outputs of the alternator are 300 V and 20 A, respectively. what is the power
output in watts if the voltage leads the current by 30
o
?
A. 2598 C. 6000
B. 5196 D. 3000
42. The phase b line voltage and the phase a line current of a balanced three-phase system are v = 220 sin (wt + 210
o
) and i = 10
sin (wt – 30
o
), respectively. What is the power of the system?
A. 1005 w C. 3300 W
B. 5716 W D. 3810 W
43. The power input to a 500 V, 50 Hz, 6-pole, 3 phase induction motor running at 975 RPM is 40 kW. The stator losses are 1 KW
and the friction and windage losses total 2 KW. Calculate the slip.
A. 0.025 C. 0.03
B. 0.055 D. 0. 04
44. The Q-factor in a given parallel resonant circuit is given by
A. 1/R
L
C
C. 1/R
1
CL
B.1/R
C
L D. ) R
C
1L
45. Three single-phase 167 KVA, 14400/24940 y – 240/480 volts transformers are connected delta-delta to supply an assorted
load of 400 KW at 0.80 pf lagging. If one transformer is taken out for repair, determine by how much in KVA each of the
remaining transformers will be overloaded.
A. 63.4 kva B. 334 KVA C. 121.67 KVA D. no overload
46. Two distribution transformer are connected in parallel supplying a load of 125 kVA. If the transformer A is rated 50 kVA, with
14 ohms equivalent reactance and transformer B is rated 75 kVA with 11 ohms equivalent reactance. Solve for the loading in
kVA of each transformer.
A. 55 kVA, 70 kVA C. 50 kVA, 75 kVA
B. 58 kVA, 67 kVA D. 52 kVA, 73 kVA
47. Two lumens pass through a circular hole of diameter 0.5 m in a screen located 6 m from an omnidirectional source. What
luminous flux is emitted by the source?
A. 5790 lm B. 4608 lm C. 6490 lm D. 1085 lm
48. Two parallel connected loads A and B are supplied by a 440 V, 3 phase, 60 Hz generator. Load A draws an apparent power of
100 kVA at 0.80 pf lagging and load B draws an apparent power of 70 kVA at unity pf. Determine the feeder current.
A. 208 A B. 212 A C. 214 A D. 202A
49. Two single-phase wattmeters are connected to a balanced three-phase, Y-connected load, as shown below. The impedances
are, Z=4+j3, and the line voltage is 440 volts. Phase sequence is a-b-c. Calculate total power dissipation of the load.
A. 30,972 W C. 40,534W
B. 45,123W D. 25,234W
50. What will be the phase angle difference between the current and the voltage of a series RC circuit containing R=4Ω and C=-
j7Ω with an impressed voltage of 120V(rms), 60 Hz? Take the voltage as the reference.
A. -60° B. -35° C. -30° D. +60°
COMPREHENSIVE EXAM Page 5 of 5
March 27-29, 2006

6. DEPARTMENT OF ELECTRICAL ENGINEERING
Tuesday, March 29, 2006 8:00-12:00 PM
ELECTRICAL ENGINEERING SET A SEAT NO.____
INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
51. What is the force on a +5x10
-11
C charge that is 5 cm from each of two +2x10
-9
C charges that are separated by 8 cm?
A. 0.8906 µ N C. O. 4314 µ N
B. 0. 6927 µ N D. 0. 7924 µ N
52. A 0 –10 ampere ammeter with internal resistance of 0.01 ohm. What shunt resistance do the ammeter be connected to have a
range of 0-100 ammeter?
A. 1.11 x 10
-3
C. 0.111
B. 1.0 x 10
-3
D. 0.1
53. A 10 kw, 250 v shunt generator, having an armature resistance of 0.1 Ω and a field resistance of 250 Ω, delivers full-load at
rated voltage and 800 rpm. The machine is now running as a motor while taking 10 KW at 250 V. What is the speed of the
motor? Neglect brush contact drop.
A. 896 RPM C. 650 RPM
B. 774.8 RPM D. 980 RPM
54. A 240 v motor requiring 2000 W is located 1 km from a power source. What minimum copper wire diameter is to be used if the
power loss is to be kept less than 5% of the motor power?
A. 0.217 in C. 0.424 in
B. 0.325 in D. 0.675 in
55. Determine the efficiency of single phase 20 KVA, 2200/200 V transformer at full load 0.8 pf and half load 0.4pf. Take full load
copper loss = 400 W and iron loss = 350 watts.
A. 90.1 % C. 89.88 %
B. 85.68 % D. 94.5 %
56. A 200 microfarad capacitor is connected in series with a 10 ohm resistors. The circuit is connected to a 24v battery. What is
the initial current on putting the switches on?
A. 2.4 amperes C. 0.025 ampere
B. 1.2 ampere D. 0.26 ampere
57. The power input to a 500 V, 50 Hz, 6 poles , 3 phase induction motor running at 975 RPM is 40 kW. The stator losses are 1
KW and the friction and windage losses total 2 KW. Calculate the slip.
A. 0.025 C. 0.03
B. 0.055 D. 0. 04
58. A 5 km long, three-phase line has a horizontal configuration of 4 ft spacing. The conductor is 336.4 MCM ACSR with GMR of
0.0244 ft and a resistance of 0.306 ohms per mile. What is the impedance?
B. 2.22 cis 65 C. 1.19 cis 46
C. 6.66 cis 65 D. 3.57 cis 46
59. A 55,000 kW thermal plant delivers an annual output of 238,000,000 kW-hr with peak load of 44 MW. What is the capacity
factor?
A. 49.4% B. 42.4% C. 48.2% D. 44.6%
COMPREHENSIVE EXAM Page 6 of 5
March 27-29, 2006

7. 60. A classroom 15ft. x 10ft height , having 2ft. ceiling cavity and 3f. floor cavity. What is the height of the room cavity of the said
classroom?
A. 300 ft B. 5 ft C. 3000 ft. D. 3 ft
61. A DC series motor is running at rated speed, voltage, and current when the load torque increases by 25%. Determine the
effects of this change (power drop), assuming that the line voltage remains the same.
A. 5% B. 1% C. 15% D. 10%
62. A diesel plant as has an overall efficiency of 30%, the heating value of diesel is 18,000 btu per lb. If diesel cost of P6.00 per
liter. What is the fuel cost of production in peso per kwh. Take density of diesel to be 900 grams per litter.
A. 1.91 kwh C. 1.12 kwh
B. 1.85 kwh D. 2.45 kwh
63. A farm is supplied with 30kW at 0.8 pf and 415 V from two small hydro-electric plants A and B. Station A has an alternator and
is at the end of a 3 phase line of impedance 0.6 + j0.8 Ω per phase. Station B at the middle if this line has an induction
generator supplying 15 kW at power factor 0.09. Find the power supplied by the alternator.
A. 19.4 KW C. 9.8 KW
B. 12.5 KW D. 29.3 KW
64. An operational amplifier has a gain-bandwidth product of 2π x 10
7
rad/s. The amplifier is used as an inverting mode with a
feedback resistance of 25, 000 ohms and an input resistance of 5, 000 ohms. The gain of the circuit is
A. -10 B. -5 C. 0 D. 10
65. A manufacturing firm operates a 10 MW power plants, the voltage is 480 volts, 3-phase and rated power factor is 85%. The
monthly generation is 5,000,000 Kw-hr at 90% power factor. What is the average plant load factor?
A. 69.4% C. 76.66%
B. 90% D. 85%
66. What will be the phase angle difference between the current and the voltage of a series RC circuit containing R=4Ω and C=-
j7Ω with an impressed voltage of 120V(rms), 60 Hz? Take the voltage as the reference.
A. -60° B. -35° C. -30° D. +60°
67. A piezoelectric transducer is
A. an Italian C. a ceramic disk to produce sound
B. a device used as a receiver D. a device used as a transmitter
˚
68. Natural gas consists mostly of ________ and to some extent ___________
A. propane, ethane C. propane, methane
B. butane, ethane D. methane, ethane
69. Two distribution transformer are connected in parallel supplying a load of 125 kVA. If the transformer A is rated 50 kVA, with
14 ohms equivalent reactance and transformer B is rated 75 kVA with 11 ohms equivalent reactance. Solve for the loading in
kVA of each transformer.
A. 55 kVA, 70 kVA C. 50 kVA, 75 kVA
B. 58 kVA, 67 kVA D. 52 kVA, 73 kVA
70. A series RC circuit consist of R = 2 M ohms and a uncharged capacitors C = 5 µF. The circuit voltage E of 100 volts is applied
across the series circuit at t = 0 and the initial current i900 = 5a. The applicable differential equation is : R (di/dt) + i/c=0.
Solve the differential equation and determine the resulting current I(t) at t = 0.01 seconds
A. 3.34 A C. 3.67 A
B. 2.78 A D. 3.03 A
71. A separately excited motor runs at 1045 rpm, with a constant field current, while taking an armature current of 50 A at 120 V.
The armature resistance is 0.1 ohms. If the load on a motor changes such that it now takes 95 A at 120 V , determined the
speed at this load
COMPREHENSIVE EXAM Page 7 of 5
March 27-29, 2006

8. A. 1004 rpm B. 1020 rpm C. 1110 rpm D. 975 rpm
72. An impedance draws a current i = 10 cos (wt – 30
o
) from a voltage v = 220 sin wt. What is the maximum power?
A. 2200 watts C. 1100 watts
B. 190.5 watts D. 1320 watts
73. A germanium diode which has an offset voltage of 0.2 V and an incremental resistance of 20 ohms, is connected in series with
a 10, 000 ohm resistor across a 100 V DC source. What is the current?
A. 9.98 mA C. 9.78 mA
B. 10 mA D. 9.96 mA
74. An unbalanced wye connected system
Ia = 10 cis (-32
o
) Vna = 132 cis 0
o
Ib = 13 cis (212
o
) Vnb = 130 cis 235
o
Ic = 14 cis 86
o
Vnc = 133 cis 117
o
A. 2820 B. 4271 C. 4325 D. 3650
75. At a certain location an electric system, the available faults MVA is 400 MVA. A 15 MVA, 34.5 kV/6.24 kV, 25% impedance,
wye-wye grounded transformer is installed at the location. Determine the short circuit MVA at the secondary side of the
transformer
A. 195 MVA B. 150 MVA C. 90 MVA D. 240 MVA
76. For ac transmission, whether overhead or underground, the most unsuitable system is the
E. three phase, three wire
F. three phase, four wire
G. single phase
H. two phase, three wire
77. In a short circuit study, the positive , negative and the zero sequence impedance are 0.25 p.u. and 0.25 p.u and 0.3 p.u
respectively. The base MVA is 100. Determine the fault current for a three-phase fault at 155 kV level.
C. 3000 A C. 2000 A
D. 2500 A D. 3500 A
78. Interior and exterior wiring, including power, lighting, control and signal circuit wiring together with associated hardware,
fittings, and wiring devices, both temporarily and permanently installed is called _____________ wiring.
A. Premises C. Branch circuit
B. Feeder D. General circuit
79. A parabolic reflector:
A. can be used for solar collection systems only if the overall efficiency is less than 5%
B. focuses both the direct and diffuse components of sunlight
C. focuses only the diffuse component of sunlight
D. focuses only the direct component of sunlight
80. Range of carrier frequencies for commercial FM broadcasting.
A. 535 Khz - 1605 Khz C. 88 Ghz - 108 Ghz
B. 88 Mhz - 108 Mhz D. 0.88 Khz - 1.08 Khz
81. The flux density emanating from a pole of generator is 20000 gauss. A conductor 1 meter long cuts the flux perpendicularly at
a speed of 40 m per second. What voltage is developed?
A. 80 volts C. 230 volts
B. 800 volts D. 8 volts
82. The amount of kinetic energy by which an electron increases when it falls through a potential of 1 V and is equal to 1.6 x 10
-19
J
is
COMPREHENSIVE EXAM Page 8 of 5
March 27-29, 2006

9. A. 1.0 eV C. 1.1 Ev
B. 1.6 eV D. 0.67 eV
83. The connected electrical load of an office building is 300 KVA. The main circuit breaker to be installed is 1, 600 A, 2 poles, 250
volts. The distribution transformer is rated 20, 000/230 volts. It is to serve this load with a rated connected load of 500 KVA,
single phase, 60 Hz, 3% volts. What interrupting rating should be required of the main circuit breaker ?
A. 50, 000 A B. 15, 000 A C. 100, 000 A D. 75, 000 A
84. The differential equation of a series RC circuit with DC applied voltage is : Ri +1/C ƒidt = E, if R = 50 ohms , C = 0.0001 farad,
e = 100 volts and I(o) = 2.0 amperes, determine the Laplace transform expression for I(s).
A. 1 (s) = 2 / s + 200 C. 1 (s) = 2 / s (s + 2)
B. 1 (s) = 2 / s + 50 D. 1 (s) = 2 / s + 2
85. The distribution system is 34.5 kv grounded, which arrester shall be installed to protect a distribution transformer.
A. 34.5 KV B. 27KV C. 38 KV D. 30 KV
86. The electric energy required to raise the temperature of a water in a pool is 1000 kWh. If the heat losses are 25%, the heating
energy required will be________
A. 1111 kWh C. 1266 kWh
B. 1750 kWh D. 1333 kWh
87. Solenoid has magnetic reluctance of 2.2x10 raised to the (-3). It has 300 turns when the current flowing is ½ ampere. What is
the total flux?
A. 9.12 X 10
4
maxwell C. 8.57 X 10
4
maxwell
B. 9.82 X 10
4
maxwell D. 9.52 X 10
4
maxwell
88. The function of moderator in nuclear reaction is
C. to accelerate the reaction C. to control the reaction
D. to absorb excessive neutrons D. to liberate excessive neutrons
89. The illumination of a room being designed. The illumination intensity required is 50 FC. The maintenance factor is 70% and
coefficient of utilization is 0.6. If is the room is 20 ft. by 15 ft. What is the total required lumen output of the lamp?
A. 10,500 lumens C. 6,300 lumens
B. 12,800 lumens D. 35,000 lumens
90. A series circuit with R = 10 W and L = 20 mH has a current of I = 2 sin 500t. Determine total voltage across the circuit and the
angle by which current lags voltage
A. 10 v, 60
0
C. 20 v, 60
0
B. 20 v, 45
0
D. 10 v, 45
0
91. The main difference between the circuits of the AM and FM receivers lies in the
a. Mixer circuit b. Oscillator circuit
c. Demodulator circuit d. power amplifier circuit
92. A synchronous motor
E. will have a low power factor when run below rated speed
F. may have its speed varied by inserting a rheostat in the D.C. field circuit
G. will slow down with an increase in load within the limits of its pull-out torque
H. will take minimum line current at any load when operating at unity power factor
93. The maximum instantaneous voltage and current outputs of the alternator are 300 V and 20 A, respectively. what is the power
output in watts if the voltage leads the current by 30
o
?
A. 2598 C. 6000
B. 5196 D. 3000
94. Two single-phase wattmeters are connected to a balanced three-phase, Y-connected load, as shown below. The impedances
COMPREHENSIVE EXAM Page 9 of 5
March 27-29, 2006

10. are, Z=4+j3, and the line voltage is 440 volts. Phase sequence is a-b-c. Calculate total power dissipation of the load.
A. 30,972 W C. 40,534W
B. 45,123W D. 25,234W
95. Three single-phase 167 KVA, 14400/24940 y – 240/480 volts transformers are connected delta-delta to supply an assorted
load of 400 KW at 0.80 pf lagging. If one transformer is taken out for repair, determine by how much in KVA each of the
remaining transformers will be overloaded.
A. 63.4 kva B. 334 KVA C. 121.67 KVA D. no overload
96. A 3-phase alternator generates an open-circuit phase voltage of 4000 V when exciting current is 50 A; the short circuit current
for the same excitation being 800 A. The synchronous reactance per phase is ____.
A. 80Ω B. 5Ω C. 15Ω D 46.2 Ω
97. Two lumens pass through a circular hole of diameter 0.5 m in a screen located 6 m from an omnidirectional source. What
luminous flux is emitted by the source?
A. 5790 lm B. 4608 lm C. 6490 lm D. 1085 lm
98. A wattmeter and varmeter are connected into a 120 V single-phase line that feeds an ac motor. They respectively indicate
1800 W and 960 var. Determine the phase angle between line voltage and current.
A. 28.1
0
B. 56.2
0
C. 35.8
0
D. 19.7
0
99. The Q-factor in a given parallel resonant circuit is given by
A. 1/R
L
C
C. 1/R
1
CL
B.1/R
C
L D. ) R
C
1L
100. The phase b line voltage and the phase a line current of a balanced three-phase system are v = 220 sin (wt + 210
o
) and 1 =
10 sin ( wt – 30
o
), respectively. What is the power of the system?
A. 1005 w C. 3300 W
B. 5716 W D. 3810 W
DEPARTMENT OF ELECTRICAL ENGINEERING
Tuesday, Mar 28, 2006 8:00-12:00 NN
ENGINEERING SCIENCES AND ALLIED SUBJECTS SET A SEAT
NO.____
INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
1. A group of persons who have organized a joint venture for the purpose of supplying electric energy to a specific area.
A. corporation C. cooperatives
B. supplier D. joint business
2. The radical ion (NO2)
-
is called
A. Nitrate C. Nitrite
B. Nitride D. Binitrate
3. The hexadecimal number B6C7 is equal to the decimal number
A. 46791 C. 49761
COMPREHENSIVE EXAM Page 10 of 5
March 27-29, 2006

11. B. 47691 D. 49671
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18. The codes specifies that one equipment is “ in sight from” another equipment if it is visible and at a distance of
A. not more than 15 meters C. not more than 20 meters
B. not less than 15 meters D. not less than 20 meters
19. One classification of cause of contracts in which the cause is a pure liberality of the giver is
A. onerous C. gratuitous
B. remuneratory D. valid
20.
21. The member of the board shall hold office for a term of ___ years from the date of appointment or until the successors shall
have been appointed and qualified.
A. 4 C. 5
B. 3 D. 6
22.
23. For service drop conductors not exceeding 600 volts its minimum clearance over commercial areas parking lots subject to
truck traffic is
A. 3100 mm C. 4600 mm
B. 3700 mm D. 5500 mm
24. The unit of lighting load for dwelling unit expressed in volt-amperes per square meter shall be
A. 8 C. 16
COMPREHENSIVE EXAM Page 11 of 5
March 27-29, 2006

12. B. 24 D. 40
25.
26.
27.
28. What ampacity of conductors supplying a 40-hp and 50-hp, three-phase, 460-volt motor with a full load current of 52 and 65 A
respectively, having the code letter F and service factor of 1.15 with full voltage starting?
A. 134 A C. 117 A
B. 130 A D. 142 A
29.
30.
31. Which of the following does not belong to the Code of Ethics?
A. penal provisions
B. relation with the client and employer
C. preparation and signing of plans
D. professional life
32. Each member of the Board of Electrical Engineering must be at least ___ years of age.
A. 40 C. 30
B. 35 D. 28
33. Is any building, room or separate place which houses or encloses electrical supply equipment connected to transmission or
distribution lines and the interior of which is accessible, as a rule, only to properly qualified persons.
A. general room C. electric plant
B. electric supply room D. substation
34. A deliberate and voluntary act to evade fulfillment of an obligation.
A. fraud C. default
B. contravention D. delay
35.
36.
37.
38. Which of the following statements is false?
A. Ceramics are inorganic, nonmetallic solids that are processed or used at high temperatures.
B. Most metals are strong, ductile and malleable. In general, they are heavier than most other substances.
C. Metals are chemical elements that form substances that are opaque, lustrous, and good conductors of heat and
electricity.
D. Oxides, carbon, and nitrides are considered to be within the class of materials known as glasses.
39.
40.
41.
COMPREHENSIVE EXAM Page 12 of 5
March 27-29, 2006

13. 42. Carbon materials used in the field of electrical engineering are manufactured mostly from
A. dolomite C. manganese
B. magnetite D. graphite
43. Tin is produced from
A. Cassiterite C. Sphalerite
B. Bauxite D. Magnitite
44.
45.
46.
47.
48.
49.
50.
DEPARTMENT OF ELECTRICAL ENGINEERING
Tuesday, Mar 27, 2006 8:00-4:00 PM
ENGINEERING SCIENCES AND ALLIED SUBJECTS SET A SEAT
NO.____
INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
COMPREHENSIVE EXAM Page 13 of 5
March 27-29, 2006

14. 62.
63.
64.
65.
66.
67.
68. DPWH Form No. 96-001E as amended under Art. 1.2.1.2 requires Box (s), which Box is for electrical practitioner in charge of
installation?
A. Box 4 C. Box 3
B. Box 2 D. Box 5
69. Generally a contractor may be sued in court for damages when he fails to comply with a contract. In certain cases, the law
does not require a demand for damages. Which one of the following is this?
a. When a contract is explicit about damage for non-compliance
b. When the contractor failed to perform due to his own faults
c. When the obligation or the law expressly declares
d. When the time for delivery of service is not controlling motive in the contract
70.
71. Section 17 (e) of ARTICLE III: Examination and Registration, Qualification of Applicants for Registered Electrical Engineer
states that: ______?
A. He is of good reputation with high moral values
B. He is a holder of the degree of BSEE from a university, school, college, etc. recognized and
accredited by the Philippine government
C. He is a citizen of the Philippines
D. He is at least twenty-one (21) years of age
72.
73. According to P.E.C , what is the minimum size of overhead service drop of overhead conductor to a building or other structure
in which a disconnecting meter is installed from the pole?
A. 8.00 sq. mm C. 10.0 sq.mm
B. 5.5 sq. mm D. 2.0 sq. mm
74. A protective technique where under normal operating conditions, any arcing or thermal effects are not capable of igniting the
flammable gas, vapor or dust-in-air mixture.
a. Nonincendive C. Non-inductive
b. inflammable D. Non-conductive
75.
76.
77.
78. A new certificate of final electrical inspection shall be required before reconnection if the service has been cut off
A. more than 6 months C. more than a month
COMPREHENSIVE EXAM Page 14 of 5
March 27-29, 2006

15. B. more than a year D. none of these
79.
80.
81. Section 4 (a) Power and Duties of the Board of ARTICLE II Board of Electrical Engineering is to ________.
A. determined and evaluate the qualifications of the applicants for registration with or without licensure examinations for
special permits.
B. Issue special permits to individual foreign electrical engineers and electricians.
C. Supervise and regulate the practice of electrical engineering in the Philippines.
D. Promulgate rules and regulations including a code of ethics, administrative policies, orders and issuances to carry out
issuances to carry out the provisions of this Act.
82. An electrical technology graduated applicant who finished two(2) years of school may apply for a license when he has
accumulated a minimum of
___________ actual experience under Sec 18 (2) Art III, RA 7920.
A. 3 years C. no experience required
B. 2 years D. 1 year
83. Section 29 of Article III: Revocation of certificates of Registration and Suspension from the practice of Profession. The board
shall have the power, upon notice of hearing, revoke any certificate of registration of any registrant, to suspend him from the
practice of his profession, for fraud, deceit, gross negligence or incompetence. Which will satisfy the above policy?
A. Rules & regulation, policies & code of professional ethics of this acts
B. Act of government
C. PRC ruling
D. Order of court
84. John owed Joseph P3000 due on November 18, 2003. Joseph in turn owed John P 3000 due on December 15, 2003. On
November 10, they both agreed on the compensation of their respective debts and credits. This illustrates what kind of
compensation
A. total compensation C. voluntary compensation
B. judicial compensation D. legal compensation
85.
86.
87.
88. The Miller indices of a plane in a crystal are (2 1 0). What do these indices mean?
E. (2 – 1- 0) 1/5 : 1/6 : 1/ 04
F. (2 – 1- 0) 1/7 : 1/3 : 1/ 10
G. (2 – 1- 0) 1/9 : 1/5 : 1/ 100
H. (2 – 1- 0) 1/1/2 : 1/1 : 1/ 100
89.
90.
91.
92. Molecules of higher molecular mass form by joining together large number of small molecules.
A. Polymer C. element
COMPREHENSIVE EXAM Page 15 of 5
March 27-29, 2006

16. B. crystal D. metal
93. It is the most prevalent engineering metals due to abundance of iron, simplicity of product, low cost and predictable
performance
A. steel C. carbon
B. copper D. aluminum
94.
95.
96.
97.
98.
99.
100.
DEPARTMENT OF ELECTRICAL ENGINEERING
Tuesday, 29 March 2005 8:00-12:00 PM
MATHEMATICS SET A SEAT NO._______
INSTRUCTION: select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
1.
1
Solve for y : x
2
y =36, y
2
z = 80, z
2
x = 75.
a. y = 4 b. y = 2 c. y = 6 d. y = 10
2. Find the indicated power (√2 / 2 + √2 /2 i)
–8
.
a. 1 b. 2 c. 3 d. 4
3.
3
From 10 tickets marked with the first 10 numerals, 2 are drawn at random. What is the chance that the sum is greater
than 5?
a. 41/45 b. 43/45 c. 38/45 d. 37/45
4.
5.
A flagpole 15 ft high in situated on top of a building 10 ft high. At a point on the ground x ft from the base of the building ,
the flagpole and the building subtend equal angles. Determine x.
a. 8√5 b. 10√5 c. 12√5 d. 14√5
5.
2
Assume that a body cools according to Newton’s Law dT/dt = -K (T – T0) where t is the time , T is the temperature of the
body and T0 is the temperature of the surrounding medium. Find the time it takes the boiler of water initially boiling at 100
0
c to drop from 90
0
c to 80
0
c if the temperature dropped 10
0
c during the first 20 min. ( T0 = 0
0
c ).
a. 42.4 min b. 22.4 min c. 24.2 min d. 16.2 min
6.
2.
Determine the gradient of the function f(x,y,z) = x
2
+ y
2
+ z
2
at point (1,2,3). Give the magnitude of the gradient of f.
a. 7.21 b. 8.25 c. 6.00 d. 7.48
7. Obtain the first 3 terms of the Taylor series in expanding the function f(x) = ln (x) about x =1. Using this expansion,
COMPREHENSIVE EXAM Page 16 of 5
March 27-29, 2006

17. 1 calculate for f(1.1).
a. 0.0850 b. 0.08534 c. 0.0854 d. 0.8525
8.
2
Two turtles Leonardo and Michael Angelo start at the same time towards each other at a distance of 1.5 meters. The rate
of Leonardo is 10cm/sec, while that of Michael Angelo is 20 cm/sec. A fly named Ronvills flies from one turtle to another
at the same time that the turtles start to move towards each other. The rate of the fly is 100 cm/sec. Find the total distance
traveled by the fly until the two turtles meet.
a. 500 cm b. 450 cm. c. 1000cm d. 100 cm
9.
2
Six times the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its
digits, the answer is 51 and the remainder is 11. If the digits are reversed, the number becomes smaller by 198. Find the
number.
a. 525 b. 650 c. 375 d. 725
10.
3
In a manufacturing assembly line, A can complete a certain work in 20 days. B can complete the same work in 30 days.
Three men A, B, and C can complete the same work in 10 days. How long will it take C alone to do the work?
a. 30 days b. 20 days c. 60 days d. 100 days
11.
4.
Mary is 36 years old. Mary was twice as old as Ann was when Mary was as old as Ann now. How old is Ann?
a. 48 yrs old b. 24 years old c. 36 yrs old d. 12 yrs old
12.
2
It is now between 9 and 10 o’clock, in four minutes time the hour hand will be directly opposite the position occupied by
the minute hand 3 minutes ago. What time is it?
a. 9:20 b. 10:20 c. 3:20 d. 6:40
13.
4
The sum of the interior angle of dodecagon is:
a. 540
0
b. 1800
0
c. 720
0
d. 1200
0
14. A rectangle is 5 cm long and 3 cm wide. The obtuse angle between its diagonals, correct to the nearest degree, is
a. 118
0
b. 120
0
c. 125
0
d. 128
0
15. Two perpendicular chords both 5 cm from the center of the circle divides the circle into 4 parts. If the radius of the circle is
13 cm., find the area of the smallest part.
a. 13.01 cm
2
b. 31.01 cm
2
c. 30.10 cm
2
d. 33.01 cm
2
16. A ship sails 15.0 miles on a course S 40
0
10
1
W and then 21.0 mi on a course N 28
0 20
1 W. Find the direction of the last
position from the first.
a. N 30
0
7
1
W b. N 70
0
30
1
W c. N 3
0
7
1
W d. N 7
0
30
1
W
17. How many times does the volume of a sphere increases if the radius is doubled?
a. 4 times b. 2 times c. 6 times d. 8 times
18. In a portion of an electrical railway cutting, the areas of cross section taken every 50 m are 2556, 2619, 2700, 2610
and 2484 sq. m. Find its volume.
a. 522, 600 m
3
b. 520, 500 m
3
c. 540, 600 m
3
d. 534, 200 m
3
19. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the
cylinder is 6. 283 cu m. Find its altitude.
a. 4.00 b. 3.75 c. 3.50 d. 3.25
COMPREHENSIVE EXAM Page 17 of 5
March 27-29, 2006

18. 20.
5
Find the volume common to two spheres of radii 9m and 6m, respectively, if the distance between their centers is 12m.
a. 39.66 m
2
b. 93.66 m
2
c. 66.93 m
2
d. 69.63 m
2
21.
5
A regular octahedron has an edge of 2m. Find its volume in m
3
.
a. 7.37 b. 3.77 c. 7.73 d. 4.77
22.
5
On a certain clock the minute hand is 2 meters long and the hour hand is 1 meter long. How fast is the distance between
the tip of the hand changing at 3:00 P.M.
a. –0.418 mph b. –0.814 mph c. -0. 481 mph d. -0.148mph
23.
6
Find the length of a rod that can be carried from one 4 m wide corridor to a similar corridor at right angle to the first.
Assume that the rod has negligible diameter.
a. L=11.31 m b. L=12.13 m c. L=13.31 m d. L=10.31 m
24.
6
A ship lies 10 km from shore, and opposite a point 14 km farther along the shore another ship lies 22 km offshore. A boat
from the first ship is to land a passenger and then proceed to the other ship. What is the least distance the boat can
travel?
a. 26.38 b. 23.68 c. 28.36 d. 32.86
25.
6
Suppose an object is dropped from a height of 100 meters, its height S at time t is S(t) = -4.9 t
2
where S is measured in
meters and t in seconds.
a. – 19.6 mps b. –44.3 mps c. -16.9 mps d. –29.4 mps
26. The sum of two numbers is 120. Find one of the number if the product of the first and the square of the other is maximum.
a. 30 b. 40 c. 60 d. 100
27. Find the area of the largest isosceles triangle that can be draw with equal sides 10 cm long.
a. 100 b. 75 c. 50 d. 25
28.
5
Find one of the bisectors of the angles between the lines: x + 7y =8, x-y = 10.
a. 3x+y =29 b. 3x –y =29 c. 2x +6y =21 d. 2x +6y =-21
29.
5
Two sides of a square lie along the lines 2y = 20 –3x, 3x + 2y = -6. Find the area of the square.
a. √52 b. 52 c. 153 d. √153
30.
5
Find the equation of the circle whose center at (1,3) and tangent to the line 3x + 4y + 10 =0.
a. x
2
+ y
2
–2x–6y–15=0 b. x
2
+ y
2
+2x+6y–15=0
c. x
2
+ y
2
–2x+6y+15=0 d. x
2
+ y
2
–2x–6y+15=0
31.
5
Find the distance between the lines : x + 3y =5, x + 3y = 25
a. 2√10 b. 3√10 c. √10 d. 2√5
32.
5
In the triangle with vertices (2,0), (3,2), (4,-3), find the point of intersection of the medians.
a. (3, -1/3) b. (3, 1/3) c. (-3,1/3) d. (-3,-1/3)
33. Find the area bounded by the curve y -= x
2
+ 2 and the lines x = 0 and y = 0 and x = 4.
a. 88/3 b. 64/3 c. 54/3 d. 65/5
34. 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
35. From the following tabulation, calculate the correlation coefficient between x and y.
COMPREHENSIVE EXAM Page 18 of 5
March 27-29, 2006

19. 1 X: 80 84 88 92 98 104
Y: 4 8 10 8 12 14
a. 0.8862 b. 0.9585 c. 0.9217 d. 0.8521
36.
2
What is the number of permutations of the letters in the word BANANA?
a. 36 b. 60 c. 52 d. 42
37.
2
Given the following statistical data, determine the standard deviation:
112 132 144 156 164 176 183 197
a. 26.22 b. 27.53 c. 28.84 d. 30.15
38.
4
How many sides does a regular polygon have if there are 54 diagonals can be formed from it.
a. 10 b. 12 c. 14 d. 16
39.
4
If any 10 of the 26 letters of the alphabet are chosen to represent the 10 digit 0,1,2,3,4,5,6,7,8,9, how many possible
coding patterns are there?
a. 1. 93 x 10
13
b. 1.13 x 10
12
c. 6.3 x 10
10
d. 3.08 x 10
14
40.
4
A coil having a resistance of 9.6 ohms and an inductance of 2.4 H is switched across a 25 V DC supply. Determine the
time constant of the circuit.
a. 0.24 s b. 4 s c. 0.25 s d. 2.6 s
41.
7
A voltage is described by 0.01 dv/dt + 0.0025 v = 0, v= 100 volts, at t = 0. Determine v for t>0
a. 50 e
–t /4
volts b. 120 e
–t / 0.001
volts
c. 100 e
–t /4
volts d. 125 e
–t /4
volts
42.
7
An electromotive force of 60 volts is applied to a simple electrical circuit consisting of a resistor of 20 ohms and an
inductor of 4 henrys. If i amperes is the current at t seconds and i=0 when t = 0, express i as a function of t.
a. i = 3 – 3e
-5t
b. i =3 –e
-5t
c. i = 3 - 3e
-t
d. i = 3 – e
-t
43.
7
A series circuit has R = 10 ohms, L= 0.1 henry and C = 0.0001 farad. An AC voltage e = 100 sin377t is applied across
the series circuit and the applicable differential equation is:
L (d
2
i / dt
2
) + R (di /dt) + (1/C)i = de/dt
Solve for the particular solution ( without complimentary solution), and determine the amplitude of the resulting sinusoidal
current i(t).
a. 5.51 amperes b. 6.67 amperes
c. 7.34 amperes d. 6.06 amperes
44.
7
In the series RLC circuit, R 2 ohms, L = I H, C = 0.5 F, V = 50 V. Determine the Laplace Transform of the current. (note:
there is no initial charge on the capacitor)
a. I(s)= (50)/ (s
2
+ 2s –2) b. I(s)= (50)/ (s
2
- 2s –2)
c. I(s)= (50)/ (s
2
+ 2s +2) d. I(s)= (50)/ (s
2
- 2s +2)
45.
7
The Power series of cos x = [(-1)
n
x
2n
]/ (2n)!, where x is in radians, find the value of cos 45
0
using only 4 terms of the
series.
a. 0.7071 b. 0.7074 c. 0.7066 d. 0.7069
46.
1
Given I1 –2 I2 –2I3 = 7 1
I1 +3 I2 – I3 = 0 2 Solve for I1 by determinants.
I1 + 4I2 –3I3 = 3 3
a. –1 b. 1 c. –2 d. 2
COMPREHENSIVE EXAM Page 19 of 5
March 27-29, 2006

20. 47.
6
Find the inverse of the matrix 1 0 2
0 -1 1
0 3 0
a. 3 -6 -2 b. –3 6 2 c. 3 -6 -2 d. 3 -7 -2
-1 2 -1 -1 2 1 -1 2 1 1 2 1
-1 5 0 1 3 0 -1 3 1 -1 -3 0
48.
6
What is the equivalent Y of the balance delta load 16 –j 12 ohms?
a. 8 –j6 ohms b. 4 – j 3 ohms
c. 5.33 – j4 ohms d. 10 – j8 ohms
49.
6
For a high-voltage long transmission line, we have the per-phase vector relation.
Es = AER + BIR
If ER = 127,000 volts at 0 degree, IR = 100 amperes at –30 deg. A = 0.9 at 0 deg., and B = 100 at 90 deg. , determine the
magnitude of the sending end voltage Es.
a. 120,614 V b. 119,614 V c. 120,615 V d. 119,615 V
50.
1
What is the simplified complex expression of (4.33 + j2.5) square?
a. 12.5 + j21.65 c. 20 + j20
b. 15 + j20 d. 21.65 +j12.5
MATHEMATICS
ALGEBRA
1.The Expression bx
= N can be expressed in logarithmic form as
A) log N = b + x B) b = logx N
C) N = logb x D) x = logb N
2. If n is any positive integer , then (n-1)(n-2)(n-3) … (3)(2)(1) is equal to
A) e[exp(n-1)] B) (n-2)!
C) n! D) (n-1) exp n
3. If n › 1 and has no factor except by itself and ±1 , n is
A) an improper fraction B) a proper fraction
C) a mixed number D) a prime number
4. A fair coin is tossed 5 times. What is the probability of obtaining 2 heads.
A) 0.1235 B) 0.3125
B) 0.2135 D) 0.5213
5. To build a dam 60 men must work 72 days. If all 60 men are employed at the start
but the number working decreased by 5 men at the end of each 12 day period, how
long will it take to complete the dam.
A) 108 days B) 120 days
C) 124 days D) 96 days
6. The base of the number system is called
A) index B) radix
C) cologarithm D) logarithm
7. The first term of A.P. is 6 and the 10th
term is three times the second term. What is
the common difference?
A) 1 B) 2
C) 3 D) 4
8. If A = -2 – i3, and B = 3 +i4, what is A/B ?
A) (18 – i)/25 B) (-18 – i)/25
C) (-18 + i)/25 D) (18 + i)/25
9. A class 40 students took examination in English and Science. If 30 passed English,
36 passed in Science and 2 failed in both subjects, the number of students passing in
both subjects is
A) 26 B) 28
C) 30 D) 32
10. Find the missing number in a series of 1, 5, 14, 30, ___, 91, …
A) 33 B) 40
C) 55 D) 60
11. In the discriminant b2
– 4ac = 0, the roots are
COMPREHENSIVE EXAM Page 20 of 5
March 27-29, 2006

21. A) imaginary B) imaginary and real
C) imaginary and equal D) equal and real
12. Factor the expression x2
+ 6x + 8 as completely as possible.
A) ( x + 8 ) ( x - 2 ) B) ( x + 4 ) ( x -2 )
C) ( x + 4 ) ( x + 2 ) D) ( x - 4 ) ( x -2 )
13. What is the natural log of e to the xy power?
A) 1 / xy B) 2.718 / xy
C) xy D) 2.718 xy
14. Any one of the individual constants of an expressed sum of constants is called
A) addend B) multiple
C) factor D) summation
15. Write in the form a + bi the expression i(exp 3219) – i(exp 427) + i(exp 18).
A) i B) –i
C) -1 D) +1
SOLID GEOMETRY AND TRIGONOMETRY
1. Of what quadrant is A , if secA is positive and cscA is negative?
A) 1st
B) 2nd
C) 3rd
D) 4th
2. Find the value of tan (A + B), where tanA = ⅓ and tanB = ¼ .
A) 7/10 B) 7/11
C) 7/12 D) 7/13
3. Solve for X if csc (11X – 16o
) = sec (5X + 26o
).
A) 7o
B) 5o
C) 6o
D) 4o
4. The flagship of the Naval fleet guarding the Sulu Sea is 4 miles from the destroyer,
3 miles from the cruiser and 5 miles from the battleship. The flagship is within the
triangle formed by the ships. If the line connecting the cruiser and destroyer is
perpendicular to the line joining the cruiser and battleship determine the distance
between cruiser and battleship.
A) 5.98 miles B) 8.59 miles
C) 59.8 miles D) 85.9 miles
5. The sides of a triangle are 5, 7, and 10, respectively, find the radius of the inscribed
circle.
A) 17.7 B) 14.7
C) 1.48 D) 8.41
6. A man owns a triangular lot on the corner of two intersecting roads. The frontage on
one side of the road is 300 ft on the other is 250 ft. the third side of the lot is 350 ft.
he was later on able to buy land adding 275 ft. to the 300 ft. frontage. By how much
is his lot increased?
A) 733,000 ft2
B) 373,000 ft2
C) 37,000 ft2
D) 370,300 ft2
7. A boat leaves a certain port, taking the direction N 68o
E at the rate of 19 kph. After
one hour, another boat B leaves the same port, taking the direction S 59o
E at the
rate of 26 kph. After how many hours after B leaves will it be directly south of A.
A) 3.772 hrs. B) 7.372 hrs.
C) 2.737 hrs. D) 7.273 hrs.
8. Given the polar equation r = 5sinφ. Determine the rectangular coordinates (x,y) of a
point in a curve when φ is 30o
.
A) (2.17, 1.25) B) (3.20, 1.50)
C) (2.51, 4.12) D) (6.00, 3.00)
9. The equation r2
= a2
cosθ is the
A) rosette B) limacon
C) lemniscate D) spiral
COMPREHENSIVE EXAM Page 21 of 5
March 27-29, 2006