FE ELECTRICAL – THIRD SIMULATION

#1. [Signal Processing] A tone at 5500 Hz is sampled at fs=12000 Hz. Observed baseband alias frequency is:

5500 Hz

6490 Hz

4950 Hz

6875 Hz

#2. [Control Systems] Increasing integral gain Ki in a PID controller most directly tends to:

Reduce sensor noise sensitivity at high frequency

Reduce steady-state error while risking increased overshoot/oscillation

Increase phase margin and always improve damping

Eliminate need for derivative action in all plants

#3. [Properties of Electrical Materials] Estimate skin depth δ for a conductor with σ=1.45e+07 S/m, μr=100, at f=1000000 Hz.

1.32e-05 m

1.46e-05 m

9.92e-06 m

1.56e-05 m

#4. [Circuit Analysis] In an RL step response with V=20 V, R=35 Ω, L=0.247 H, find i(t) at t=0.010 s.

0.534 A

0.427 A

0.32 A

0.504 A

#5. [Software Engineering] A loop nest runs: for i=1..n, for j=1..i. Time complexity is:

O(log n)

O(n)

O(n^2)

O(n^3)

#6. [Digital Systems] A static-1 hazard in combinational logic is typically mitigated by:

Reducing supply voltage to slow transitions

Clocking the combinational block

Replacing all AND gates with XOR gates

Adding consensus terms to cover adjacent minterms

#7. [Electronics] A BJT in active mode has β=148 and base current 55.5 µA. Collector current is closest to:

8.213 mA

6.16 mA

9.691 mA

9.034 mA

#8. [Circuit Analysis] A Thevenin source Vth=31 V with Rth=10 Ω feeds RL=6 Ω. Load current is:

2.131 A

1.938 A

2.286 A

2.422 A

#9. [Probability and Statistics] 25% of failures are due to power-stage faults. A thermal alarm appears with conditional probabilities P(A|power) and P(A|non-power) as given. What is P(power | alarm)?

0.858

0.596

0.727

0.8

#10. [Properties of Electrical Materials] A package heat spreader has k=174.6 W/m·K, area=3.60e-04 m², thickness=0.015 m, and ΔT=59 K. Conduction heat rate is:

220.4 W

306.1 W

200.8 W

244.9 W

#11. [Electromagnetics] For a lossless medium with εr=2.25 and μr=1.5, intrinsic impedance η is:

307.8 Ω

363.2 Ω

384.8 Ω

277.0 Ω

#12. [Circuit Analysis] In an RL step response with V=31 V, R=10 Ω, L=0.277 H, find i(t) at t=0.010 s.

0.767 A

0.935 A

1.169 A

1.029 A

#13. [Electronics] Ideal inverting op-amp with Rin=11 kΩ, Rf=104 kΩ, Vin=0.549 V. Output is:

-4.674 V

-6.128 V

-5.193 V

-3.895 V

#14. [Probability and Statistics] A lot has independent defect probability 0.02 per board. For 8 boards, what is P(at least 1 defect)?

0.187

0.176

0.134

0.149

#15. [Digital Systems] Pipeline stage has tCQ=1.23 ns, combinational delay=3.43 ns, setup=0.81 ns. Max clock frequency is:

182.8 MHz

215.7 MHz

201.1 MHz

228.5 MHz

#16. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=10, unit-step steady-state error is:

0.082

0.091

0.1

0.068

#17. [Engineering Economics] For a test fixture: fixed cost $137,936, unit price $72, variable cost $49. Break-even quantity is closest to:

6596.9 units

7496.5 units

5997.2 units

7076.7 units

#18. [Probability and Statistics] Assuming normal process variation with mean 93 and std dev 10, what is the 95th percentile?

136.8

129.2

89.749

109.5

#19. [Software Engineering] Which testing strategy is best for validating boundary behavior of ADC register parsing logic?

Boundary value analysis with explicit min/max and off-by-one cases

Random testing only, without deterministic edge cases

Integration testing only after deployment

Code formatting checks as primary validation

#20. [Properties of Electrical Materials] A parallel-plate capacitor originally has air dielectric and unchanged geometry. If replaced by a dielectric with relative permittivity εr, capacitance changes by what factor?

2.608

6.8

46.24

0.147

#21. [Power Systems] A component has reactance 0.191 pu on 50 MVA base (same kV base). On 75 MVA base, pu reactance is:

0.314 pu

0.257 pu

0.286 pu

0.357 pu

#22. [Linear Systems] For a 2nd-order system with damping ratio ζ=0.35 and ωn=11.79 rad/s, estimate 2% settling time.

1.138 s

0.723 s

0.791 s

0.965 s

#23. [Engineering Economics] Two design alternatives have scenario payoffs (high/medium/low demand): A=[140k,60k,-20k], B=[90k,70k,10k] with probabilities [0.2,0.5,0.3]. Best EMV is:

56000 USD

61600 USD

50400 USD

66080 USD

#24. [Control Systems] A loop has crossover ωc=4.4 rad/s and phase margin 42.6°. Which interpretation is best?

Phase margin does not relate to time-domain overshoot

Positive phase margin indicates closed-loop stability with moderate robustness

System is marginally stable only if gain margin is exactly 0 dB

System is unstable because crossover frequency is finite

#25. [Mathematics] An engineer linearizes a calibration model and obtains equations 2x + 2y = 16 and x + 8y = 10. What is x?

7.029

6.429

8.571

10.714

#26. [Digital Systems] Which expression is equivalent to Boolean function F = A’B + AB (sum of products)?

A + B

A

A’ + B’

B

#27. [Communications] For M-ary signaling with M=4 and bit rate 250 kb/s, symbol rate is:

125 ksym/s

156.2 ksym/s

147.5 ksym/s

112.5 ksym/s

#28. [Ethics and Professional Practice] A vendor offers expensive gifts while a bid decision is pending. Which action best aligns with professional ethics?

Accept gifts and disclose after award

Decline gifts and ensure procurement remains impartial and documented

Accept gifts under a personal relationship exemption

Accept gifts if no explicit contract terms are changed

#29. [Computer Networks] A router has routes 10.2.0.0/16, 10.2.32.0/19, and 10.2.32.128/25. Packet to 10.2.32.200 follows which route?

10.2.0.0/16

Default route only

10.2.32.128/25 (longest-prefix match)

10.2.32.0/19

#30. [Digital Systems] Pipeline stage has tCQ=1.46 ns, combinational delay=6.62 ns, setup=1.99 ns. Max clock frequency is:

117.1 MHz

74.441 MHz

124.1 MHz

99.254 MHz

#31. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=7, unit-step steady-state error is:

0.125

0.094

0.156

0.102

#32. [Linear Systems] For system y” + 4y’ + 1y = u(t), which statement about stability is true?

Unstable unless b > a^2

Stable because all coefficients are positive and roots have negative real parts

Unstable because input is a step function

Marginally stable because second-order systems always oscillate

#33. [Mathematics] Compute the integral ∫_0^6 x^2 dx.

54

84.96

72

79.2

#34. [Signal Processing] A first-order analog low-pass has cutoff 800 Hz. At cutoff frequency, output magnitude relative to passband is:

+3 dB (resonant peak)

0 dB (unity)

-6 dB (half amplitude)

-3 dB (approximately 0.707 of passband amplitude)

#35. [Mathematics] In a fully connected sensor graph with 7 nodes, how many unique undirected links exist?

21

23.1

18.9

15.75

#36. [Signal Processing] For FIR filter y[n]=x[n]+0.5x[n-1]+0.25x[n-2], with x[0]=4, x[1]=3, x[2]=1, find y[2].

2.625

3.5

2.87

3.85

#37. [Circuit Analysis] A branch dissipates 483 W with RMS current 2.67 A. Equivalent resistance is:

60.808 Ω

50.673 Ω

67.565 Ω

55.403 Ω

#38. [Ethics and Professional Practice] You discover a grounding omission that violates code, but correcting it will delay commissioning and trigger penalties. What is the MOST ethical action?

Let the contractor decide whether to disclose the issue

Proceed temporarily and note it in final report

Inform only your manager verbally and continue work

Document the hazard, notify responsible authority immediately, and halt affected work until corrected

#39. [Ethics and Professional Practice] A client asks you to stamp a design prepared entirely by another engineer that you did not supervise. What should you do?

Decline to seal until you have sufficient responsible charge and verification

Seal it if the other engineer signs an email attestation

Seal only the pages that look correct on quick review

Seal it if the schedule is critical

#40. [Mathematics] Compute the integral ∫_0^3 x^2 dx.

9.9

9

10.62

6.75

#41. [Computer Systems] By Amdahl’s law, fraction parallelizable p=0.66 with accelerator speedup 3.64. Overall speedup is:

1.564

1.43

1.907

1.717

#42. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.57. Percent overshoot is closest to:

10.259 %

14.249 %

9.347 %

11.399 %

#43. [Power Systems] At a 17 kV bus with Thevenin reactance 0.295 Ω (line-line basis), 3-phase bolted fault current is approximately:

33293.9 A

27301.0 A

36623.3 A

41617.4 A

#44. [Power Systems] Transformer no-load secondary voltage is 126 V and full-load is 109 V. Voltage regulation is:

19.495 %

15.596 %

14.037 %

12.789 %

#45. [Engineering Economics] A retrofit costs $150,703 now and saves $34,874/year for 8 years. At MARR = 10%, what is NPV?

28984.7 USD

38881.9 USD

35347.2 USD

44184.0 USD

#46. [Computer Networks] Which security control BEST addresses lateral movement after initial endpoint compromise?

Disabling all ICMP traffic globally

Increasing WAN bandwidth

Using only perimeter firewalls without internal controls

Network segmentation with least-privilege access and east-west monitoring

#47. [Signal Processing] For an ideal 10-bit ADC, quantization-limited SQNR is closest to:

61.96 dB

55.764 dB

46.47 dB

77.45 dB

#48. [Mathematics] An engineer linearizes a calibration model and obtains equations 5x + 2y = 10 and x + 3y = 11. What is x?

2.031

1.846

2.178

1.385

#49. [Power Systems] Ideal transformer with turns ratio Np:Ns=4:1 feeds load 17 Ω on secondary. Reflected primary impedance is:

0.797 Ω

1.254 Ω

1.062 Ω

1.169 Ω

#50. [Computer Systems] A 32-bit, direct-mapped cache has 256 sets and 32-byte blocks. Tag bits per line are:

23.75

15.58

22.42

19

#51. [Mathematics] For f(t) = t^3 – t^2 + 5t, evaluate d f/dt at t = 2.

13

10.66

9.75

14.3

#52. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.52. Percent overshoot is closest to:

11.339 %

15.119 %

17.841 %

12.398 %

#53. [Computer Systems] Cache hit rate=0.96, hit time=2.20 ns, miss penalty=119.3 ns. AMAT is:

6.143 ns

8.84 ns

7.492 ns

8.241 ns

#54. [Digital Systems] In unsigned 4-bit arithmetic, adding 14 and 11 sets carry-out flag to:

undefined

depends on signed interpretation

0

1

#55. [Communications] Using Shannon capacity C = B log2(1+SNR), with B=1.0 MHz and linear SNR=10, capacity is:

3.459 Mb/s

3.113 Mb/s

4.082 Mb/s

3.805 Mb/s

#56. [Electronics] In instrumentation design, which action most effectively reduces common-mode interference in low-level sensor measurements?

Use single-ended wiring and average more samples

Use differential signaling with high CMRR front-end and proper shield grounding

Increase ADC sampling rate without changing front-end topology

Place the sensor farther from the instrumentation amplifier

#57. [Circuit Analysis] A current source 6 A feeds two parallel resistors 10 Ω and 9 Ω. Node voltage across the pair is:

21.316 V

23.305 V

28.421 V

25.579 V

#58. [Power Systems] A 4-pole induction motor on 60 Hz runs at 1785 rpm. Rotor current frequency is closest to:

0.45 Hz

0.59 Hz

0.375 Hz

0.5 Hz

#59. [Software Engineering] Worst-case comparisons for binary search on sorted array of size 256 are closest to:

8

6

10

9.44

#60. [Power Systems] A balanced 3-phase load consumes 191 kW at 265 V line-line and pf=0.89 lagging. Line current is:

382.4 A

466.3 A

419.7 A

349.7 A

#61. [Circuit Analysis] A current source 8 A feeds two parallel resistors 9 Ω and 8 Ω. Node voltage across the pair is:

27.784 V

25.412 V

33.882 V

37.271 V

#62. [Electromagnetics] For a long straight conductor carrying 31 A, magnetic flux density at radius 0.076 m is:

1.03e-04 T

9.69e-05 T

9.03e-05 T

8.21e-05 T

#63. [Probability and Statistics] A communication node retransmits X times with PMF P(X=0,1,2,3) = {0.10, 0.35, 0.40, 0.15}. What is E[X]?

1.6

1.44

2

1.888

#64. [Properties of Electrical Materials] A conductor has resistivity 1.64e-08 Ω·m at 20°C and temperature coefficient 0.0039/°C. Estimate resistivity at 89°C.

2.38e-08 Ω·m

2.09e-08 Ω·m

1.53e-08 Ω·m

1.82e-08 Ω·m

#65. [Computer Networks] Ignoring loss, TCP throughput with receive window 128 kB and RTT 20 ms is approximately:

61.866 Mb/s

42.992 Mb/s

52.429 Mb/s

65.536 Mb/s

#66. [Ethics and Professional Practice] During RF testing, PPE requirements are being ignored in a high-field area. Your best professional response is to:

Move only your own team out of the area

Record violations and address them at project closeout

Continue if measured exposure is usually below limits

Stop testing and enforce safety controls before resuming

#67. [Digital Systems] Minimum number of flip-flops required for a MOD-11 synchronous counter is:

4

4.72

3

5

#68. [Electronics] Half-wave rectifier with peak input 20 V, diode drop 0.7 V, RL=931 Ω. Approximate average load current:

7.259 mA

6.599 mA

7.786 mA

5.411 mA

#69. [Circuit Analysis] Node A is connected to 16 V through 3 Ω and to 10 V through 6 Ω. What is node voltage Va (no load)?

17.5 V

15.4 V

14 V

12.6 V

#70. [Mathematics] An engineer linearizes a calibration model and obtains equations 4x + 2y = 18 and x + 5y = 7. What is x?

4.1

5.694

3.736

4.556

#71. [Mathematics] For first-order decay dy/dt = -4y with y(0)=1, find y(0.92 s).

0.026

0.021

0.03

0.023

#72. [Electromagnetics] If electric field changes at dE/dt=2.33e+06 V/m·s in a dielectric with permittivity 3.54e-11 F/m, displacement current density Jd is:

7.43e-05 A/m²

8.26e-05 A/m²

6.19e-05 A/m²

9.75e-05 A/m²

#73. [Electronics] Using square-law saturation model Id=0.5k(VGS−VT)^2, find Id for k=0.0033 A/V², VGS=3.89 V, VT=1.38 V.

11.37 mA

7.752 mA

10.336 mA

8.476 mA

#74. [Electronics] A BJT in active mode has β=94 and base current 68.8 µA. Collector current is closest to:

4.849 mA

7.112 mA

7.629 mA

6.465 mA

#75. [Circuit Analysis] A Thevenin source Vth=36 V with Rth=11 Ω feeds RL=13 Ω. Load current is:

1.5 A

1.35 A

1.125 A

1.23 A

#76. [Software Engineering] Worst-case comparisons for binary search on sorted array of size 512 are closest to:

9.9

9

11.25

7.38

#77. [Engineering Economics] Compute capital recovery (EUAC) for P=$248,684, S=$35,621, n=6 years, i=10%.

39362.2 USD/yr

65603.7 USD/yr

52482.9 USD/yr

47234.6 USD/yr

#78. [Mathematics] A phasor is V = 7 + j4. What is |V|?

8.868

10.078

6.047

8.062

#79. [Digital Systems] Minimum number of flip-flops required for a MOD-9 synchronous counter is:

4

3.28

5

4.4

#80. [Computer Systems] Cache hit rate=0.95, hit time=1.38 ns, miss penalty=80.6 ns. AMAT is:

7.247 ns

5.798 ns

4.348 ns

4.754 ns

#81. [Computer Systems] Compared with programmed I/O, DMA primarily improves system performance by:

Eliminating the need for interrupts

Increasing ALU clock frequency directly

Transferring bulk data with minimal CPU intervention

Making memory accesses deterministic under all loads

#82. [Electromagnetics] Transmission line has Z0=55 Ω and load ZL=120 Ω (real). Reflection coefficient Γ at load is:

0.279

0.438

0.305

0.371

#83. [Digital Systems] Which statement about asynchronous inputs to flip-flops is most accurate?

They can induce metastability and require synchronization before use in synchronous logic

They are safe if setup time is met at the source

They eliminate race conditions by definition

They never affect MTBF in digital systems

#84. [Engineering Economics] What present value is equivalent to a future replacement cost of $63,901 in 9 years at 11%?

22482.4 USD

24980.5 USD

18735.4 USD

29477.0 USD

#85. [Power Systems] Ideal transformer with turns ratio Np:Ns=5:1 feeds load 19 Ω on secondary. Reflected primary impedance is:

0.684 Ω

0.95 Ω

0.76 Ω

0.897 Ω

#86. [Mathematics] In a fully connected sensor graph with 9 nodes, how many unique undirected links exist?

29.52

45

27

36

#87. [Linear Systems] For G(s)=1/(s+2), unit-step response final value is:

0.333

0.417

0.367

0.393

#88. [Circuit Analysis] A branch dissipates 167 W with RMS current 1.89 A. Equivalent resistance is:

41.985 Ω

46.65 Ω

51.314 Ω

58.312 Ω

#89. [Signal Processing] A tone at 5500 Hz is sampled at fs=10000 Hz. Observed baseband alias frequency is:

4950 Hz

3690 Hz

4500 Hz

4050 Hz

#90. [Linear Systems] A transfer function has poles at s=-6.58 and s=-12.77. Dominant time constant is closest to:

0.167 s

0.125 s

0.114 s

0.152 s

#91. [Communications] For an AM wave, envelope Vmax=4.27 and Vmin=1.42. Modulation index m is:

0.5

0.59

0.375

0.41

#92. [Circuit Analysis] An AC source of 127 Vrms drives impedance Z = 17 + j6 Ω. RMS current magnitude is:

5.284 A

7.045 A

5.777 A

7.749 A

#93. [Computer Networks] For IPv4 subnet /25, how many usable host addresses are available?

148.7

103.3

126

138.6

#94. [Control Systems] For characteristic equation s^2 + 4s + 3=0, which range of k ensures stability?

k = 0 only

k < 0

k > 16 only

k > 0

#95. [Signal Processing] For y[n]=0.56y[n-1]+(-0.38)y[n-2]+x[n], which is correct?

BIBO stable (dominant poles inside unit circle)

Cannot determine stability without x[n]

Always unstable for second-order IIR filters

Always stable because coefficients are finite

#96. [Circuit Analysis] An AC source of 216 Vrms drives impedance Z = 25 + j7 Ω. RMS current magnitude is:

6.24 A

8.32 A

7.488 A

10.4 A

#97. [Computer Systems] In interrupt-driven embedded systems, which design choice best reduces worst-case interrupt latency?

Disable caches during interrupt handling

Move all ISR work into polling loops

Keep critical sections short and prioritize ISRs with bounded execution

Use deeply nested interrupts without masking policy

#98. [Mathematics] For first-order decay dy/dt = -3y with y(0)=1, find y(0.59 s).

0.189

0.129

0.141

0.172

#99. [Mathematics] A phasor is V = 9 + j3. What is |V|?

9.487

11.194

7.115

11.859

#100. [Ethics and Professional Practice] A former employer’s proprietary control code could shorten your current project by weeks. What is the proper action?

Use it temporarily and remove before delivery

Do not reuse protected code; obtain permission or develop an original implementation

Reuse code if variable names are changed

Reuse only non-commented sections

#101. [Electronics] Ideal inverting op-amp with Rin=18 kΩ, Rf=90 kΩ, Vin=0.483 V. Output is:

-1.811 V

-2.173 V

-2.414 V

-2.849 V

#102. [Software Engineering] For recursive DFS on a graph with V vertices and E edges using adjacency lists, complexity is:

O(VE)

O(log V)

O(V^2E)

O(V + E)

#103. [Power Systems] A balanced 3-phase load consumes 335 kW at 404 V line-line and pf=0.84 lagging. Line current is:

569.3 A

466.8 A

427.0 A

711.6 A

#104. [Software Engineering] Which data structure gives O(1) average-time lookup for symbol tables while allowing occasional rehash operations?

Binary heap

Hash table

Unbalanced binary search tree

Singly linked list

#105. [Electronics] An ideal 10-bit ADC with Vref=3.3 V measures Vin=2.379 V. Output code is closest to:

604.3

921.2

737

552.8

#106. [Communications] Compared with pure FDM, which is a key advantage of CDMA in multipath-rich mobile channels?

It guarantees zero near-far effects without power control

It requires fewer chips than symbols for spread-spectrum operation

It eliminates the need for synchronization entirely

Processing gain enables interference averaging and supports soft capacity

#107. [Circuit Analysis] Node A is connected to 31 V through 4 Ω and to 16 V through 5 Ω. What is node voltage Va (no load)?

24.333 V

18.25 V

28.713 V

26.767 V

#108. [Communications] A TDM PCM system multiplexes 20 channels, each sampled at 16000 Hz with 12 bits/sample. Aggregate data rate is:

4.8 Mb/s

3.84 Mb/s

3.149 Mb/s

4.531 Mb/s

#109. [Linear Systems] For low-pass H(jω)=1/(1+jωτ) with τ=0.123 s, find |H(jω)| at ω=19 rad/s.

0.353

0.322

0.392

0.49

#110. [Mathematics] For f(t) = t^3 – t^2 + 5t, evaluate d f/dt at t = 4.

33.75

56.25

53.1

45

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