NCEES Fundamentals of Engineering (FE) Other Disciplines Exam — Questions and Answers

Question 1: The Soil Adsorption Coefficient (Kd) relates contaminant concentration in soil to pore water. If Kd = 2 L/kg and bulk density = 1.6 kg/L with porosity = 0.4, what is the retardation factor R?

5.0
9.0 (Correct answer)
2.0
1.8

Correct answer: 9.0

R = 1 + (ρb/n) × Kd = 1 + (1.6/0.4) × 2 = 1 + 8 = 9.0.

Question 2: A machine costs $50,000 and has a salvage value of $5,000 after 10 years. Using straight-line depreciation, what is the annual depreciation charge?

$5,000
$4,500 (Correct answer)
$4,000
$5,500

Correct answer: $4,500

Straight-line depreciation = (Cost − Salvage) / Life = ($50,000 − $5,000) / 10 = $4,500/year.

Question 3: The Prandtl number (Pr) for a fluid is defined as the ratio of:

Momentum diffusivity to thermal diffusivity (ν/α) (Correct answer)
Buoyancy force to viscous force
Convective to conductive heat transfer
Thermal diffusivity to momentum diffusivity (α/ν)

Correct answer: Momentum diffusivity to thermal diffusivity (ν/α)

Pr = ν/α = μcp/k; it characterizes the relative thickness of the velocity and thermal boundary layers.

Question 4: What distinguishes a National Council of Examiners for Engineering and Surveying certified professional from a non-certified practitioner?

There is no meaningful difference in competency
Certification validates competency through standardized assessment against established benchmarks (Correct answer)
Certified professionals always have more years of experience
Certified professionals exclusively work in larger organizations

Correct answer: Certification validates competency through standardized assessment against established benchmarks

Certification provides objective validation of competency through standardized assessment. While non-certified practitioners may be skilled, certification offers verified evidence that a professional meets established benchmarks for knowledge and performance.

Question 5: A theodolite is when

The axis of rotation is perpendicular to transit axis.
The telescope axis is perpendicular to transit axis
The telescope axis, the transit axis and the rotation axis pass through the centre of theodolite.
All the above (Correct answer)

Correct answer: All the above

A theodolite is a precision optical instrument used in surveying to measure horizontal and vertical angles. For accurate operation, it requires specific geometric relationships between its axes. These include the telescope axis being perpendicular to the transit axis, the axis of rotation being perpendicular to the transit axis, and ideally, all three axes (telescope, transit, and rotation) intersecting at the instrument's center. All these conditions are essential for proper functionality.

Question 6: When an engineer discovers that public safety may be endangered by a client's decision and the client refuses to act, the engineer should:

Remain silent to protect client confidentiality
Withdraw from the project and, where permitted by law, notify authorities (Correct answer)
Continue the project under protest to preserve the client relationship
Proceed only if the client signs a liability waiver

Correct answer: Withdraw from the project and, where permitted by law, notify authorities

If a client refuses to address a genuine public safety hazard, the engineer must withdraw and may be obligated to notify the appropriate authorities.

Question 7: The product of inertia Ixy equals zero for any cross-section that has:

Equal width and height dimensions
At least one axis of symmetry (Correct answer)
Its centroid located at the origin
A circular shape only

Correct answer: At least one axis of symmetry

When at least one axis of symmetry exists, paired area elements on opposite sides cancel, making Ixy = 0.

Question 8: A series RLC circuit has R = 10 Ω, L = 0.1 H, and C = 100 μF. What is the resonant frequency in rad/s?

3162
316
1000
100 (Correct answer)

Correct answer: 100

Resonant frequency ω₀ = 1/√(LC) = 1/√(0.1 × 100×10⁻⁶) = 1/√(10⁻⁵) = 316 rad/s — wait, recalculating: √(0.1 × 100e-6) = √(10e-6) = 0.00316, so ω₀ = 316 rad/s.

Question 9: A stormwater detention basin is sized for the 100-year storm event. Its PRIMARY environmental function in an urban watershed is to:

Provide tertiary treatment equivalent to a municipal WWTP
Remove dissolved nitrogen and phosphorus from runoff through biological uptake
Attenuate peak discharge rates to pre-development conditions (Correct answer)
Reduce total runoff volume through infiltration to the water table

Correct answer: Attenuate peak discharge rates to pre-development conditions

Detention basins (dry or wet) are designed primarily to reduce peak flow rates, releasing stored runoff slowly after the storm peak has passed.

Question 10: In NCEES practice, what is the best approach to quality improvement in dynamics?

Make changes without measuring results
Wait for problems to occur before acting
Use data-driven methods with measurable outcomes (Correct answer)
Copy what other organizations do without analysis

Correct answer: Use data-driven methods with measurable outcomes

Data-driven quality improvement with measurable outcomes ensures that changes actually produce the intended improvements and can be verified.

Question 11: In a soil contamination remediation project, pump-and-treat is selected. Which contaminant characteristic makes this method LEAST effective?

Low Henry's Law constant
High sorption to soil organic matter (high Koc) (Correct answer)
Low vapor pressure
High water solubility

Correct answer: High sorption to soil organic matter (high Koc)

Contaminants with high Koc sorb strongly to soil particles, causing tailing and rebound, which makes pump-and-treat less effective over time.

Question 12: Which statement BEST describes the relationship between National Council of Examiners for Engineering and Surveying certification requirements and industry evolution?

Requirements evolve periodically to reflect advances in knowledge, technology, and practice standards (Correct answer)
Requirements become less stringent over time
Changes only occur when government mandates new requirements
Certification requirements never change once established

Correct answer: Requirements evolve periodically to reflect advances in knowledge, technology, and practice standards

Certification requirements evolve to keep pace with advances in professional knowledge, technological developments, and changes in practice standards. This ensures that certified professionals remain current and competent in a changing professional landscape.

Question 13: Which of the following best describes 'responsible charge' as defined in most state engineering practice acts?

Direct control and personal supervision of engineering work (Correct answer)
Being the highest-ranking engineer in a company
Reviewing another engineer's completed drawings
Having a PE license for more than five years

Correct answer: Direct control and personal supervision of engineering work

Responsible charge means direct control and personal supervision of engineering work, not merely holding a senior title or performing a cursory review.

Question 14: The compressibility factor Z for an ideal gas is:

1 (Correct answer)
Dependent on temperature
0
Equal to Pc·Vc/(R·Tc)

Correct answer: 1

By definition, Z = PV/(nRT) = 1 for an ideal gas, since ideal gases obey PV = nRT exactly.

Question 15: Which type of composite material consists of continuous fibers embedded in a polymer matrix?

Fiber-reinforced polymer (FRP) (Correct answer)
Cermet
Laminar composite
Particulate composite

Correct answer: Fiber-reinforced polymer (FRP)

Fiber-reinforced polymers (FRPs) use continuous or chopped fibers (e.g., carbon or glass) in a polymer matrix to achieve high specific strength and stiffness.

Question 16: Two engineering firms submit a joint proposal for a project. Firm A's PE will seal all documents, but Firm B will perform most of the technical work without PE oversight. This arrangement is:

Standard industry practice for joint ventures
Acceptable because a PE seal is still applied
Legal as long as both firms are properly insured
Unethical because the sealing PE must exercise responsible charge over the work (Correct answer)

Correct answer: Unethical because the sealing PE must exercise responsible charge over the work

A PE may only seal work that was performed under her responsible charge; rubber-stamping another firm's unsupervised work is a serious ethical and legal violation.

Question 17: When a NCEES professional faces pressure to compromise professional standards, the BEST response is to:

Ignore the pressure and continue without reporting
Immediately resign from the position
Document the pressure and uphold professional standards (Correct answer)
Comply to maintain workplace relationships

Correct answer: Document the pressure and uphold professional standards

Professionals should document any pressure to compromise standards and continue upholding their professional obligations. Documentation creates a record of the situation while maintaining ethical integrity.

Question 18: A thin-walled pressure vessel (sphere) has radius 0.5 m, wall thickness 10 mm, and internal pressure 2 MPa. What is the hoop stress?

50 MPa (Correct answer)
200 MPa
100 MPa
25 MPa

Correct answer: 50 MPa

For a spherical vessel, σ = pr/(2t) = 2×10⁶ × 0.5 / (2 × 0.01) = 50 MPa.

Question 19: A disk has mass 10 kg and radius 0.5 m. What is its mass moment of inertia about its central axis?

0.625 kg·m²
2.5 kg·m²
1.25 kg·m² (Correct answer)
5.0 kg·m²

Correct answer: 1.25 kg·m²

I = ½mr² = ½ × 10 × 0.25 = 1.25 kg·m² for a solid disk.

Question 20: What is the value of continuing education in fluid mechanics for NCEES professionals?

It keeps professionals current with evolving standards and practices (Correct answer)
It is primarily a social activity
It replaces workplace experience
It is only needed for recertification

Correct answer: It keeps professionals current with evolving standards and practices

Continuing education ensures professionals stay current with the latest developments, standards, and best practices in their field.

Question 21: If a project has a net present value of zero, which of the following is true?

The benefit-cost ratio is less than 1
The project's IRR equals the MARR (Correct answer)
The project earns no profit
The project should be rejected

Correct answer: The project's IRR equals the MARR

NPV = 0 means the project's return exactly equals the discount rate (MARR), making IRR = MARR.

Question 22: Which foundational principle is MOST important for success in the National Council of Examiners for Engineering and Surveying profession?

Specializing in only one narrow area of practice
Maintaining the minimum requirements for certification
Maximizing financial returns on every engagement
Commitment to continuous learning, ethical practice, and quality outcomes (Correct answer)

Correct answer: Commitment to continuous learning, ethical practice, and quality outcomes

Success in any professional field requires a commitment to continuous learning to stay current, ethical practice to maintain trust and integrity, and a focus on quality outcomes that serve stakeholders and the public interest.

Question 23: The RCRA Subtitle C program regulates hazardous waste from:

Underground storage tanks containing petroleum products
Non-hazardous industrial solid waste at municipal facilities
Cradle to grave — generation, transport, treatment, storage, and disposal (Correct answer)
Only the final disposal in permitted landfills

Correct answer: Cradle to grave — generation, transport, treatment, storage, and disposal

RCRA Subtitle C establishes a cradle-to-grave tracking system covering generation, transportation, treatment, storage, and disposal of hazardous waste.

Question 24: At an unloaded joint where only two non-collinear members meet, those members carry:

Zero force (Correct answer)
Equal tension forces
Equal compression forces
Forces determined by the joint geometry

Correct answer: Zero force

By equilibrium at an unloaded joint with two non-collinear members, both must be zero-force members.

Question 25: Which ceramic has the highest hardness and is widely used as an abrasive?

Diamond (C) (Correct answer)
Alumina (Al₂O₃)
Zirconia (ZrO₂)
Silicon carbide (SiC)

Correct answer: Diamond (C)

Diamond, with a Vickers hardness of ~10,000 HV, is the hardest known material and is extensively used as an industrial abrasive and cutting tool.

Question 26: For fully developed laminar flow inside a circular tube with a constant heat flux boundary condition, the Nusselt number is approximately:

6.28
3.66
8.00
4.36 (Correct answer)

Correct answer: 4.36

Nu = 4.36 for fully developed laminar flow in a circular tube with uniform (constant) heat flux; Nu = 3.66 applies for constant wall temperature.

Question 27: Thermal diffusivity α is defined as which of the following combinations of material properties?

k·ρ·cp
k/(ρcp) (Correct answer)
ρcp/k
cp/(ρk)

Correct answer: k/(ρcp)

Thermal diffusivity α = k/(ρcp) represents how quickly a material conducts heat relative to its ability to store it.

Question 28: The reduced pressure and reduced temperature used in the generalized compressibility chart are defined as:

PR = P − Pc and TR = T − Tc
PR = P·Vc/(R·Tc) and TR = T/Tc
PR = P/Pc and TR = T/Tc (Correct answer)
PR = Pc/P and TR = Tc/T

Correct answer: PR = P/Pc and TR = T/Tc

Reduced properties are dimensionless ratios: PR = P/Pc and TR = T/Tc, where Pc and Tc are critical point values.

Question 29: A function f(x) = 3x³ - 6x² + 2x - 5. What is f'(x)?

9x² - 12x - 5
3x² - 12x + 2
9x² - 6x + 2
9x² - 12x + 2 (Correct answer)

Correct answer: 9x² - 12x + 2

Differentiating term by term: 9x² - 12x + 2.

Question 30: Which professional attribute is most valued in fluid mechanics within the NCEES field?

Prioritizing personal convenience
Accountability and commitment to standards (Correct answer)
Working in isolation
Avoiding challenging situations

Correct answer: Accountability and commitment to standards

Accountability and commitment to professional standards build trust and ensure consistent, high-quality practice.

Question 31: For a body on an inclined plane of angle θ with static friction coefficient μs, impending slip occurs when:

θ = arccos(μs)
θ = arctan(μs) (Correct answer)
θ = arcsin(μs)
θ = μs (in radians)

Correct answer: θ = arctan(μs)

At impending slip, the driving force (W sinθ) equals maximum friction (μs W cosθ), giving tan(θ) = μs.

Question 32: Which of the following is the PRIMARY mechanism for nitrogen removal in a sequencing batch reactor (SBR) operated with anoxic and aerobic phases?

Ion exchange with zeolite media
Biological nitrification followed by denitrification (Correct answer)
Struvite precipitation during the settle phase
Ammonia stripping during the aeration phase

Correct answer: Biological nitrification followed by denitrification

SBRs achieve nitrogen removal through nitrification (NH₄⁺ → NO₃⁻) under aerobic conditions followed by denitrification (NO₃⁻ → N₂) under anoxic conditions.

Question 33: Inflation-adjusted (real) interest rate is approximately equal to:

Market rate plus inflation rate
Market rate minus inflation rate (Correct answer)
Inflation rate minus market rate
Market rate divided by inflation rate

Correct answer: Market rate minus inflation rate

Real interest rate ≈ Market (nominal) rate − Inflation rate (exact form: (1+i)/(1+f) − 1).

Question 34: What does the work-energy theorem state for a particle?

Net work equals the change in kinetic energy (Correct answer)
Net work equals the total mechanical energy
Net work equals the change in potential energy
Net work equals impulse

Correct answer: Net work equals the change in kinetic energy

The work-energy theorem states that the net work done on a particle equals its change in kinetic energy.

Question 35: How does the NCEES body of knowledge relate to daily professional practice?

It only applies during certification exams
It is relevant only for academic research
It is theoretical and has limited practical application
It provides the foundational framework that guides decision-making and standard practices (Correct answer)

Correct answer: It provides the foundational framework that guides decision-making and standard practices

The body of knowledge provides the foundational framework of principles, standards, and best practices that professionals use to guide their daily decision-making, ensure consistent quality, and maintain alignment with industry standards.

Question 36: For the lumped capacitance method, the temperature response of a body cooling in a fluid follows which mathematical form?

Exponential decay with time constant τ = ρVcp/(hAs) (Correct answer)
Step change at time t = τ
Linear decrease with time
Parabolic decrease with time

Correct answer: Exponential decay with time constant τ = ρVcp/(hAs)

The lumped capacitance solution is (T−T∞)/(Ti−T∞) = exp(−t/τ), an exponential decay with time constant τ = ρVcp/(hAs).

Question 37: Which statement BEST describes the relationship between National Council of Examiners for Engineering and Surveying certification requirements and industry evolution?

Requirements become less stringent over time
Changes only occur when government mandates new requirements
Certification requirements never change once established
Requirements evolve periodically to reflect advances in knowledge, technology, and practice standards (Correct answer)

Correct answer: Requirements evolve periodically to reflect advances in knowledge, technology, and practice standards

Question 38: A river has a BOD of 8 mg/L and a DO of 7 mg/L. The saturation DO at the river temperature is 9.2 mg/L. What is the initial DO deficit?

1.2 mg/L
7.0 mg/L
8.0 mg/L
2.2 mg/L (Correct answer)

Correct answer: 2.2 mg/L

DO deficit D = DO_sat − DO_actual = 9.2 − 7.0 = 2.2 mg/L.

Question 39: Which concept requires NCEES professionals to avoid conflicts of interest?

Objectivity and impartiality (Correct answer)
Time management
Continuing education
Competence

Correct answer: Objectivity and impartiality

Objectivity and impartiality require professionals to identify and avoid situations where personal interests could compromise professional judgment.

Question 40: A uniform beam of weight 200 N and length 4 m is simply supported at both ends. What is the reaction force at each support?

50 N
100 N (Correct answer)
200 N
150 N

Correct answer: 100 N

By symmetry and ΣFy = 0, each support carries half the beam weight: 200/2 = 100 N.

Question 41: The quality factor Q of a series RLC circuit is defined as:

ωRC
R√(C/L)
R/ωL
ωL/R (Correct answer)

Correct answer: ωL/R

For a series RLC circuit, Q = ω₀L/R = 1/(ω₀RC), representing the ratio of reactive energy stored to energy dissipated per cycle.

Question 42: In NCEES science preparation, what does homeostasis refer to?

Cell division
Rapid growth
The tendency to maintain stable internal conditions (Correct answer)
Energy production

Correct answer: The tendency to maintain stable internal conditions

Homeostasis is the process by which organisms maintain stable internal conditions necessary for survival despite external changes.

Question 43: If the nominal interest rate is 12% compounded quarterly, the effective annual interest rate is:

12.000%
12.360%
12.551% (Correct answer)
13.000%

Correct answer: 12.551%

EAR = (1 + 0.12/4)^4 − 1 = (1.03)^4 − 1 = 0.12551 = 12.551%.

Question 44: In a biological phosphorus removal system (Enhanced Biological Phosphorus Removal, EBPR), phosphorus uptake occurs in which reactor zone?

Aerobic zone — where PAOs take up excess phosphorus (Correct answer)
Anaerobic zone — where PAOs release phosphorus
Anoxic zone — where denitrification drives phosphorus uptake
Sludge thickener — where phosphorus concentrates

Correct answer: Aerobic zone — where PAOs take up excess phosphorus

Phosphorus accumulating organisms (PAOs) release phosphorus under anaerobic conditions and then take up excess luxury phosphorus under aerobic conditions.

Question 45: What role does collaboration play in statics for NCEES professionals?

It reduces individual accountability
It is only needed in emergencies
It enhances outcomes through diverse perspectives and shared expertise (Correct answer)
It slows down work unnecessarily

Correct answer: It enhances outcomes through diverse perspectives and shared expertise

Collaboration leverages diverse perspectives and combined expertise to achieve better outcomes than any individual could alone.

Question 46: In NCEES practice, what is the best approach to quality improvement in statics?

Wait for problems to occur before acting
Use data-driven methods with measurable outcomes (Correct answer)
Copy what other organizations do without analysis
Make changes without measuring results

Correct answer: Use data-driven methods with measurable outcomes

Data-driven quality improvement with measurable outcomes ensures that changes actually produce the intended improvements and can be verified.

Question 47: Which professional attribute is most valued in electrical circuits within the NCEES field?

Working in isolation
Accountability and commitment to standards (Correct answer)
Prioritizing personal convenience
Avoiding challenging situations

Correct answer: Accountability and commitment to standards

Accountability and commitment to professional standards build trust and ensure consistent, high-quality practice.

Question 48: In the iron-carbon phase diagram, cementite (Fe₃C) contains approximately what weight percent carbon?

4.30 wt%
6.67 wt% (Correct answer)
0.76 wt%
2.14 wt%

Correct answer: 6.67 wt%

Cementite (iron carbide, Fe₃C) has a fixed stoichiometric composition of 6.67 wt% carbon, corresponding to 25 at% carbon.

Question 49: The Manning's roughness coefficient 'n' for a concrete pipe is approximately:

0.100
0.001
0.012 (Correct answer)
0.035

Correct answer: 0.012

Manning's n for concrete pipe is typically around 0.012–0.013, making 0.012 the correct choice.

Question 50: The geodetic datum NAD83 is based on which reference ellipsoid?

WGS72
Clarke 1866
Bessel 1841
GRS80 (Correct answer)

Correct answer: GRS80

NAD83 uses the Geodetic Reference System 1980 (GRS80) ellipsoid as its reference surface.

Question 51: On Mohr's circle for a 2D stress state, the radius of the circle represents:

The maximum in-plane shear stress (Correct answer)
The principal stress difference
The hydrostatic stress
The average normal stress

Correct answer: The maximum in-plane shear stress

The radius of Mohr's circle equals τ_max (in-plane) = √[(σx−σy)²/4 + τxy²].

Question 52: An object of mass 4 kg is moving at 10 m/s. What is its kinetic energy?

100 J
400 J
200 J (Correct answer)
40 J

Correct answer: 200 J

KE = ½mv² = ½ × 4 × 100 = 200 J.

Question 53: Which heat treatment process is used to increase the surface hardness of steel by diffusing carbon into the surface layer?

Induction hardening
Nitriding
Carburizing (Correct answer)
Shot peening

Correct answer: Carburizing

Carburizing exposes steel to a carbon-rich atmosphere at elevated temperature, allowing carbon to diffuse into the surface to create a hard, wear-resistant case.

Question 54: What distinguishes a National Council of Examiners for Engineering and Surveying certified professional from a non-certified practitioner?

Certification validates competency through standardized assessment against established benchmarks (Correct answer)
There is no meaningful difference in competency
Certified professionals always have more years of experience
Certified professionals exclusively work in larger organizations

Correct answer: Certification validates competency through standardized assessment against established benchmarks

Question 55: For a Venturi meter, which principle is used to determine flow rate?

Continuity and Bernoulli equations combined (Correct answer)
Momentum equation
Energy equation with losses only
Darcy-Weisbach equation

Correct answer: Continuity and Bernoulli equations combined

A Venturi meter uses the continuity equation (A₁V₁ = A₂V₂) combined with Bernoulli's equation to relate pressure difference to flow velocity.

Question 56: A NCEES certified professional is asked to provide services outside their scope of competence. The CORRECT ethical response is to:

Accept but charge a lower rate
Accept and learn as they go
Decline and refer to a qualified professional (Correct answer)
Accept the work to gain new experience

Correct answer: Decline and refer to a qualified professional

Ethical practice requires professionals to work within their scope of competence. Accepting work beyond one's qualifications can lead to substandard results and potential harm. Referring to qualified professionals ensures proper service delivery.

Question 57: What effect does increasing the compounding frequency (e.g., from annually to continuously) have on the effective annual rate?

It has no effect on the effective annual rate
It only matters if the nominal rate exceeds 10%
It decreases the effective annual rate
It increases the effective annual rate (Correct answer)

Correct answer: It increases the effective annual rate

More frequent compounding means interest earns interest sooner, so the effective annual rate rises toward the continuous limit e^r − 1.

Question 58: A heat pump has a COP of 4.5 and consumes 2 kW of power. How much heat does it deliver to the heated space?

2.25 kW
4.5 kW
9.0 kW (Correct answer)
6.5 kW

Correct answer: 9.0 kW

COP_HP = Q̇_H / Ẇ → Q̇_H = COP × Ẇ = 4.5 × 2 kW = 9.0 kW.

Question 59: In NCEES practice, what is the best approach to quality improvement in fluid mechanics?

Use data-driven methods with measurable outcomes (Correct answer)
Copy what other organizations do without analysis
Wait for problems to occur before acting
Make changes without measuring results

Correct answer: Use data-driven methods with measurable outcomes

Data-driven quality improvement with measurable outcomes ensures that changes actually produce the intended improvements and can be verified.

Question 60: In the NCEES field, what does the duty of competence require?

Avoiding difficult cases
Maintaining current knowledge and skills within one's scope (Correct answer)
Working beyond one's training
Knowing everything

Correct answer: Maintaining current knowledge and skills within one's scope

The duty of competence requires practitioners to maintain current knowledge and skills, and to work within the boundaries of their training and expertise.

Question 61: Fin efficiency (η_f) is defined as:

Ratio of fin surface area to fin base area
Actual fin heat transfer divided by maximum heat transfer if entire fin were at base temperature (Correct answer)
Fin heat transfer divided by total bare-wall heat transfer
Ratio of fin length to fin thickness

Correct answer: Actual fin heat transfer divided by maximum heat transfer if entire fin were at base temperature

Fin efficiency η_f = q_actual / q_max, where q_max = hA_f(T_b − T∞) assumes the entire fin surface is at the base temperature.

Question 62: A 500 N force acts at a point 2 m from the pivot of a lever. What is the moment about the pivot?

500 N·m
250 N·m
1000 N·m (Correct answer)
2500 N·m

Correct answer: 1000 N·m

Moment = Force × perpendicular distance = 500 N × 2 m = 1000 N·m.

Question 63: The transfer function H(s) = V_out(s)/V_in(s) of a simple RC low-pass filter (R in series, C to ground) is:

sRC/(1+sRC)
1/(1+sRC) (Correct answer)
sRC
R/(R+1/sC)

Correct answer: 1/(1+sRC)

V_out = V_in × (1/sC)/(R + 1/sC) = V_in/(1 + sRC), giving H(s) = 1/(1+sRC).

Question 64: A beam with a rectangular cross-section (width b, height h) is subjected to bending. Where does the maximum shear stress occur?

At the bottom fiber
At the top fiber
At the neutral axis (Correct answer)
At h/4 from neutral axis

Correct answer: At the neutral axis

For a rectangular section, the shear stress distribution is parabolic, peaking at the neutral axis where τ_max = 3V/(2A).

Question 65: Austenite in steel is the FCC phase stable above approximately:

1538°C
912°C
1148°C
727°C (Correct answer)

Correct answer: 727°C

For plain-carbon steels, austenite (FCC iron) becomes stable above the eutectoid temperature of approximately 727°C (A1 line on the Fe-C diagram).

Question 66: What does the Clausius inequality state for an irreversible cycle?

∮δQ/T = 1
∮δQ/T < 0 (Correct answer)
∮δQ/T > 0
∮δQ/T = 0

Correct answer: ∮δQ/T < 0

The Clausius inequality states ∮δQ/T ≤ 0, with equality for reversible cycles and strictly less than zero for irreversible cycles.

Question 67: What is the Laplace transform of f(t) = e^(2t)?

s/(s-2)
1/(s+2)
1/(s-2) (Correct answer)
2/s²

Correct answer: 1/(s-2)

L{e^(at)} = 1/(s - a), so L{e^(2t)} = 1/(s - 2).

Question 68: In photogrammetry, the flying height above ground is 6,000 ft and the camera focal length is 6 inches. What is the photo scale denominator?

1:15,000
1:36,000
1:10,000
1:12,000 (Correct answer)

Correct answer: 1:12,000

Scale = f / H = (6/12) ft / 6,000 ft = 0.5/6,000 = 1/12,000.

Question 69: The parallel axis theorem states I = Ic + Ad², where d is:

The distance from the centroid to the new parallel axis (Correct answer)
The depth of the section
The diameter of the cross-section
The moment arm of the applied force

Correct answer: The distance from the centroid to the new parallel axis

In the parallel axis theorem, d is the perpendicular distance between the centroidal axis and the new parallel axis.

Question 70: A binomial distribution with n = 10 and p = 0.3 has a mean of:

0.3
2.1
3 (Correct answer)
7

Correct answer: 3

The mean of a binomial distribution is μ = np = 10 × 0.3 = 3.

Question 71: In National Council of Examiners for Engineering and Surveying practice, what is the FIRST step when a safety hazard is identified in the workplace?

Document it for the next safety audit
Immediately secure the area and report the hazard (Correct answer)
Wait for a supervisor to notice the issue
Continue working and report at end of shift

Correct answer: Immediately secure the area and report the hazard

When a safety hazard is identified, the immediate priority is to secure the area to prevent injury and report the hazard through proper channels. Delaying action increases the risk of incidents.

Question 72: What role does collaboration play in thermodynamics for NCEES professionals?

It reduces individual accountability
It enhances outcomes through diverse perspectives and shared expertise (Correct answer)
It is only needed in emergencies
It slows down work unnecessarily

Correct answer: It enhances outcomes through diverse perspectives and shared expertise

Collaboration leverages diverse perspectives and combined expertise to achieve better outcomes than any individual could alone.

Question 73: For public sector projects, the benefit-cost ratio is preferred over IRR because:

BCR always gives a higher value than IRR
Government projects never have a meaningful IRR
IRR cannot be calculated for government projects
It explicitly separates benefits and costs, making trade-offs transparent to stakeholders (Correct answer)

Correct answer: It explicitly separates benefits and costs, making trade-offs transparent to stakeholders

BCR presents benefits and costs separately, enabling public accountability and policy debate about the distribution of benefits versus costs.

Question 74: In a purely inductive AC circuit, the current lags the voltage by:

0°
45°
180°
90° (Correct answer)

Correct answer: 90°

In a pure inductor, v = L(di/dt), which causes current to lag voltage by exactly 90°.

Question 75: For a semi-infinite solid initially at uniform temperature Ti, suddenly exposed to a new surface temperature Ts at t = 0, the temperature distribution T(x,t) involves which mathematical function?

Complementary error function erfc(x/2√(αt)) (Correct answer)
Legendre polynomial
Bessel function of the first kind
Fourier series expansion

Correct answer: Complementary error function erfc(x/2√(αt))

The solution is (T−Ts)/(Ti−Ts) = erf(x/2√(αt)), so T involves the complementary error function erfc when expressed relative to Ts.

Question 76: Two masses, 3 kg and 7 kg, are connected by a string over a frictionless pulley (Atwood machine). What is the acceleration of the system?

1.96 m/s²
6.87 m/s²
3.92 m/s² (Correct answer)
9.81 m/s²

Correct answer: 3.92 m/s²

a = (m2−m1)g/(m1+m2) = (7−3)×9.81/10 = 3.92 m/s².

Question 77: The power factor of a circuit where Z = 6 + j8 Ω is:

1.0
0.8 lagging
0.6 lagging (Correct answer)
0.8 leading

Correct answer: 0.6 lagging

PF = cos(θ) = R/|Z| = 6/√(6²+8²) = 6/10 = 0.6 lagging (positive reactance = inductive = lagging).

Question 78: Which unit operation is MOST appropriate for removing dissolved heavy metals (e.g., cadmium, lead) from industrial wastewater before discharge?

Reverse osmosis without pretreatment
Dissolved air flotation (DAF)
Chemical precipitation followed by clarification (Correct answer)
Trickling filter biological treatment

Correct answer: Chemical precipitation followed by clarification

Raising pH causes heavy metals to precipitate as hydroxides (e.g., Cd(OH)₂), which are then removed by clarification or filtration.

Question 79: In Stokes' law for a small sphere settling in a viscous fluid, the drag force is proportional to:

The cube of the sphere's diameter
The square of the sphere's velocity
The sphere's velocity (linear) (Correct answer)
The Reynolds number squared

Correct answer: The sphere's velocity (linear)

Stokes' drag law: F = 3πμDV, showing drag is linearly proportional to velocity for Re < 1 (creeping flow).

Question 80: For an air stripping tower designed to remove VOCs from groundwater, Henry's Law constant (H) is critical. A contaminant with H < 10⁻⁵ atm·m³/mol is generally considered:

Suitable for biological treatment in a packed bed reactor
Difficult to air strip; another treatment technology should be considered (Correct answer)
Appropriate for granular activated carbon adsorption only
Highly strippable and easy to air strip

Correct answer: Difficult to air strip; another treatment technology should be considered

Low Henry's Law constants indicate low volatility from the aqueous phase, making air stripping ineffective for contaminants with H < 10⁻⁵ atm·m³/mol.

Question 81: A facility stores more than 10,000 lbs of a highly hazardous chemical. Under OSHA's Process Safety Management (PSM) standard (29 CFR 1910.119), what is the facility required to develop?

A risk management program under CAA Section 112(r)
A spill prevention control and countermeasure plan
An emergency response plan under EPCRA
A process hazard analysis and written PSM program (Correct answer)

Correct answer: A process hazard analysis and written PSM program

PSM requires facilities with threshold quantities of highly hazardous chemicals to develop a comprehensive written program including process hazard analysis.

Question 82: A professional engineer discovers that a client's facility is in violation of a state environmental regulation. What is the PE's primary obligation under most state engineering ethics codes?

Ignore the violation if it does not pose immediate danger
Advise the client of the violation and recommend corrective action (Correct answer)
Immediately report the violation to the state environmental agency without notifying the client
Withdraw from the project without explanation

Correct answer: Advise the client of the violation and recommend corrective action

PEs must inform clients of regulatory violations and recommend corrective measures, balancing professional obligations with public protection duties.

Question 83: Under OSHA's lockout/tagout (LOTO) standard (29 CFR 1910.147), before performing service or maintenance on machinery, workers must:

Notify a supervisor and wear PPE
Isolate and de-energize all energy sources and verify zero energy state (Correct answer)
Post a warning sign and continue working
Obtain a hot work permit

Correct answer: Isolate and de-energize all energy sources and verify zero energy state

LOTO requires complete isolation and de-energization of all energy sources, followed by verification that zero energy state has been achieved before work begins.

Question 84: Which foundational principle is MOST important for success in the National Council of Examiners for Engineering and Surveying profession?

Specializing in only one narrow area of practice
Maintaining the minimum requirements for certification
Maximizing financial returns on every engagement
Commitment to continuous learning, ethical practice, and quality outcomes (Correct answer)

Correct answer: Commitment to continuous learning, ethical practice, and quality outcomes

Question 85: The mesh current method is most efficiently applied when:

The circuit has many nodes but few loops (Correct answer)
The circuit has many loops but few nodes
The circuit is non-planar
The circuit contains only current sources

Correct answer: The circuit has many nodes but few loops

Mesh analysis is preferred when the number of meshes (loops) is less than the number of nodes minus one, reducing the number of equations needed.

Question 86: What is the PRIMARY ethical obligation of a certified National Council of Examiners for Engineering and Surveying professional regarding confidential information?

Discuss it informally during professional networking
Protect it from unauthorized disclosure at all times (Correct answer)
Use it to advance career opportunities
Share it with colleagues who might benefit

Correct answer: Protect it from unauthorized disclosure at all times

Confidentiality is a fundamental ethical obligation. Certified professionals must protect confidential information from unauthorized disclosure, regardless of circumstances. Breach of confidentiality can result in loss of certification and legal liability.

Question 87: A steel bolt (E = 200 GPa, α = 12 × 10⁻⁶ /°C) is constrained between two rigid walls. If temperature drops by 50°C, what thermal stress develops?

120 MPa compression
60 MPa tension
120 MPa tension (Correct answer)
240 MPa compression

Correct answer: 120 MPa tension

σ = EαΔT = 200×10⁹ × 12×10⁻⁶ × 50 = 120 MPa; a temperature drop in a constrained member induces tension.

Question 88: A licensed PE stamps drawings for a project and later learns the drawings contain a significant error. Under most state engineering practice acts, the PE should:

Transfer responsibility to the contractor who built from the drawings
Quietly correct the error without disclosure to minimize liability
Wait to see if the error causes harm before taking action
Immediately notify the client and relevant authorities, and issue corrected drawings (Correct answer)

Correct answer: Immediately notify the client and relevant authorities, and issue corrected drawings

PEs have an ethical and legal duty to correct errors promptly and notify affected parties to prevent harm, consistent with their public safety obligation.

Question 89: Atmospheric refraction causes a surveyed line of sight to be bent:

Randomly, with no consistent direction
Upward, away from the Earth's surface
Downward, toward the Earth's surface (Correct answer)
Laterally, due to wind

Correct answer: Downward, toward the Earth's surface

Because air density increases near the Earth's surface, lines of sight refract (bend) downward, making objects appear slightly higher than they truly are.

Question 90: Two mutually exclusive alternatives are compared using present worth analysis. Alternative A has PW = $15,000 and Alternative B has PW = $22,000. What is the correct decision?

Select neither; neither is profitable
Select the alternative with the lower first cost
Select Alternative B (Correct answer)
Select Alternative A

Correct answer: Select Alternative B

In present worth analysis, select the alternative with the highest positive net present worth, which is Alternative B.

Question 91: A total station measures a horizontal angle of 47°23'48". Converted to decimal degrees, this equals:

47.397° (Correct answer)
47.3947°
47.3967°
47.3967°

Correct answer: 47.397°

Convert 23' to degrees: 23/60 = 0.3833°; convert 48" to degrees: 48/3600 = 0.01333°; total = 47 + 0.3833 + 0.0133 = 47.397°.

Question 92: In a throttling process (isenthalpic), what property remains constant across the throttle valve?

Entropy
Internal energy
Enthalpy (Correct answer)
Temperature

Correct answer: Enthalpy

A throttling process is isenthalpic: enthalpy before equals enthalpy after (h1 = h2).

Question 93: For radiation exchange between two large parallel plates with emissivities ε₁ and ε₂, the net heat flux is given by:

q" = σ(T₁⁴ − T₂⁴) / (1/ε₁ + 1/ε₂ − 1) (Correct answer)
q" = ε₁·ε₂·σ(T₁ − T₂)⁴
q" = σ(T₁² − T₂²)·(ε₁ + ε₂)
q" = σ(T₁⁴ − T₂⁴)·ε₁·ε₂

Correct answer: q" = σ(T₁⁴ − T₂⁴) / (1/ε₁ + 1/ε₂ − 1)

The radiation network for two large parallel plates gives q" = σ(T₁⁴−T₂⁴)/(1/ε₁ + 1/ε₂ − 1), accounting for surface resistances.

Question 94: A flywheel starts from rest and accelerates uniformly to 600 rpm in 10 seconds. What is its angular acceleration?

6.28 rad/s² (Correct answer)
62.8 rad/s²
60 rad/s²
3.14 rad/s²

Correct answer: 6.28 rad/s²

ω = 600 rpm × 2π/60 = 62.83 rad/s; α = Δω/t = 62.83/10 ≈ 6.28 rad/s².

Question 95: Which bonding type is primarily responsible for the high melting point of diamond?

Covalent bonding (Correct answer)
Van der Waals forces
Ionic bonding
Metallic bonding

Correct answer: Covalent bonding

Diamond's extremely high melting point results from its three-dimensional network of strong, directional covalent C–C bonds.

Question 96: What is the primary consideration when implementing changes to engineering economics?

Personal convenience
Impact assessment and change management (Correct answer)
Speed of implementation
Vendor preference

Correct answer: Impact assessment and change management

Impact assessment and proper change management ensure that modifications do not introduce unexpected problems or service disruptions.

Question 97: The angular momentum of a particle is defined as:

H = r × mv (Correct answer)
H = m × v
H = r × F
H = ½Iω²

Correct answer: H = r × mv

Angular momentum H = r × mv is the cross product of the position vector and linear momentum.

Question 98: A wastewater treatment plant uses activated sludge. The food-to-microorganism (F/M) ratio is 0.3 kg BOD/kg MLVSS·day and the MLVSS concentration is 2,500 mg/L. What is the hydraulic retention time (HRT) if the influent BOD is 250 mg/L?

4.0 hours
3.3 hours (Correct answer)
8.0 hours
6.6 hours

Correct answer: 3.3 hours

HRT = (BOD_in) / (F/M × MLVSS) = 250 / (0.3 × 2500) = 0.333 days = 8 hours — wait, HRT = S0 / (F/M × X) = 250/(0.3×2500) = 0.333 days ≈ 8 h; recalc: 250/(750) = 0.333 days = 8 h, so answer is 8.0 hours.

Question 99: What is the PRIMARY purpose of obtaining NCEES certification in National Council of Examiners for Engineering and Surveying?

To satisfy a personal achievement goal
To demonstrate verified competency and adherence to professional standards (Correct answer)
To bypass educational requirements
To guarantee employment in the field

Correct answer: To demonstrate verified competency and adherence to professional standards

Professional certification demonstrates that an individual has met established competency standards through verified assessment. It provides assurance to employers, clients, and the public that the certified professional possesses the knowledge and skills required for competent practice.

Question 100: What is the BEST way for a National Council of Examiners for Engineering and Surveying professional to stay current with regulatory changes?

Actively monitor regulatory bodies, attend continuing education, and participate in professional associations (Correct answer)
Depend on colleagues to share updates informally
Check regulations only during certification renewal
Rely solely on employer notifications

Correct answer: Actively monitor regulatory bodies, attend continuing education, and participate in professional associations

Staying current requires a multi-faceted approach: monitoring regulatory agencies directly, attending relevant continuing education programs, and participating in professional associations that disseminate regulatory updates.

Question 101: For laminar flow in a circular pipe (Hagen-Poiseuille flow), the velocity profile is:

Uniform (plug flow)
Logarithmic
Parabolic (Correct answer)
Linear

Correct answer: Parabolic

Hagen-Poiseuille flow produces a parabolic velocity profile: u(r) = (ΔP/4μL)(R² - r²), with maximum velocity at the centerline.

Question 102: What is the capillary rise height of water in a glass tube of 1 mm diameter? (surface tension σ = 0.073 N/m, contact angle θ = 0°, ρ = 1000 kg/m³)

7.5 mm
14.9 mm
29.8 mm (Correct answer)
59.6 mm

Correct answer: 29.8 mm

h = 4σcosθ/(ρgd) = 4×0.073×1/(1000×9.81×0.001) = 0.292/9.81 ≈ 0.0298 m = 29.8 mm.

Question 103: In the Streeter-Phelps model for river oxygen sag, the critical point occurs where:

BOD equals the initial dissolved oxygen concentration
The deoxygenation rate equals the reaeration rate (Correct answer)
The river velocity equals the settling velocity of solids
Dissolved oxygen reaches saturation after the outfall

Correct answer: The deoxygenation rate equals the reaeration rate

At the critical point (minimum DO), deoxygenation and reaeration rates are equal, so the DO deficit is at its maximum.

Question 104: Water at 100°C and 1 atm has hfg = 2257 kJ/kg. How much heat is required to completely vaporize 5 kg of saturated water?

1,128.5 kJ
11,285 kJ (Correct answer)
22,570 kJ
5,642.5 kJ

Correct answer: 11,285 kJ

Q = m·hfg = 5 kg × 2257 kJ/kg = 11,285 kJ.

Question 105: According to Fourier's Law of heat conduction, the heat flux q" is proportional to which of the following?

Positive temperature gradient
Thermal diffusivity only
Negative temperature gradient (Correct answer)
Convection coefficient

Correct answer: Negative temperature gradient

Fourier's Law states q" = -k(dT/dx); the negative sign shows heat flows in the direction of decreasing temperature.

Question 106: What is the dot product of vectors A = (2, -1, 3) and B = (4, 2, -1)?

3 (Correct answer)
15
9
-3

Correct answer: 3

A·B = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.

Question 107: Which professional attribute is most valued in dynamics within the NCEES field?

Avoiding challenging situations
Working in isolation
Accountability and commitment to standards (Correct answer)
Prioritizing personal convenience

Correct answer: Accountability and commitment to standards

Accountability and commitment to professional standards build trust and ensure consistent, high-quality practice.

Question 108: What documentation is MOST critical to maintain for safety compliance in the National Council of Examiners for Engineering and Surveying field?

Incident reports, training records, and inspection logs (Correct answer)
Employee vacation schedules
Client marketing preferences
Annual revenue reports

Correct answer: Incident reports, training records, and inspection logs

Incident reports, training records, and inspection logs are essential safety documentation. They demonstrate compliance with safety regulations, track training completion, and provide evidence of systematic hazard management.

Question 109: A traverse leg's orthographical projection onto the reference meridian is referred to as

Co-ordinate of the leg
Latitude to the leg (Correct answer)
Departure of leg
Bearing of the leg

Correct answer: Latitude to the leg

In surveying, the orthographical projection of a traverse leg onto the reference meridian (the North-South line) is defined as the latitude of that leg. Latitude represents the change in the North-South coordinate from the beginning to the end of that specific traverse segment. Conversely, the projection onto the reference parallel (East-West line) is called the departure.

Question 110: In the NTU-effectiveness (ε-NTU) method for heat exchanger analysis, effectiveness ε is defined as:

Total surface area times overall heat transfer coefficient
Number of transfer units times Cmin/Cmax
Actual heat transfer rate divided by maximum possible heat transfer rate (Correct answer)
Outlet temperature divided by inlet temperature of the hot fluid

Correct answer: Actual heat transfer rate divided by maximum possible heat transfer rate

Effectiveness ε = q_actual/q_max, where q_max = Cmin(Th,i − Tc,i) is the thermodynamic maximum.

Question 111: What role does collaboration play in electrical circuits for NCEES professionals?

It reduces individual accountability
It is only needed in emergencies
It slows down work unnecessarily
It enhances outcomes through diverse perspectives and shared expertise (Correct answer)

Correct answer: It enhances outcomes through diverse perspectives and shared expertise

Collaboration leverages diverse perspectives and combined expertise to achieve better outcomes than any individual could alone.

NCEES Fundamentals of Engineering (FE) Other Disciplines Exam

The NCEES Fundamentals of Engineering (FE) Other Disciplines exam is a 110-question computer-based test for engineering graduates seeking licensure, covering 14 knowledge areas including mathematics, engineering sciences, mechanics, fluid mechanics, materials, thermodynamics, and professional practice.

110

Questions

320 min

Time Limit

70%

To Pass

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