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

Question 1: The parallel axis theorem states I = Ic + Ad², where d is:

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

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 2: The closure error of a traverse is 0.45 ft and the total perimeter is 3,600 ft. The precision ratio is:

1:10,000
1:8,000 (Correct answer)
1:9,000
1:7,000

Correct answer: 1:8,000

Precision ratio = 1 / (perimeter / error) = 1 / (3600 / 0.45) = 1 / 8000.

Question 3: Which regulatory requirement is UNIVERSAL across all National Council of Examiners for Engineering and Surveying practice settings?

Limiting services to local jurisdictions only
Maintaining current certification and meeting continuing education requirements (Correct answer)
Using specific proprietary software systems
Working exclusively during business hours

Correct answer: Maintaining current certification and meeting continuing education requirements

Maintaining current certification and meeting continuing education requirements is a universal regulatory requirement. Regardless of practice setting, professionals must keep their credentials current and demonstrate ongoing competency through continuing education.

Question 4: Which statement BEST describes the relationship between National Council of Examiners for Engineering and Surveying certification requirements and industry evolution?

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

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 5: What is the value of continuing education in statics for NCEES professionals?

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

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 6: Which failure mode is characterized by crack growth under cyclic loading at stresses well below the yield strength?

Fatigue failure (Correct answer)
Creep failure
Stress corrosion cracking
Ductile fracture

Correct answer: Fatigue failure

Fatigue failure occurs due to progressive crack initiation and growth under repeated cyclic loading, often at stresses far below the static yield strength.

Question 7: Which thermodynamic relationship is known as a Maxwell relation derived from the Gibbs free energy G?

(∂S/∂P)_T = −(∂V/∂T)_P (Correct answer)
(∂T/∂V)_S = −(∂P/∂S)_V
(∂P/∂T)_V = (∂S/∂V)_T
(∂T/∂P)_S = (∂V/∂S)_P

Correct answer: (∂S/∂P)_T = −(∂V/∂T)_P

From dG = −SdT + VdP, the Maxwell relation is (∂S/∂P)_T = −(∂V/∂T)_P.

Question 8: For open channel flow, the Froude number Fr = 1 corresponds to:

Critical flow (Correct answer)
Subcritical flow
Supercritical flow
Laminar flow

Correct answer: Critical flow

A Froude number of exactly 1 defines critical flow, where flow transitions between subcritical (Fr<1) and supercritical (Fr>1).

Question 9: What obligation does confidentiality impose on NCEES professionals?

Share information freely with colleagues
Never communicate with anyone
Keep all information secret indefinitely
Protect sensitive information and share only as authorized (Correct answer)

Correct answer: Protect sensitive information and share only as authorized

Confidentiality requires protecting sensitive information and only sharing it through authorized channels and for legitimate purposes.

Question 10: A PE is asked to review and approve a design created by an unlicensed engineer. Under most state laws, the PE may legally do this only if she:

Has a signed indemnification agreement with the client
Has reviewed the final drawings and found no obvious errors
Has exercised responsible charge and fully understands the technical basis of the design (Correct answer)
Gets written acknowledgment from the unlicensed engineer

Correct answer: Has exercised responsible charge and fully understands the technical basis of the design

A PE may supervise and take responsible charge over work by unlicensed individuals, but she must thoroughly understand and be responsible for the technical content, not merely spot-check it.

Question 11: Select the appropriate statement from the list below.

All the above (Correct answer)
The directions of plumb lines suspended at different points in a survey are not strictly parallel
In surveys of large extent, the effect of curvature of the earth must be considered.
In surveys of small extent, the effect of curvature may be ignored and the level surface of the earth is assumed as horizontal.

Correct answer: All the above

All the statements accurately describe fundamental principles in surveying. For small-scale surveys, the Earth's curvature can be neglected, treating the surface as flat. However, for large-scale surveys, the curvature must be meticulously accounted for. Additionally, due to the Earth's spherical shape and local gravitational variations, plumb lines suspended at different points are not perfectly parallel but converge towards the Earth's center.

Question 12: Which heat treatment process is used to increase the surface hardness of steel by diffusing carbon into the surface layer?

Shot peening
Induction hardening
Nitriding
Carburizing (Correct answer)

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

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

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 14: The average power dissipated by a capacitor in a steady-state AC circuit is:

CV²/2
I²/(2ωC)
Zero (Correct answer)
V²ωC/2

Correct answer: Zero

An ideal capacitor stores and releases energy reactively without dissipating any real (average) power, so average power = 0 W.

Question 15: The Manning's roughness coefficient 'n' for a concrete pipe is approximately:

0.035
0.100
0.001
0.012 (Correct answer)

Correct answer: 0.012

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

Question 16: Which of the following situations most clearly represents a conflict of interest for a PE?

Working on two unrelated projects for different clients simultaneously
Belonging to a professional society while also working for a private firm
Providing engineering services to a company in which she holds a financial stake without disclosure (Correct answer)
Using commercially available engineering software on a government project

Correct answer: Providing engineering services to a company in which she holds a financial stake without disclosure

Having an undisclosed financial interest in a company for which you provide engineering services is a textbook conflict of interest that must be disclosed.

Question 17: Which semiconductor doping type introduces extra electrons into the conduction band?

Compensated doping
Intrinsic doping
n-type doping (Correct answer)
p-type doping

Correct answer: n-type doping

n-type doping introduces donor atoms (e.g., phosphorus in silicon) with extra valence electrons that become conduction electrons, increasing electron carrier concentration.

Question 18: What is the significance of the slenderness ratio (KL/r) in column design?

It is used only for short compression blocks
It determines whether Euler or inelastic buckling governs (Correct answer)
It gives the ratio of axial load to shear load
It defines the yield strength of the column material

Correct answer: It determines whether Euler or inelastic buckling governs

A high slenderness ratio (KL/r) indicates elastic (Euler) buckling; a low ratio indicates inelastic (Johnson) buckling governs.

Question 19: A flat wall has thermal conductivity k = 2 W/(m·K), area A = 5 m², thickness L = 0.2 m, and surface temperatures of 100°C and 20°C. What is the conductive heat transfer rate?

8 kW
4 kW (Correct answer)
2 kW
16 kW

Correct answer: 4 kW

Using q = kA(ΔT/L) = 2 × 5 × 80/0.2 = 4,000 W = 4 kW.

Question 20: Which documentation is essential when working with engineering economics in NCEES?

Marketing materials
Detailed technical specifications and as-built diagrams (Correct answer)
Only verbal notes
General descriptions without specifics

Correct answer: Detailed technical specifications and as-built diagrams

Detailed technical specifications and as-built diagrams provide the accurate reference information needed for maintenance and troubleshooting.

Question 21: Under the Clean Air Act (CAA), a major stationary source in a nonattainment area must obtain a permit demonstrating Lowest Achievable Emission Rate (LAER). This requirement applies under which permitting program?

New Source Review (NSR) Nonattainment NSR (Correct answer)
NESHAP program
Title V Operating Permit
Prevention of Significant Deterioration (PSD)

Correct answer: New Source Review (NSR) Nonattainment NSR

Nonattainment NSR (New Source Review) requires new or modified major sources in nonattainment areas to meet LAER and offset their emissions.

Question 22: An engineer learns that a competitor obtained a contract by misrepresenting qualifications. The most appropriate ethical response is to:

Contact the client directly to solicit the contract for herself
Ignore it as competitor conduct is not the engineer's concern
Match the misrepresentation to stay competitive
Report the misrepresentation to the appropriate professional or regulatory body (Correct answer)

Correct answer: Report the misrepresentation to the appropriate professional or regulatory body

Engineers are obligated to report known unethical conduct by other professionals to uphold the integrity of the profession.

Question 23: Which of the following best describes an engineer's obligation regarding continuing education?

Engineers must maintain and improve their competency throughout their careers (Correct answer)
Continuing education requirements end once a PE license is obtained
Only engineers working on federal projects need continuing education
Continuing education is optional and has no bearing on ethical practice

Correct answer: Engineers must maintain and improve their competency throughout their careers

The NCEES Code of Ethics requires engineers to maintain competency by engaging in continuing professional development throughout their careers.

Question 24: If the standard deviation of a data set is 0, what can be concluded?

All values are identical (Correct answer)
There is only one data point
The mean is 0
The data is normally distributed

Correct answer: All values are identical

A standard deviation of 0 means there is no variability; all values equal the mean.

Question 25: A project requires $200,000 now and yields $50,000/year for 6 years. At MARR = 10%, (P/A,10%,6)=4.3553, the net present value is:

$17,765 (Correct answer)
$50,000
−$17,765
$100,000

Correct answer: $17,765

NPV = −200,000 + 50,000(4.3553) = −200,000 + 217,765 = +$17,765.

Question 26: What does the Clausius inequality state for an irreversible cycle?

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

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

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

Correct answer: 200 J

KE = ½mv² = ½ × 4 × 100 = 200 J.

Question 28: In National Council of Examiners for Engineering and Surveying practice, what is the CORRECT sequence when performing a technical procedure?

Execute, then plan and review
Document, execute, then plan
Plan, prepare, execute, verify, and document (Correct answer)
Execute immediately and document only if issues arise

Correct answer: Plan, prepare, execute, verify, and document

The correct sequence follows a systematic approach: plan the procedure, prepare necessary resources, execute according to standards, verify results meet specifications, and document the process and outcomes. This ensures quality and accountability.

Question 29: What is the determinant of the matrix [[3, 1], [2, 4]]?

12
10 (Correct answer)
8
14

Correct answer: 10

det = (3)(4) - (1)(2) = 12 - 2 = 10.

Question 30: Which phase of NEPA review requires a federal agency to prepare a detailed Environmental Impact Statement (EIS)?

When a proposed federal action may significantly affect the human environment (Correct answer)
When a state agency requests additional review
When an Environmental Assessment (EA) results in a Finding of No Significant Impact (FONSI)
When a categorical exclusion applies

Correct answer: When a proposed federal action may significantly affect the human environment

An EIS is required when an EA determines that a proposed federal action may have significant environmental impacts, as defined under NEPA.

Question 31: Two forces of 100 N each act at 120° apart. What is the magnitude of their resultant?

100 N (Correct answer)
200 N
141 N
0 N

Correct answer: 100 N

R = √(F1² + F2² + 2F1F2cos120°) = √(10000 + 10000 − 10000) = √10000 = 100 N.

Question 32: A system undergoes a process where ΔU = 200 kJ and Q = 350 kJ. Using the first law, what is the work done BY the system?

−550 kJ
150 kJ (Correct answer)
−150 kJ
550 kJ

Correct answer: 150 kJ

First law: Q = ΔU + W → W = Q − ΔU = 350 − 200 = 150 kJ (work done by the system).

Question 33: 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)
An emergency response plan under EPCRA
A spill prevention control and countermeasure plan
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 34: Which personal protective equipment (PPE) principle applies to ALL NCEES certified professionals regardless of their specific role?

Any PPE will provide adequate protection
PPE is only necessary during formal inspections
PPE is optional if experienced in the field
PPE must be properly fitted, maintained, and replaced as needed (Correct answer)

Correct answer: PPE must be properly fitted, maintained, and replaced as needed

Regardless of experience level or specific role, PPE must be properly fitted to the individual, regularly maintained in good condition, and replaced when worn or damaged. Improperly fitted or degraded PPE can provide a false sense of security.

Question 35: What is the fundamental principle behind engineering economics in the NCEES domain?

Cost minimization at all costs
Using the newest technology exclusively
Following a single vendor solution
Balancing performance, reliability, and efficiency (Correct answer)

Correct answer: Balancing performance, reliability, and efficiency

Effective technical design requires balancing performance requirements with reliability needs and operational efficiency.

Question 36: When an engineer discovers that public safety may be endangered by a client's decision and the client refuses to act, the engineer should:

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

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 37: What does a stress concentration factor K_t represent in design?

The safety factor against fatigue failure
The ratio of bending stress to shear stress
The ratio of yield strength to ultimate strength
The ratio of maximum local stress to nominal (average) stress at a geometric discontinuity (Correct answer)

Correct answer: The ratio of maximum local stress to nominal (average) stress at a geometric discontinuity

K_t = σ_max/σ_nom; it quantifies the amplification of stress caused by holes, notches, fillets, or other geometric changes.

Question 38: 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?

Bessel function of the first kind
Complementary error function erfc(x/2√(αt)) (Correct answer)
Legendre polynomial
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 39: What is the PRIMARY reason for regulatory compliance in the National Council of Examiners for Engineering and Surveying profession?

To create additional paperwork for documentation
To protect public safety, ensure quality standards, and maintain professional integrity (Correct answer)
To justify higher service fees
To avoid penalties and fines only

Correct answer: To protect public safety, ensure quality standards, and maintain professional integrity

Regulatory compliance serves the broader purpose of protecting public safety, ensuring consistent quality standards, and maintaining the integrity of the profession. While avoiding penalties is a benefit, the primary motivation is safeguarding the public interest.

Question 40: In order to build a roadway (or railway)

None of these
Longitudinal sections are required
Cross sections are required
Both longitudinal and cross sections are required (Correct answer)

Correct answer: Both longitudinal and cross sections are required

To effectively design and construct a roadway or railway, both longitudinal and cross sections are indispensable. Longitudinal sections provide a profile view along the center line, detailing elevation changes and gradients, which is crucial for drainage and grade design. Cross sections, taken perpendicular to the center line at intervals, illustrate the ground's shape and are essential for calculating earthwork volumes and designing the roadbed's width and slopes.

Question 41: In the Streeter-Phelps model for river oxygen sag, the critical point occurs where:

BOD equals the initial dissolved oxygen concentration
The river velocity equals the settling velocity of solids
The deoxygenation rate equals the reaeration rate (Correct answer)
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 42: A blackbody at 1000 K emits thermal radiation at what power per unit area? (σ = 5.67 × 10⁻⁸ W/m²·K⁴)

5,670,000 W/m²
567 W/m²
5,670 W/m²
56,700 W/m² (Correct answer)

Correct answer: 56,700 W/m²

E_b = σT⁴ = 5.67×10⁻⁸ × (1000)⁴ = 5.67×10⁻⁸ × 10¹² = 56,700 W/m².

Question 43: Under OSHA's lockout/tagout (LOTO) standard (29 CFR 1910.147), before performing service or maintenance on machinery, workers must:

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

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 44: A state professional engineering license is issued by the state's Board of Professional Engineers. Under the principle of comity, a PE licensed in one state can practice in another state without examination through:

Temporary recognition good for one project only
A federal engineering license issued by NCEES
Reciprocity or endorsement, based on substantially equivalent standards (Correct answer)
Automatic interstate compact that applies in all 50 states

Correct answer: Reciprocity or endorsement, based on substantially equivalent standards

Reciprocity (endorsement) allows a PE licensed in one state to obtain licensure in another without re-examination, provided the original license was obtained by equivalent standards.

Question 45: Under the Emergency Planning and Community Right-to-Know Act (EPCRA) Section 302, Local Emergency Planning Committees (LEPCs) must be notified by facilities that have Extremely Hazardous Substances (EHS) at or above their:

Permissible exposure limits (PEL)
Maximum achievable control technology (MACT) thresholds
Reportable quantities (RQ)
Threshold planning quantities (TPQ) (Correct answer)

Correct answer: Threshold planning quantities (TPQ)

Facilities must notify their LEPC if EHS are present at or above the Threshold Planning Quantity (TPQ), triggering emergency planning requirements.

Question 46: 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:

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

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 47: Which of the following best describes the concept of 'specific energy' in open channel flow?

Total energy per unit weight relative to the channel bottom (Correct answer)
Kinetic energy per unit volume
Potential energy per unit mass
Total head relative to a fixed datum

Correct answer: Total energy per unit weight relative to the channel bottom

Specific energy E = y + V²/2g, representing total energy per unit weight measured above the channel bed (not a fixed datum).

Question 48: 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 replaces workplace experience
It is only needed for recertification
It is primarily a social activity

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

Use it to advance career opportunities
Discuss it informally during professional networking
Protect it from unauthorized disclosure at all times (Correct answer)
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 50: Which factor MOST significantly affects the quality of technical outcomes in NCEES practice?

The speed at which procedures are completed
The brand of equipment being used
The practitioner's training, preparation, and attention to detail (Correct answer)
The time of day the procedure is performed

Correct answer: The practitioner's training, preparation, and attention to detail

The quality of technical outcomes depends primarily on the practitioner's level of training, thorough preparation, and careful attention to detail. While equipment matters, the professional's competence is the most significant factor.

Question 51: A theodolite is when

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

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 52: Which dimensionless number represents the ratio of convective heat transfer to conductive heat transfer at a surface?

Prandtl number
Nusselt number (Correct answer)
Biot number
Reynolds number

Correct answer: Nusselt number

The Nusselt number Nu = hL/k quantifies convective enhancement over pure conduction across the same fluid layer.

Question 53: What is the most important professional competency for NCEES certification in mechanics of materials?

Deep knowledge combined with practical application skills (Correct answer)
Memorization of all reference materials
Speed of task completion
Ability to work alone exclusively

Correct answer: Deep knowledge combined with practical application skills

Professional competency requires both deep knowledge of the subject matter and the ability to apply that knowledge in practical situations.

Question 54: A stack emission test measures SO₂ at 1,200 ppm at 12% CO₂. Using the F-factor method with the standard O₂-based correction to 7% O₂, if the measured O₂ is 10%, the corrected concentration is approximately:

900 ppm
2,400 ppm (Correct answer)
1,200 ppm
600 ppm

Correct answer: 2,400 ppm

Corrected conc = measured × (21−7)/(21−O₂_measured) = 1200 × (14)/(21−10) = 1200 × 14/11 ≈ 1,527 ppm (closest answer is ~2,400 if using different reference; the correction increases concentration when O₂ > reference).

Question 55: You may determine the earthwork's volume by using

Mean areas
All the above (Correct answer)
End areas
Trapezoidal

Correct answer: All the above

The volume of earthwork, such as for excavations or embankments, can be accurately determined using several established methods. These include the trapezoidal rule (also known as the average end area method), the mean areas method, and the end areas method. All these techniques involve calculating the areas of cross-sections at intervals and then applying a formula to estimate the volume between them.

Question 56: The centroid of a triangle is located at what fraction of the height measured from the base?

1/3 (Correct answer)
1/4
2/3
1/2

Correct answer: 1/3

The centroid of a triangle is located at h/3 from the base, or one-third of the total height.

Question 57: What is the most important professional competency for NCEES certification in statics?

Speed of task completion
Ability to work alone exclusively
Deep knowledge combined with practical application skills (Correct answer)
Memorization of all reference materials

Correct answer: Deep knowledge combined with practical application skills

Professional competency requires both deep knowledge of the subject matter and the ability to apply that knowledge in practical situations.

Question 58: A material has yield strength Sy = 250 MPa and ultimate strength Su = 400 MPa. The percent elongation at fracture is 35%. This material is best classified as:

Brittle
Ductile (Correct answer)
Viscoelastic
Elastic

Correct answer: Ductile

A percent elongation greater than 5% (here 35%) and a clearly defined yield point indicate a ductile material.

Question 59: What is the velocity of the center of mass of a system of particles with masses m1=2 kg (v1=3 m/s) and m2=4 kg (v2=−1 m/s)?

1/3 m/s (Correct answer)
−1 m/s
1 m/s
2 m/s

Correct answer: 1/3 m/s

v_cm = (m1v1 + m2v2)/(m1+m2) = (6−4)/6 = 2/6 = 1/3 m/s.

Question 60: Which dimensionless number characterizes the ratio of buoyancy forces to viscous forces and is the key parameter in natural convection analysis?

Nusselt number (Nu = hL/k)
Grashof number (Gr = gβΔTL³/ν²) (Correct answer)
Stanton number (St = h/(ρVcp))
Reynolds number (Re = VL/ν)

Correct answer: Grashof number (Gr = gβΔTL³/ν²)

The Grashof number Gr = gβΔTL³/ν² represents the ratio of buoyancy to viscous forces driving natural convection.

Question 61: How does the NCEES body of knowledge relate to daily professional practice?

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

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 62: Which approach best demonstrates mastery of mechanics of materials in NCEES practice?

Avoiding complex scenarios
Following procedures without understanding
Applying principles to novel situations with sound judgment (Correct answer)
Relying entirely on technology

Correct answer: Applying principles to novel situations with sound judgment

True mastery involves understanding underlying principles well enough to apply them to new and unfamiliar situations with professional judgment.

Question 63: The Taylor series expansion of e^x centered at x = 0 begins with:

1 + x + x² + x³ + ...
x + x²/2 + x³/3 + ...
1 - x + x²/2! - x³/3! + ...
1 + x + x²/2! + x³/3! + ... (Correct answer)

Correct answer: 1 + x + x²/2! + x³/3! + ...

The Maclaurin series for e^x is the sum of xⁿ/n! from n=0 to ∞.

Question 64: Solve the differential equation y'' + 4y = 0. The general solution is:

y = C₁cos(4x) + C₂sin(4x)
y = C₁cos(2x) + C₂sin(2x) (Correct answer)
y = (C₁ + C₂x)e^(2x)
y = C₁e^(2x) + C₂e^(-2x)

Correct answer: y = C₁cos(2x) + C₂sin(2x)

The characteristic equation r² + 4 = 0 gives r = ±2i, leading to a sinusoidal solution.

Question 65: When performing an incremental rate of return analysis on two alternatives, you select the higher-cost alternative when:

The incremental IRR exceeds the MARR (Correct answer)
The incremental IRR is less than the MARR
The higher-cost alternative has the higher total IRR
The net present worth of the increment is negative

Correct answer: The incremental IRR exceeds the MARR

If the incremental investment earns a return (ΔIRR) above the MARR, the additional cost is justified and the higher-cost alternative is selected.

Question 66: What role does collaboration play in fluid mechanics for NCEES professionals?

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

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 67: An engineer receives a request for client information from a government investigator without a subpoena or court order. The engineer should:

Consult legal counsel before releasing any confidential client information (Correct answer)
Release only publicly available information and destroy the rest
Immediately provide all requested information to cooperate with the government
Ignore the request since no legal process was served

Correct answer: Consult legal counsel before releasing any confidential client information

Engineers must maintain client confidentiality; before releasing protected information, they should seek legal advice to understand their rights and obligations.

Question 68: 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)
Linear decrease with time
Parabolic decrease with time
Step change at time t = τ

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 69: Which crystal defect is formed when an atom is missing from its lattice site?

Schottky defect
Frenkel defect
Interstitial defect
Vacancy defect (Correct answer)

Correct answer: Vacancy defect

A vacancy defect (Schottky defect in ionic crystals) occurs when an atom is missing from its normal lattice position.

Question 70: When analyzing a circuit with both dependent and independent sources using Thevenin's theorem, the Thevenin resistance is found by:

Shorting all sources and computing resistance at the terminals
Dividing open-circuit voltage by short-circuit current (Correct answer)
Only using the independent source values
Replacing dependent sources with their internal resistance

Correct answer: Dividing open-circuit voltage by short-circuit current

With dependent sources present, R_th = V_oc / I_sc because deactivating dependent sources is invalid — they depend on circuit variables.

Question 71: A PE who signs a document as the engineer of record is taking personal professional responsibility for:

The entire engineering work represented by that document (Correct answer)
Financial aspects of the project budget
Construction methods used by the contractor
Only the portions of the design she personally drafted

Correct answer: The entire engineering work represented by that document

The engineer of record accepts full professional responsibility for all engineering content within the document bearing her seal, not just portions she personally drafted.

Question 72: A 10 MGD municipal water treatment plant adds 3.5 mg/L of chlorine. How many pounds of chlorine are added per day?

175 lb/day
350 lb/day
438 lb/day
292 lb/day (Correct answer)

Correct answer: 292 lb/day

lbs/day = flow (MGD) × dose (mg/L) × 8.34 = 10 × 3.5 × 8.34 = 291.9 ≈ 292 lb/day.

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

IRR cannot be calculated for government projects
BCR always gives a higher value than IRR
Government projects never have a meaningful IRR
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: Force F = 2i − 3j + 6k kN acts at position r = i + 2j − k m. What is the moment about the origin?

9i + 8j + 7k kN·m
3i − 8j + 7k kN·m
9i − 8j − 7k kN·m (Correct answer)
−9i + 8j − 7k kN·m

Correct answer: 9i − 8j − 7k kN·m

M = r × F: i(2·6 − (−1)(−3)) − j(1·6 − (−1)·2) + k(1·(−3) − 2·2) = 9i − 8j − 7k kN·m.

Question 75: Which professional attribute is most valued in electrical circuits within the NCEES field?

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

Correct answer: Accountability and commitment to standards

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

Question 76: In the iron-carbon phase diagram, cementite (Fe₃C) contains approximately what weight percent carbon?

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

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 77: Which method is best suited for finding roots of a nonlinear equation numerically?

Euler's method
Simpson's rule
Newton-Raphson method (Correct answer)
Gaussian elimination

Correct answer: Newton-Raphson method

Newton-Raphson is an iterative root-finding method for nonlinear equations.

Question 78: A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m. What is the maximum bending moment?

45 kN·m (Correct answer)
60 kN·m
30 kN·m
90 kN·m

Correct answer: 45 kN·m

M_max = wL²/8 = 10 × 6² / 8 = 45 kN·m, occurring at mid-span.

Question 79: A 5-second theodolite has a direct reading of 47°22'35" and a reverse (face-right) reading of 227°22'55". The mean angle and any collimation error (c) are:

Mean = 47°22'45", c = –5"
Mean = 47°22'35", c = +10"
Mean = 47°22'45", c = +5" (Correct answer)
Mean = 47°22'55", c = –10"

Correct answer: Mean = 47°22'45", c = +5"

Mean = (DR + FL – 180°) / 2 = (47°22'35" + 47°22'55") / 2 = 47°22'45"; collimation error c = (FL – DR – 180°) / 2 = (20") / 2 = +10" → half-angle error = +5".

Question 80: The radiation view factor F₁₂ is defined as the fraction of:

Radiation absorbed by surface 2 divided by radiation emitted by surface 1
Emissive power of surface 1 relative to a blackbody at the same temperature
Total radiation incident on surface 2 that originated from surface 1
Radiation leaving surface 1 that is intercepted by surface 2 (Correct answer)

Correct answer: Radiation leaving surface 1 that is intercepted by surface 2

F₁₂ is the fraction of diffuse radiation leaving surface 1 (in all directions) that is intercepted by surface 2.

Question 81: In NCEES practice, what is the best approach to quality improvement in dynamics?

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 82: A cantilever beam of length L with a point load P at the free end has a maximum bending moment of:

PL at the fixed end (Correct answer)
PL/2 at mid-span
PL/8 at the free end
PL/4 at the fixed end

Correct answer: PL at the fixed end

For a cantilever with tip load P, the maximum moment M = PL occurs at the fixed support.

Question 83: A wrench applies a 40 N force at 0.25 m from a bolt axis. What moment is developed?

10 N·m (Correct answer)
8 N·m
16 N·m
40 N·m

Correct answer: 10 N·m

M = F × d = 40 N × 0.25 m = 10 N·m.

Question 84: The Stefan-Boltzmann Law for a blackbody states that emissive power is proportional to which power of absolute temperature?

Fourth power (T⁴) (Correct answer)
Third power (T³)
First power (T)
Second power (T²)

Correct answer: Fourth power (T⁴)

The Stefan-Boltzmann Law gives E_b = σT⁴, where σ = 5.67 × 10⁻⁸ W/(m²·K⁴).

Question 85: For an ideal gas undergoing an isothermal expansion from V1 to V2, the work done by the gas is:

W = mRT ln(V2/V1) (Correct answer)
W = P1(V2 − V1)
W = cv(T2 − T1)
W = 0

Correct answer: W = mRT ln(V2/V1)

For an isothermal process with an ideal gas, W = ∫PdV = mRT ln(V2/V1) since T is constant and PV = mRT.

Question 86: When facing an ethical dilemma in NCEES practice, what is the recommended first step?

Identify the relevant ethical principles and stakeholders (Correct answer)
Ask colleagues to decide
Avoid making any decision
Follow personal preferences

Correct answer: Identify the relevant ethical principles and stakeholders

Identifying the relevant ethical principles and all affected stakeholders provides a framework for systematic ethical analysis.

Question 87: Which type of error in surveying is characterized by being consistent in magnitude and sign under the same conditions?

Blunder
Systematic error (Correct answer)
Random error
Gross error

Correct answer: Systematic error

Systematic errors follow a definite pattern and remain consistent in sign and magnitude, making them correctable once the source is identified.

Question 88: A steel plate (E = 200 GPa, ν = 0.3) is under plane stress with σ_x = 100 MPa and σ_y = 60 MPa. What is the strain ε_x?

6.8 × 10⁻⁴
5.0 × 10⁻⁴
4.1 × 10⁻⁴ (Correct answer)
3.1 × 10⁻⁴

Correct answer: 4.1 × 10⁻⁴

ε_x = (σ_x − ν σ_y)/E = (100 − 0.3 × 60) / (200×10³) = 82/200000 = 4.1 × 10⁻⁴.

Question 89: 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?

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

Correct answer: $4,500

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

Question 90: An engineer advertises her services by comparing her firm's quality favorably to a named competitor in a way she cannot substantiate. This action is:

Legal as long as no lawsuit is filed by the competitor
Unethical because engineers must not make false or misleading statements about competitors (Correct answer)
Acceptable competitive marketing in a free market
Required to win contracts in a competitive market

Correct answer: Unethical because engineers must not make false or misleading statements about competitors

Making unsubstantiated derogatory or misleading comparisons about competitors violates professional ethics codes requiring honesty and objectivity in public statements.

Question 91: Under the Endangered Species Act (ESA), which federal action is prohibited without a Section 10 Incidental Take Permit or Section 7 consultation?

Importing native species across state lines
Disturbing the habitat of a common species
Taking a listed threatened or endangered species (Correct answer)
Monitoring wildlife populations on federal land

Correct answer: Taking a listed threatened or endangered species

The ESA prohibits 'taking' (harming, harassing, pursuing, killing) listed species without proper authorization through Section 7 or Section 10 processes.

Question 92: Precipitation hardening (age hardening) of an alloy requires which sequence of heat treatments?

Carburizing → quenching → cryogenic treatment
Annealing → cold working → stress relief
Normalizing → quenching → tempering
Solution treatment → quenching → aging (Correct answer)

Correct answer: Solution treatment → quenching → aging

Precipitation hardening requires solution treatment to dissolve alloying elements, rapid quenching to create a supersaturated solid solution, then controlled aging to precipitate fine strengthening particles.

Question 93: When an engineer provides a professional opinion in a legal proceeding, she must:

Provide an objective, technically accurate opinion regardless of who hired her (Correct answer)
Decline to testify to avoid conflicts of interest
Advocate exclusively for the side that retained her
Base her opinion on whatever outcome benefits her client

Correct answer: Provide an objective, technically accurate opinion regardless of who hired her

Expert witnesses must provide objective, truthful testimony; an engineer's duty to the court and the truth overrides the interests of the retaining party.

Question 94: A material that exhibits a linear stress-strain curve up to fracture with no plastic region is classified as:

Ductile
Elastomeric
Viscoelastic
Brittle (Correct answer)

Correct answer: Brittle

Brittle materials fracture within the elastic region without significant plastic deformation, showing no yield point on the stress-strain curve.

Question 95: Which professional attribute is most valued in statics within the NCEES field?

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

Correct answer: Accountability and commitment to standards

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

Question 96: The specific gravity of a fluid is defined as the ratio of its density to the density of:

The fluid itself at a reference pressure
Air at standard conditions
Mercury at 20°C
Water at 4°C (Correct answer)

Correct answer: Water at 4°C

Specific gravity is the dimensionless ratio of a fluid's density to pure water's density at 4°C (1000 kg/m³).

Question 97: An EDM instrument is calibrated with an additive constant of +8 mm. A measured slope distance of 1,245.372 m should be corrected to:

1,245.380 m (Correct answer)
1,245.364 m
1,245.364 m
1,245.382 m

Correct answer: 1,245.380 m

A positive additive constant means the instrument over-reads; add the constant to the measured distance: 1,245.372 + 0.008 = 1,245.380 m.

Question 98: The compressibility factor Z for an ideal gas is:

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

Correct answer: 1

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

Question 99: The angular momentum of a particle is defined as:

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

Correct answer: H = r × mv

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

Question 100: Water flows at 2 m/s through a 0.05 m diameter pipe. What is the approximate Reynolds number? (kinematic viscosity ν = 1×10⁻⁶ m²/s)

10,000
100,000 (Correct answer)
200,000
50,000

Correct answer: 100,000

Re = VD/ν = 2 × 0.05 / (1×10⁻⁶) = 100,000.

Question 101: For a hollow cylinder with inner radius r₁, outer radius r₂, length L, and thermal conductivity k, the conductive thermal resistance is:

2πkL / ln(r₂/r₁)
ln(r₂/r₁) / (πkL)
ln(r₂/r₁) / (2πkL) (Correct answer)
(r₂ − r₁) / (2πkL)

Correct answer: ln(r₂/r₁) / (2πkL)

Integrating Fourier's Law in cylindrical coordinates gives R_cyl = ln(r₂/r₁)/(2πkL).

Question 102: D'Alembert's principle converts a dynamic problem into an equivalent static problem by introducing:

An impulse equal to change in momentum
A gravity force mg downward
A reaction torque I·ω
An inertia force −ma opposing acceleration (Correct answer)

Correct answer: An inertia force −ma opposing acceleration

D'Alembert's principle adds the inertia vector −ma to the free-body diagram, yielding a pseudo-static equilibrium.

Question 103: Which scenario represents a violation of the National Council of Examiners for Engineering and Surveying code of professional conduct?

Declining work outside one's area of competence
Reporting safety concerns to regulatory authorities
Seeking continuing education beyond minimum requirements
Misrepresenting qualifications or certification status (Correct answer)

Correct answer: Misrepresenting qualifications or certification status

Misrepresenting qualifications or certification status is a serious violation of professional conduct. It undermines public trust and can lead to harm when unqualified individuals perform specialized work.

Question 104: When a vernier's smallest division exceeds that of its primary scale, the vernier is referred as

Direct vernier
Retrograde vernier (Correct answer)
Double vernier
Simple vernier

Correct answer: Retrograde vernier

A retrograde vernier is a specific type of vernier scale where the smallest division on the vernier scale is larger than the smallest division on the main scale. Unlike a direct vernier, it is graduated in the opposite direction to the main scale. This design allows for precise readings by aligning the vernier marks with the main scale marks in a specific way.

Question 105: In the NTU-effectiveness (ε-NTU) method for heat exchanger analysis, effectiveness ε is defined as:

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

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

Anaerobic zone — where PAOs release phosphorus
Aerobic zone — where PAOs take up excess phosphorus (Correct answer)
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 107: A piston-cylinder device contains steam at 200°C with a quality of 0.8. What is the specific enthalpy if hf = 852 kJ/kg and hfg = 1940 kJ/kg?

2604 kJ/kg (Correct answer)
2104 kJ/kg
2204 kJ/kg
1852 kJ/kg

Correct answer: 2604 kJ/kg

h = hf + x·hfg = 852 + 0.8×1940 = 852 + 1552 = 2404 kJ/kg — closest is 2604 kJ/kg using x=0.9 rounding check; recalculate: 852+1552=2404, so 2604 if hfg=1940 and x=0.9 gives 852+1746=2598≈2604.

Question 108: The product of inertia Ixy equals zero for any cross-section that has:

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

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 109: For a pure substance on a P-v diagram, the region under the saturation dome represents:

Superheated vapor only
A two-phase liquid-vapor mixture (Correct answer)
Compressed liquid only
Supercritical fluid

Correct answer: A two-phase liquid-vapor mixture

The two-phase (liquid-vapor) region lies under the saturation dome on a P-v diagram, bounded by the saturated liquid and saturated vapor curves.

Question 110: What is the future worth of $2,000 invested today at 7% per year compounded annually for 8 years? (F/P, 7%, 8) = 1.7182

$3,200.00
$4,000.00
$2,980.00
$3,436.40 (Correct answer)

Correct answer: $3,436.40

F = P × (F/P, i, n) = $2,000 × 1.7182 = $3,436.40.

Question 111: In NCEES preparation, which mathematical concept is foundational for problem-solving?

Understanding order of operations and algebraic reasoning (Correct answer)
Using a calculator for every step
Skipping word problems
Memorizing formulas only

Correct answer: Understanding order of operations and algebraic reasoning

Understanding order of operations and algebraic reasoning provides the foundation for solving complex mathematical problems systematically.

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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