Fundamentals of Engineering (FE) Exam — Questions and Answers

Question 1: During an isentropic process, which pair of properties remains constant?

Enthalpy and volume
Entropy and heat transfer
Entropy (constant) with no heat transfer (Correct answer)
Temperature and pressure

Correct answer: Entropy (constant) with no heat transfer

An isentropic process is both adiabatic (no heat transfer) and reversible, so entropy remains constant.

Question 2: What is the hydrostatic pressure at a depth h in a fluid of density ρ?

ρg/h
ρ/gh
gh/ρ
ρgh (Correct answer)

Correct answer: ρgh

Hydrostatic pressure is p = ρgh, where ρ is fluid density, g is gravitational acceleration, and h is depth.

Question 3: Products made of steel that have been coated with

Silicon
Zinc (Correct answer)
Boron
Iron

Correct answer: Zinc

Steel products are often coated with zinc through a process called galvanization to protect them from corrosion. Zinc acts as a sacrificial coating, corroding preferentially to the steel and forming a protective layer of zinc oxides and carbonates that prevents the underlying steel from rusting. This significantly extends the lifespan of steel structures and components.

Question 4: What type of matrix has all entries below the main diagonal equal to zero?

Lower triangular matrix
Diagonal matrix
Symmetric matrix
Upper triangular matrix (Correct answer)

Correct answer: Upper triangular matrix

An upper triangular matrix has all entries below the main diagonal equal to zero.

Question 5: What is the Second Law of Thermodynamics associated with?

Entropy always increases in an isolated system (Correct answer)
All processes are reversible
Heat flows from cold to hot spontaneously
Energy cannot be converted

Correct answer: Entropy always increases in an isolated system

The Second Law states that entropy of an isolated system always increases, indicating irreversibility of natural processes.

Question 6: Stagnation pressure in compressible flow is the pressure measured at a point where:

The flow velocity is reduced to zero isentropically (Correct answer)
The temperature is at a maximum
The flow is fully turbulent
The density is at atmospheric value

Correct answer: The flow velocity is reduced to zero isentropically

Stagnation (total) pressure is the pressure that would result if the flow were brought to rest isentropically.

Question 7: A steel rod 2 m long with cross-sectional area 0.001 m² is subjected to a tensile force of 100 kN. If E = 200 GPa, what is the elongation?

0.5 mm
2.0 mm
0.1 mm
1.0 mm (Correct answer)

Correct answer: 1.0 mm

δ = FL/(AE) = 100,000×2/(0.001×200×10⁹) = 200,000/200,000,000 = 0.001 m = 1.0 mm.

Question 8: The endurance limit of a steel refers to:

The maximum achievable hardness after quenching
The alternating stress amplitude below which fatigue failure will not occur regardless of cycles (Correct answer)
The maximum static stress the material can sustain
The temperature above which creep deformation becomes significant

Correct answer: The alternating stress amplitude below which fatigue failure will not occur regardless of cycles

Ferrous materials exhibit an endurance limit — a stress amplitude below which the S-N curve becomes horizontal, implying infinite fatigue life.

Question 9: The standard deviation of the data set {4, 8, 6, 5, 7} is closest to:

1.67
1.41 (Correct answer)
2.00
1.14

Correct answer: 1.41

Mean = 6; squared deviations: 4,4,0,1,1 → variance = 10/5 = 2; σ = √2 ≈ 1.41.

Question 10: Which fluid property describes resistance to shear deformation (resistance to flow)?

Density
Surface tension
Dynamic viscosity (Correct answer)
Compressibility

Correct answer: Dynamic viscosity

Dynamic viscosity μ is the property that quantifies a fluid's resistance to shear stress and flow.

Question 11: A 3 Ω and 6 Ω resistor are connected in parallel. What is the equivalent resistance?

2 Ω (Correct answer)
9 Ω
4.5 Ω
0.5 Ω

Correct answer: 2 Ω

1/R_eq = 1/3 + 1/6 = 2/6 + 1/6 = 3/6, so R_eq = 2 Ω.

Question 12: What is the capital recovery (CR) cost of an asset?

The total depreciation over the asset's life
The equivalent annual cost of owning and financing the asset (Correct answer)
The salvage value at end of life
The initial purchase price divided by useful life

Correct answer: The equivalent annual cost of owning and financing the asset

Capital recovery cost is the equivalent annual amount to recover the initial investment and opportunity cost of capital.

Question 13: In chemical engineering, what does the term 'steady-state' mean for a process?

Temperature is uniform throughout
All flows are zero
The system is in chemical equilibrium
System properties do not change with time (Correct answer)

Correct answer: System properties do not change with time

Steady-state means all system properties (temperature, pressure, composition) remain constant over time, though flows may be nonzero.

Question 14: For a transformer with a turns ratio N₁:N₂ = 1:10, if the primary voltage is 120 V, what is the secondary voltage?

1,200 V (Correct answer)
120 V
12 V
10 V

Correct answer: 1,200 V

Transformer voltage ratio: V₂/V₁ = N₂/N₁ = 10/1, so V₂ = 120 × 10 = 1,200 V.

Question 15: A steel rod (E = 200 GPa) with a 500 mm² cross-section and 2 m length is subjected to a 100 kN tensile load. What is the elongation?

4.0 mm
0.5 mm
2.0 mm
1.0 mm (Correct answer)

Correct answer: 1.0 mm

δ = PL/(AE) = (100,000 × 2)/(500×10⁻⁶ × 200×10⁹) = 200,000/100,000,000 = 0.002 m = 2 mm — wait, δ = 1.0 mm: (100,000 × 2)/(500e-6 × 200e9) = 2e5/1e8 = 0.002 m — correcting: 100,000×2/(500×10⁻⁶×200×10⁹)=200,000/100,000,000=0.002 m=2 mm; choose 2.0 mm.

Question 16: Conservation of linear momentum applies when:

The system is at rest
No external forces act on the system (Correct answer)
All forces are equal
Kinetic energy is conserved

Correct answer: No external forces act on the system

Linear momentum is conserved when the net external force on the system is zero.

Question 17: Which numerical method uses the formula xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) to find roots?

Newton-Raphson method (Correct answer)
Secant method
Euler's method
Bisection method

Correct answer: Newton-Raphson method

The Newton-Raphson method iteratively refines root estimates using the function and its derivative.

Question 18: Which material is classified as a semiconductor?

Silicon (Correct answer)
Aluminum
Copper
Glass

Correct answer: Silicon

Silicon is the most widely used semiconductor, having conductivity between conductors and insulators.

Question 19: The present worth of $10,000 received 5 years from now at a 6% annual interest rate is approximately:

$8,100
$6,499
$5,674
$7,473 (Correct answer)

Correct answer: $7,473

PW = F/(1+i)^n = 10,000/1.06^5 = 10,000/1.3382 ≈ $7,473.

Question 20: What does a Thevenin equivalent circuit consist of?

Two voltage sources in series
A current source in parallel with a resistance
A capacitor in series with a resistor
A voltage source V_th in series with a resistance R_th (Correct answer)

Correct answer: A voltage source V_th in series with a resistance R_th

A Thevenin equivalent represents a linear network as a single voltage source V_th in series with Thevenin resistance R_th.

Question 21: Which thermodynamic law states that energy cannot be created or destroyed?

Second Law
First Law (Correct answer)
Zeroth Law
Third Law

Correct answer: First Law

The First Law of Thermodynamics is the law of conservation of energy.

Question 22: In straight-line depreciation, what is the annual depreciation for an asset costing $50,000 with a salvage value of $5,000 and useful life of 5 years?

$45,000
$10,000
$9,000 (Correct answer)
$8,000

Correct answer: $9,000

Annual depreciation = (Cost - Salvage) / Life = ($50,000 - $5,000) / 5 = $9,000.

Question 23: What is the breakeven point in engineering economics?

The output where fixed costs are recovered
The output level where profit is maximized
The output level where total revenue equals total cost (Correct answer)
The minimum production quantity

Correct answer: The output level where total revenue equals total cost

The breakeven point is where total revenue equals total cost, resulting in neither profit nor loss.

Question 24: The glass transition temperature (Tg) of a polymer is best described as the temperature:

At which the polymer melts and flows as a viscous liquid
Below which the polymer becomes glassy, stiff, and brittle (Correct answer)
At which crystallization from the melt begins
At which the polymer undergoes chemical decomposition

Correct answer: Below which the polymer becomes glassy, stiff, and brittle

Below Tg, polymer chain segments lack sufficient thermal energy to rotate or translate, making the material glassy and brittle rather than rubbery.

Question 25: Buoyancy force on a submerged object equals:

The weight of fluid displaced by the object (Correct answer)
The product of object density and gravity
The weight of the object itself
The pressure at the object's centroid times its volume

Correct answer: The weight of fluid displaced by the object

Archimedes' principle states that the buoyant force equals the weight of fluid displaced by the submerged object.

Question 26: Precipitation hardening (age hardening) increases strength by:

Dissolving interstitial impurities into the crystal lattice
Forming a complete solid solution that distorts the lattice uniformly
Increasing grain size to reduce total grain boundary area
Generating fine precipitates throughout the matrix that obstruct dislocation motion (Correct answer)

Correct answer: Generating fine precipitates throughout the matrix that obstruct dislocation motion

Fine, coherent precipitates act as obstacles that dislocations must either cut through or bypass (Orowan looping), both requiring additional stress.

Question 27: What type of force acts along a two-force member in a truss?

Pure axial (tension or compression) force only (Correct answer)
Shear force
Torsional force
Bending moment

Correct answer: Pure axial (tension or compression) force only

A two-force member has forces applied only at two points, resulting in pure axial load with no shear or bending.

Question 28: What is the work-energy theorem in dynamics?

Work equals mass times velocity
Energy is always conserved in friction systems
The net work done on a body equals the change in its kinetic energy (Correct answer)
Work equals force times time

Correct answer: The net work done on a body equals the change in its kinetic energy

The work-energy theorem states W_net = ΔKE = ½mv₂² - ½mv₁², relating net work to kinetic energy change.

Question 29: Which of the following best describes a scalar quantity?

Force
Velocity
Temperature (Correct answer)
Displacement

Correct answer: Temperature

Temperature has magnitude only, with no direction, making it a scalar; the others are vectors.

Question 30: What does the Fourier series represent for a periodic function?

A complex exponential representation only
A sum of sinusoidal components at integer multiples of the fundamental frequency (Correct answer)
A polynomial approximation of the function
A Taylor expansion about a point

Correct answer: A sum of sinusoidal components at integer multiples of the fundamental frequency

The Fourier series decomposes a periodic function into sinusoidal components at integer multiples of the fundamental frequency.

Question 31: What is the general solution to the ordinary differential equation dy/dx + 2y = 0?

y = C·sin(2x)
y = Ce^(2x)
y = C + 2x
y = Ce^(-2x) (Correct answer)

Correct answer: y = Ce^(-2x)

This first-order linear ODE has solution y = Ce^(-2x) obtained by separation of variables.

Question 32: Darcy-Weisbach equation is used to calculate:

Flow rate over a sharp-crested weir
Pressure recovery in a diffuser
Head loss due to friction in a pipe (Correct answer)
Velocity distribution in laminar pipe flow

Correct answer: Head loss due to friction in a pipe

The Darcy-Weisbach equation h_f = f(L/D)(V²/2g) computes frictional head loss in a pipe.

Question 33: What is the dot product of vectors A = (2, 3, 1) and B = (1, -1, 4)?

-1
6
3 (Correct answer)
7

Correct answer: 3

The dot product A·B = (2)(1) + (3)(-1) + (1)(4) = 2 - 3 + 4 = 3.

Question 34: Bernoulli's equation is derived from conservation of which quantity along a streamline?

Mass
Energy (Correct answer)
Momentum
Volume

Correct answer: Energy

Bernoulli's equation is an energy conservation equation along a streamline for steady, incompressible, inviscid flow.

Question 35: Which of the following is the correct formula for the determinant of a 2×2 matrix [a b; c d]?

ab - cd
ac - bd
ad - bc (Correct answer)
ad + bc

Correct answer: ad - bc

The determinant of a 2×2 matrix is calculated as ad - bc.

Question 36: Which of the following is NOT a typical reinforcing fiber used in polymer-matrix composites?

Copper fiber (Correct answer)
Carbon (graphite) fiber
Aramid (Kevlar) fiber
E-glass fiber

Correct answer: Copper fiber

Carbon, glass, and aramid fibers offer high specific strength and stiffness; copper is too dense and ductile to serve as an effective structural reinforcement fiber.

Question 37: What is the derivative of f(x) = x³ - 5x² + 3x - 7?

3x² - 10x + 3 (Correct answer)
3x² - 5x + 3
3x² - 10x - 7
x² - 10x + 3

Correct answer: 3x² - 10x + 3

Applying the power rule term by term yields 3x² - 10x + 3.

Question 38: A beam is in static equilibrium. Which two conditions must be satisfied?

ΣF = ma and ΣM = Iα
ΣF = ma and ΣM = 0
ΣF = 0 and ΣM = 0 (Correct answer)
ΣF = 0 and ΣM = Iα

Correct answer: ΣF = 0 and ΣM = 0

Static equilibrium requires that the sum of all forces and the sum of all moments about any point each equal zero.

Question 39: In an elastic collision between two objects, which quantities are conserved?

Kinetic energy only
Potential energy only
Both momentum and kinetic energy (Correct answer)
Momentum only

Correct answer: Both momentum and kinetic energy

Elastic collisions conserve both linear momentum and kinetic energy, unlike inelastic collisions.

Question 40: What is the thermodynamic process called when pressure remains constant?

Adiabatic process
Isothermal process
Isobaric process (Correct answer)
Isochoric process

Correct answer: Isobaric process

An isobaric process occurs at constant pressure; work done is W = PΔV.

Question 41: In probability, if events A and B are mutually exclusive, then P(A ∪ B) equals:

P(A) × P(B)
P(A) - P(B)
P(A) + P(B) - P(A ∩ B)
P(A) + P(B) (Correct answer)

Correct answer: P(A) + P(B)

For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).

Question 42: Without a coating, what is tin mill steel called?

Black plate (Correct answer)
Solid plate
Cladding
Coating

Correct answer: Black plate

Tin mill steel, when produced without any coating, is referred to as black plate. This uncoated steel sheet is typically thin and used as a base material before further processing, such as tin plating to create tinplate or chromium plating to create tin-free steel. The term 'black' refers to its appearance before any surface treatment.

Question 43: On the iron-carbon phase diagram, the eutectoid composition is approximately:

0.022 wt% C
0.76 wt% C (Correct answer)
4.30 wt% C
2.14 wt% C

Correct answer: 0.76 wt% C

The eutectoid point occurs at 0.76 wt% C and 727°C, where austenite transforms isothermally to pearlite (ferrite + cementite).

Question 44: What is the value of the definite integral ∫₀² (3x²) dx?

4
12
6
8 (Correct answer)

Correct answer: 8

Integrating 3x² gives x³, evaluated from 0 to 2 yields 8 - 0 = 8.

Question 45: What is the formula for Newton's second law in dynamics?

ΣF = m/a
ΣF = mv²
ΣF = ma (Correct answer)
ΣF = mv

Correct answer: ΣF = ma

Newton's second law states that the net force equals mass times acceleration: ΣF = ma.

Question 46: What is the unit of pressure in the SI system?

Pascal (Pa) (Correct answer)
Joule (J)
Watt (W)
Newton (N)

Correct answer: Pascal (Pa)

Pressure is force per unit area; 1 Pascal equals 1 N/m².

Question 47: What is the unit of electrical capacitance in the SI system?

Siemens (S)
Farad (F) (Correct answer)
Ohm (Ω)
Henry (H)

Correct answer: Farad (F)

Capacitance is measured in Farads (F), named after Michael Faraday.

Question 48: What does a capacitor store?

Magnetic energy in a magnetic field
Electrical energy in an electric field (Correct answer)
Thermal energy
Chemical energy

Correct answer: Electrical energy in an electric field

A capacitor stores electrical energy by accumulating charge on two conductive plates separated by an insulator.

Question 49: Which failure theory is most appropriate for predicting the yielding of ductile materials under multiaxial stress?

Von Mises (Distortion Energy) Theory (Correct answer)
Maximum Normal Stress Theory
Coulomb-Mohr Theory
Maximum Shear Stress Theory (Tresca)

Correct answer: Von Mises (Distortion Energy) Theory

The Von Mises criterion is the most accurate predictor of yielding in ductile metals under multiaxial loading.

Question 50: What does the Reynolds number represent in fluid mechanics?

The ratio of kinetic to potential energy
The ratio of inertial forces to viscous forces (Correct answer)
The ratio of velocity to acceleration
The ratio of pressure to density

Correct answer: The ratio of inertial forces to viscous forces

The Reynolds number Re = ρVD/μ is the ratio of inertial to viscous forces, used to predict flow regime (laminar vs. turbulent).

Question 51: A wheel rolls without slipping. If the center moves at velocity v, what is the velocity of the contact point?

2v
v/2
Zero (Correct answer)
v

Correct answer: Zero

For rolling without slipping, the instantaneous velocity at the contact point is zero (instantaneous center of rotation).

Question 52: Which integration technique is best suited for ∫ x·eˣ dx?

Substitution
Trigonometric substitution
Integration by parts (Correct answer)
Partial fractions

Correct answer: Integration by parts

Integration by parts (∫u dv = uv - ∫v du) is used when the integrand is a product of two different function types.

Question 53: For an ideal gas, which equation relates pressure, volume, temperature, and number of moles?

P = nRT/V²
PV² = nRT
PV = nRT (Correct answer)
PV = nT/R

Correct answer: PV = nRT

The ideal gas law PV = nRT relates pressure P, volume V, moles n, ideal gas constant R, and temperature T.

Question 54: The lever rule in a two-phase region of a phase diagram is used to determine:

The liquidus temperature at a given composition
The diffusivity of solute atoms in the matrix
The equilibrium crystal structure of each phase
The relative weight fractions of each phase present (Correct answer)

Correct answer: The relative weight fractions of each phase present

The lever rule uses the tie line in a two-phase region to calculate the weight fraction of each phase present at a given overall composition and temperature.

Question 55: A vacancy (point defect) in a crystal lattice is best described as:

An extra atom squeezed between lattice sites
A foreign atom substituting for a host atom
An atom displaced to an interstitial site leaving its original site empty
An atom missing from its normal lattice position (Correct answer)

Correct answer: An atom missing from its normal lattice position

A vacancy (Schottky defect) is simply a missing atom at a normally occupied lattice site.

Question 56: What happens to the entropy of a system during a reversible adiabatic process?

It decreases
It fluctuates
It remains constant (Correct answer)
It increases

Correct answer: It remains constant

A reversible adiabatic (isentropic) process has no heat transfer and no irreversibilities, so entropy remains constant.

Question 57: A 500 kg object is accelerated from rest to 20 m/s over 10 seconds on a frictionless surface. What net force is required?

500 N
1000 N (Correct answer)
250 N
10,000 N

Correct answer: 1000 N

F = ma = 500 × (20/10) = 500 × 2 = 1,000 N.

Question 58: Which thermodynamic cycle has the highest theoretical efficiency for a heat engine operating between two fixed temperatures?

Brayton cycle
Otto cycle
Rankine cycle
Carnot cycle (Correct answer)

Correct answer: Carnot cycle

The Carnot cycle sets the upper bound on efficiency for any heat engine operating between two temperature reservoirs.

Question 59: The continuity equation in fluid mechanics is an expression of:

Conservation of mass (Correct answer)
Newton's second law
Conservation of momentum
Conservation of energy

Correct answer: Conservation of mass

The continuity equation ∂ρ/∂t + ∇·(ρV) = 0 enforces conservation of mass in fluid flow.

Question 60: Galvanic corrosion is driven by:

Hydrogen embrittlement at high-stress sites
Electrical contact between two dissimilar metals in the presence of an electrolyte (Correct answer)
Uniform surface oxidation of a metal exposed to ambient air
Exposure of a single metal to high-temperature oxidizing gases

Correct answer: Electrical contact between two dissimilar metals in the presence of an electrolyte

When two metals with different electrode potentials are electrically coupled in an electrolyte, the more active (anodic) metal corrodes preferentially.

Question 61: What is the solution to the linear differential equation y'' + 4y = 0?

y = C₁cos(4x) + C₂sin(4x)
y = C₁e^(4x) + C₂
y = C₁cos(2x) + C₂sin(2x) (Correct answer)
y = C₁e^(2x) + C₂e^(-2x)

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

The characteristic equation r² + 4 = 0 gives r = ±2i, yielding the general solution y = C₁cos(2x) + C₂sin(2x).

Question 62: Which of the following best describes Bernoulli's equation?

Momentum balance across a control volume
Conservation of energy per unit volume along a streamline (Correct answer)
Conservation of mass for compressible flow
Newton's second law applied to viscous fluids

Correct answer: Conservation of energy per unit volume along a streamline

Bernoulli's equation expresses conservation of energy per unit volume (pressure + kinetic + potential) along a streamline for ideal flow.

Question 63: The continuity equation for incompressible flow through a pipe states that:

A₁ + V₁ = A₂ + V₂
A₁V₁² = A₂V₂²
A₁V₁ = A₂V₂ (Correct answer)
V₁/A₁ = V₂/A₂

Correct answer: A₁V₁ = A₂V₂

For incompressible flow, conservation of mass requires A₁V₁ = A₂V₂ (flow rate is constant).

Question 64: Which thermodynamic cycle has the highest theoretical efficiency for a heat engine operating between two fixed temperatures?

Rankine cycle
Carnot cycle (Correct answer)
Otto cycle
Brayton cycle

Correct answer: Carnot cycle

The Carnot cycle sets the upper limit of efficiency for any heat engine operating between two thermal reservoirs.

Question 65: What is head loss due to friction in a pipe best described by?

Darcy-Weisbach equation (Correct answer)
Manning's equation
Continuity equation
Bernoulli's equation

Correct answer: Darcy-Weisbach equation

The Darcy-Weisbach equation h_f = f(L/D)(V²/2g) gives the friction head loss in a pipe.

Question 66: Three resistors of 6 Ω, 3 Ω, and 2 Ω are connected in parallel. What is the equivalent resistance?

11 Ω
3.67 Ω
2 Ω
1 Ω (Correct answer)

Correct answer: 1 Ω

1/R_eq = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 6/6 = 1, so R_eq = 1 Ω.

Question 67: What is the power consumed by a device drawing 2 A at 120 V?

122 W
480 W
60 W
240 W (Correct answer)

Correct answer: 240 W

Power P = IV = 2 A × 120 V = 240 W.

Question 68: In environmental engineering, BOD (Biochemical Oxygen Demand) is a measure of:

The amount of oxygen required by bacteria to decompose organic matter (Correct answer)
The concentration of nitrogen compounds in water
The turbidity of a water sample
The dissolved oxygen content of water

Correct answer: The amount of oxygen required by bacteria to decompose organic matter

BOD quantifies the oxygen consumed by microorganisms when breaking down organic material in water, indicating pollution level.

Question 69: In statistics, what does a p-value less than 0.05 typically indicate?

The result is statistically significant at the 5% level (Correct answer)
The sample size is too small
The result occurred by chance with 95% probability
The null hypothesis is proven true

Correct answer: The result is statistically significant at the 5% level

A p-value < 0.05 indicates statistical significance at the 5% level, meaning we reject the null hypothesis.

Question 70: What is the determinant of the matrix [[2,1],[3,4]]?

11
8
5 (Correct answer)
14

Correct answer: 5

det = (2)(4) − (1)(3) = 8 − 3 = 5.

Question 71: The Burgers vector of a dislocation represents:

The magnitude and direction of the lattice distortion caused by the dislocation (Correct answer)
The critical resolved shear stress for slip
The direction of crack propagation in brittle fracture
The angle of misorientation across a grain boundary

Correct answer: The magnitude and direction of the lattice distortion caused by the dislocation

The Burgers vector characterizes a dislocation by quantifying the magnitude and direction of the lattice slip associated with it.

Question 72: The direct transformation from

Liquid to gas phase
Gas to liquid phase
Liquid to solid phase
Solid to gaseous phase (Correct answer)

Correct answer: Solid to gaseous phase

Sublimation is the phase transition of a substance directly from the solid to the gaseous phase without passing through the intermediate liquid phase. This process occurs when a substance absorbs enough energy to overcome the intermolecular forces holding it in a solid state, allowing its molecules to escape directly into the gas phase. A common example is dry ice (solid carbon dioxide) sublimating into gaseous carbon dioxide.

Question 73: An engineer receives a gift from a vendor whose company bids on the engineer's projects. According to NSPE Code of Ethics, the engineer should:

Accept it if its value is under $50
Accept it only after the project is awarded
Disclose the gift to their manager and then accept it
Decline the gift to avoid a conflict of interest (Correct answer)

Correct answer: Decline the gift to avoid a conflict of interest

Engineers must avoid gifts from parties with a vested interest in their decisions to maintain objectivity and public trust.

Question 74: What is the cutoff frequency of a first-order RC low-pass filter with R = 1 kΩ and C = 1 μF?

~159 Hz (Correct answer)
~1,000 Hz
~1,592 Hz
~100 Hz

Correct answer: ~159 Hz

f_c = 1/(2πRC) = 1/(2π × 1000 × 10⁻⁶) = 1/(2π × 10⁻³) ≈ 159 Hz.

Question 75: Which atomic bonding type is primarily responsible for the high electrical conductivity of metals?

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

Correct answer: Metallic bonding

Metallic bonding involves a 'sea' of delocalized electrons that are free to move, enabling high electrical and thermal conductivity.

Question 76: What crystal structure does α-iron (ferrite) have at room temperature?

Simple cubic
Hexagonal close-packed (HCP)
Face-centered cubic (FCC)
Body-centered cubic (BCC) (Correct answer)

Correct answer: Body-centered cubic (BCC)

α-iron (ferrite) has a BCC crystal structure at room temperature, transitioning to FCC austenite above 912°C.

Question 77: A 1,000 kg car accelerates from 0 to 20 m/s in 10 seconds. What is the net force acting on the car?

1,000 N
2,000 N (Correct answer)
200 N
20,000 N

Correct answer: 2,000 N

Acceleration a = Δv/Δt = 20/10 = 2 m/s². Net force F = ma = 1,000 × 2 = 2,000 N.

Question 78: What is the Carnot efficiency of a heat engine operating between temperatures T_H = 800 K and T_C = 400 K?

100%
50% (Correct answer)
75%
25%

Correct answer: 50%

Carnot efficiency η = 1 - T_C/T_H = 1 - 400/800 = 0.50 = 50%.

Question 79: What is the mean of the standard normal distribution?

0 (Correct answer)
1
0.5
-1

Correct answer: 0

The standard normal distribution N(0,1) has a mean of 0 and standard deviation of 1.

Question 80: Which heat treatment reduces brittleness of quenched (martensitic) steel by heating below the eutectoid temperature?

Case hardening
Normalizing
Tempering (Correct answer)
Full annealing

Correct answer: Tempering

Tempering reheats martensitic steel to a sub-eutectoid temperature, allowing some carbon precipitation and relieving internal stresses to improve toughness.

Question 81: Which kind of bonding is dominated by electrostatic attraction?

Unipolar bonding
Chemical bonding
Covalent bonding
Ionic bonding (Correct answer)

Correct answer: Ionic bonding

Ionic bonding is a type of chemical bond characterized by the strong electrostatic attraction between oppositely charged ions. This occurs when one atom donates one or more electrons to another atom, creating a positively charged ion (cation) and a negatively charged ion (anion). The strong electrostatic force between these ions holds the compound together.

Question 82: What type of filter passes low frequencies and attenuates high frequencies?

Band-stop filter
Band-pass filter
High-pass filter
Low-pass filter (Correct answer)

Correct answer: Low-pass filter

A low-pass filter allows frequencies below a cutoff frequency to pass while attenuating higher frequencies.

Question 83: It is what draws similar molecules to one another.

Adhesion
Reduction
Cohesion (Correct answer)
Conduction

Correct answer: Cohesion

Cohesion is the intermolecular force that causes similar molecules to be attracted to one another. This attraction is responsible for phenomena like surface tension in liquids, where water molecules stick together. In contrast, adhesion refers to the attraction between dissimilar molecules.

Question 84: When we discuss an object's weight, we are discussing

How long it is
How heavy it is (Correct answer)
How wide it is
How high it is

Correct answer: How heavy it is

When we discuss an object's weight, we are referring to the force exerted on it by gravity. This force is directly perceived as how heavy the object is. Options A, C, and D describe physical dimensions (length, height, width), which are distinct from the concept of weight.

Question 85: Until a steel contains at least what percentage of chromium, can it be eligible for the stainless prefix?

10% (Correct answer)
3%
12&
15&

Correct answer: 10%

For a steel to be eligible for the 'stainless' prefix, it must contain a minimum of 10% (or more precisely, 10.5%) chromium by mass. Chromium forms a passive, self-repairing oxide layer on the steel's surface, which provides its characteristic corrosion resistance. This protective layer is what distinguishes stainless steel from other types of steel.

Question 86: In an AC circuit, power factor is defined as:

The ratio of reactive power to apparent power
The ratio of resistance to impedance
The ratio of voltage to current
cos(θ), where θ is the phase angle between voltage and current (Correct answer)

Correct answer: cos(θ), where θ is the phase angle between voltage and current

Power factor = cos(θ), where θ is the phase angle between voltage and current; it ranges from 0 to 1.

Question 87: What is the centroid location (ȳ) of a rectangle with height h measured from its base?

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

Correct answer: h/2

The centroid of a rectangle is at its geometric center, which is h/2 from any edge.

Question 88: What is the power dissipated in a resistor of 10 Ω carrying a current of 3 A?

900 W
3 W
30 W
90 W (Correct answer)

Correct answer: 90 W

Power P = I²R = (3)² × 10 = 9 × 10 = 90 W.

Question 89: What is meant by MES?

Manufacturing execution system (Correct answer)
Materials enabling system
Millimeter exit space
Master of Engineering Science

Correct answer: Manufacturing execution system

MES stands for Manufacturing Execution System. It is a comprehensive, dynamic information system that monitors, tracks, documents, and controls the process of manufacturing from raw materials to finished goods. MES helps optimize production operations by providing real-time data, managing work orders, and integrating with other enterprise systems like ERP.

Question 90: Martensite in steel is formed by:

Rapid quenching of austenite (Correct answer)
Isothermal holding just below the eutectoid temperature
Slow furnace cooling of austenite
Prolonged annealing in the two-phase region

Correct answer: Rapid quenching of austenite

Rapid quenching of austenite traps carbon in a supersaturated body-centered tetragonal structure, producing hard, brittle martensite through a diffusionless transformation.

Question 91: Which dimensionless number characterizes the ratio of convective to conductive heat transfer?

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

Correct answer: Nusselt number

The Nusselt number Nu = hL/k is the ratio of convective to conductive heat transfer across a boundary.

Question 92: A hollow cylindrical pressure vessel has an inner radius of 0.5 m, wall thickness of 25 mm, and internal pressure of 2 MPa. What is the hoop stress?

40 MPa (Correct answer)
20 MPa
160 MPa
80 MPa

Correct answer: 40 MPa

Hoop stress σ_h = pr/t = (2×10⁶ × 0.5)/0.025 = 40 MPa.

Question 93: The hydraulic conductivity of a soil is tested using a sample, which is a cylindrical container 25 cm in length and 10 cm in diameter on a circular cross section. What is the soil's hydraulic conductivity when the sample is exposed to a 50 cm head and an 8 cm3/min flow rate is measured through it?

0.025 cm/min
0.05 cm/min (Correct answer)
2 cm/min
0.10 cm/min

Correct answer: 0.05 cm/min

Among the provided options: The closest option is 0.05 cm/min 0.05cm/min. Therefore, the hydraulic conductivity of the soil is approximately 0.05 cm/min 0.05cm/min.

Question 94: Which programming construct allows a block of code to repeat until a condition is false?

Switch statement
Loop (while/for) (Correct answer)
Function call
If-else statement

Correct answer: Loop (while/for)

Loop structures (while, for, do-while) repeatedly execute a code block as long as the specified condition remains true.

Question 95: What does MARR stand for in engineering economics?

Maximum Allowable Rate of Return
Mean Annual Rate of Return
Minimum Attractive Rate of Return (Correct answer)
Minimum Acceptable Revenue Ratio

Correct answer: Minimum Attractive Rate of Return

MARR (Minimum Attractive Rate of Return) is the minimum return a project must earn to be considered acceptable.

Question 96: In probability, if two events A and B are mutually exclusive, what is P(A ∪ B)?

P(A) + P(B) (Correct answer)
P(A) / P(B)
P(A) × P(B)
P(A) + P(B) − P(A∩B)

Correct answer: P(A) + P(B)

For mutually exclusive events, P(A∩B) = 0, so P(A∪B) = P(A) + P(B).

Question 97: What is the unit of angular momentum in the SI system?

kg·m²/s²
kg·m²/s (Correct answer)
kg·m/s
N·m

Correct answer: kg·m²/s

Angular momentum L = Iω has units of kg·m² × rad/s = kg·m²/s.

Question 98: Which method of economic comparison finds the interest rate that makes NPV = 0?

Internal Rate of Return (IRR) (Correct answer)
Annual Worth method
Benefit-Cost Ratio
Net Present Value (NPV)

Correct answer: Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is the discount rate that makes the net present value of all cash flows equal to zero.

Question 99: A Carnot engine operates between 800 K and 400 K. What is its maximum theoretical efficiency?

25%
50% (Correct answer)
100%
75%

Correct answer: 50%

Carnot efficiency = 1 − T_L/T_H = 1 − 400/800 = 0.50 = 50%.

Question 100: A 10 kg block rests on a 30° incline with μ_s = 0.4. What is the maximum static friction force available (g = 9.81 m/s²)?

39.2 N
19.62 N
49.0 N
34.0 N (Correct answer)

Correct answer: 34.0 N

Normal force N = mg cos30° = 10×9.81×0.866 = 84.9 N; f_s_max = μ_s × N = 0.4×84.9 ≈ 34.0 N.

Question 101: A capacitor of 100 μF is charged to 50 V. How much energy is stored?

2.5 J
0.125 J (Correct answer)
0.25 J
5.0 J

Correct answer: 0.125 J

Energy W = ½CV² = ½ × 100×10⁻⁶ × 50² = ½ × 100×10⁻⁶ × 2500 = 0.125 J.

Question 102: What is the impedance of an ideal capacitor C at angular frequency ω?

1/(jωC) (Correct answer)
R + jωL
jωC
jωL

Correct answer: 1/(jωC)

The impedance of a capacitor is Z_C = 1/(jωC), which decreases with increasing frequency.

Question 103: Which economic analysis method converts all costs and benefits to an equivalent annual amount?

Future Worth (FW) method
Present Worth (PW) method
Internal Rate of Return (IRR)
Annual Worth (AW) method (Correct answer)

Correct answer: Annual Worth (AW) method

The Annual Worth method expresses all cash flows as an equivalent uniform annual series for comparison.

Question 104: In projectile motion (neglecting air resistance), which component of velocity remains constant?

Total velocity magnitude
Horizontal velocity (Correct answer)
Vertical velocity
Both components

Correct answer: Horizontal velocity

The horizontal velocity remains constant because there is no horizontal force (neglecting air resistance).

Question 105: In pipe flow, what Reynolds number approximately marks the transition from laminar to turbulent flow?

~10,000
~100
~500
~2,300 (Correct answer)

Correct answer: ~2,300

Flow in a pipe transitions from laminar to turbulent at Re ≈ 2,300; above ~4,000 is fully turbulent.

Question 106: The First Law of Thermodynamics for a closed system states:

Entropy of an isolated system always decreases
Work done by a system equals its change in enthalpy
Change in internal energy equals heat added minus work done by system (Correct answer)
Heat added equals work done by the system

Correct answer: Change in internal energy equals heat added minus work done by system

ΔU = Q − W: the change in internal energy equals heat added to the system minus work done by the system.

Question 107: Which of the following converts electrical energy into mechanical energy?

Electric motor (Correct answer)
Transformer
Capacitor
Generator

Correct answer: Electric motor

An electric motor converts electrical energy into rotational (mechanical) energy.

Question 108: A simply supported beam of length 10 m carries a 50 kN load at mid-span. What is each reaction force?

25 kN (Correct answer)
50 kN
5 kN
10 kN

Correct answer: 25 kN

By symmetry, each support carries half the load: 50/2 = 25 kN.

Question 109: Which depreciation method gives the highest depreciation expense in the early years of an asset's life?

Double declining balance (DDB) (Correct answer)
Units of production
Straight-line method
Sum-of-years-digits (SYD)

Correct answer: Double declining balance (DDB)

The double declining balance method applies twice the straight-line rate to the book value, giving the highest early depreciation.

Question 110: In fatigue failure, crack initiation most commonly occurs at:

Surface defects, notches, or stress concentrations (Correct answer)
The geometric center of the cross-section
Uniformly distributed grain boundaries
Regions of maximum compressive stress

Correct answer: Surface defects, notches, or stress concentrations

Cyclic stress amplification at surface imperfections, machining marks, or geometric discontinuities makes them the preferred sites for fatigue crack initiation.

Fundamentals of Engineering (FE) Exam

The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a licensed professional engineer (PE). It is designed for recent graduates and students close to finishing an undergraduate engineering degree.

110

Questions

340 min

Time Limit

70%

To Pass

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