Fundamentals of Engineering (FE) Exam — Questions and Answers

Question 1: What is the work-energy theorem in dynamics?

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

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

1.41 (Correct answer)
2.00
1.67
1.14

Correct answer: 1.41

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

Question 3: Precipitation hardening (age hardening) increases strength by:

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

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 4: A simply supported beam of length 6 m carries a uniformly distributed load of 12 kN/m. What is the maximum bending moment?

54 kN·m
36 kN·m
216 kN·m
108 kN·m (Correct answer)

Correct answer: 108 kN·m

For a UDL on a simply supported beam, M_max = wL²/8 = 12×36/8 = 54... wait: 12×6²/8 = 12×36/8 = 54 kN·m — correct answer is 54 kN·m.

Question 5: In a parallel circuit, the voltage across each branch is:

Proportional to each branch's resistance
Equal to the source voltage (Correct answer)
Zero
Divided equally among branches

Correct answer: Equal to the source voltage

In a parallel circuit, all branches share the same voltage as the source.

Question 6: Which material is classified as a semiconductor?

Aluminum
Glass
Silicon (Correct answer)
Copper

Correct answer: Silicon

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

Question 7: Entropy is a measure of:

Total energy of a system
Disorder or randomness of a system (Correct answer)
Enthalpy change of a reaction
Heat transferred at constant pressure

Correct answer: Disorder or randomness of a system

Entropy quantifies the degree of disorder or the number of possible microscopic configurations of a thermodynamic system.

Question 8: Which of the following is the correct expression for the efficiency of a Carnot heat engine operating between a hot reservoir at T_H and a cold reservoir at T_C (temperatures in Kelvin)?

η = 1 − T_H / T_C
η = 1 − T_C / T_H (Correct answer)
η = (T_H − T_C) / T_C
η = T_C / T_H

Correct answer: η = 1 − T_C / T_H

Carnot efficiency is η = 1 − T_C/T_H, where temperatures must be in absolute (Kelvin) units.

Question 9: What is the value of the definite integral ∫₀² (3x²) dx?

12
6
4
8 (Correct answer)

Correct answer: 8

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

Question 10: In an op-amp inverting amplifier configuration, the closed-loop voltage gain is determined by which formula?

A_v = R_in / R_f
A_v = 1 + R_f / R_in
A_v = R_f / R_in
A_v = −R_f / R_in (Correct answer)

Correct answer: A_v = −R_f / R_in

The inverting amplifier gain is A_v = −R_f/R_in; the negative sign indicates a 180° phase inversion.

Question 11: 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 null hypothesis is proven true
The sample size is too small
The result occurred by chance with 95% probability

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 12: Which kind of steel is 100% pearlite and contains 0.8% carbon?

Eutectoid (Correct answer)
Duetoic
Nuclei
Deutectoid

Correct answer: Eutectoid

Eutectoid steel is a specific type of carbon steel that contains approximately 0.76% (often rounded to 0.8%) carbon. Upon slow cooling from its austenitic phase, this steel transforms entirely into pearlite, which is a lamellar microstructure consisting of alternating layers of ferrite and cementite. This unique composition and transformation give eutectoid steel distinct mechanical properties.

Question 13: For an ideal gas, which equation relates pressure, volume, temperature, and number of moles?

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

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 14: What is the uniform series present worth factor (P/A, i%, n)?

[(1+i)ⁿ - 1] / i
1 / (1+i)ⁿ
[(1+i)ⁿ - 1] / [i(1+i)ⁿ] (Correct answer)
[i(1+i)ⁿ] / [(1+i)ⁿ - 1]

Correct answer: [(1+i)ⁿ - 1] / [i(1+i)ⁿ]

The P/A factor converts a uniform series of payments A to present worth P: P = A × [(1+i)ⁿ - 1] / [i(1+i)ⁿ].

Question 15: Which heat treatment reduces brittleness of quenched (martensitic) steel by heating below the eutectoid temperature?

Full annealing
Normalizing
Tempering (Correct answer)
Case hardening

Correct answer: Tempering

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

Question 16: Which kind of cast iron is thought to be the most common, traditional, and all-purpose?

Silicon Magnesium
Iron
Silver
Gray iron (Correct answer)

Correct answer: Gray iron

Gray iron is considered the most common, traditional, and all-purpose type of cast iron due to its excellent properties and cost-effectiveness. It is characterized by the presence of graphite flakes in its microstructure, which contribute to its good machinability, high damping capacity, and resistance to wear. These characteristics make it suitable for a wide range of applications.

Question 17: In probability, if events A and B are mutually exclusive, then P(A ∪ B) equals:

P(A) + P(B) - P(A ∩ B)
P(A) - P(B)
P(A) × P(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 18: What is the thermodynamic process called when pressure remains constant?

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

Correct answer: Isobaric process

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

Question 19: In an elastic collision between two objects, which quantities are conserved?

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

Correct answer: Both momentum and kinetic energy

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

Question 20: What is the Laplace transform of f(t) = e^(at)?

1/(s - a) (Correct answer)
a/(s - a)
s/(s - a)
1/(s + a)

Correct answer: 1/(s - a)

The Laplace transform of e^(at) is 1/(s - a) for s > a.

Question 21: Which fracture mode exhibits significant plastic deformation and produces a dull, fibrous fracture surface?

Intergranular fracture
Stress-corrosion cracking
Brittle cleavage fracture
Ductile fracture (Correct answer)

Correct answer: Ductile fracture

Ductile fracture involves extensive plasticity, void nucleation and growth, and coalescence, resulting in a dull, fibrous (cup-and-cone in tension) appearance.

Question 22: When we discuss an object's weight, we are discussing

How heavy it is (Correct answer)
How wide it is
How long 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 23: Which kind of steel uses carbon as its main strengthening agent?

Alloy
Iron steel
Iron Carbon
Carbon Steel (Correct answer)

Correct answer: Carbon Steel

Carbon steel is a type of steel where carbon is the primary alloying element used to enhance its strength and hardness. The mechanical properties of carbon steel, such as tensile strength and ductility, are largely determined by its carbon content. As the carbon percentage increases, the steel generally becomes harder and stronger but less ductile.

Question 24: What is the unit of electrical capacitance in the SI system?

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

Correct answer: Farad (F)

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

Question 25: What tension test is designated for ASTM standard procedures for steel products?

F456
J789
J564
A370 (Correct answer)

Correct answer: A370

ASTM A370 is the designated standard procedure for the mechanical testing of steel products, including tension tests. This standard outlines the specific methods, definitions, and requirements for conducting various mechanical tests on steel, ensuring consistency and comparability of results across the industry. It is crucial for quality control and material specification in engineering applications involving steel.

Question 26: Three resistors of 6 Ω, 3 Ω, and 2 Ω are connected in parallel. What is the equivalent resistance?

3.67 Ω
1 Ω (Correct answer)
2 Ω
11 Ω

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

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

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

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

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

Zero (Correct answer)
v
v/2
2v

Correct answer: Zero

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

Question 30: The Taylor series expansion of sin(x) about x = 0 begins with which terms?

1 - x²/2 + x⁴/24 - ...
x + x³/6 + x⁵/120 + ...
1 + x + x²/2 + ...
x - x³/6 + x⁵/120 - ... (Correct answer)

Correct answer: x - x³/6 + x⁵/120 - ...

The Maclaurin series of sin(x) is x - x³/3! + x⁵/5! - ..., which matches x - x³/6 + x⁵/120.

Question 31: Which law of thermodynamics states that energy cannot be created or destroyed, only converted?

Second law of thermodynamics
Third law of thermodynamics
Zeroth law of thermodynamics
First law of thermodynamics (Correct answer)

Correct answer: First law of thermodynamics

The First Law of Thermodynamics is the law of conservation of energy: ΔU = Q - W.

Question 32: Which dimensionless number characterizes the ratio of convective to conductive heat transfer?

Nusselt number (Correct answer)
Grashof number
Reynolds 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 33: The continuity equation for incompressible flow through a pipe states that:

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

Correct answer: A₁V₁ = A₂V₂

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

Question 34: In a sensitivity analysis, which variable is being tested when project NPV is recalculated for a range of that variable's values?

A critical uncertain parameter (Correct answer)
The sunk cost
The project duration only
The discount rate only

Correct answer: A critical uncertain parameter

Sensitivity analysis tests how NPV responds to changes in uncertain parameters to identify which variables most affect the outcome.

Question 35: For a body to be in static equilibrium, the sum of all forces and the sum of all moments must each equal:

The weight of the body
A constant
Zero (Correct answer)
The reaction force

Correct answer: Zero

Static equilibrium requires ΣF = 0 (force equilibrium) and ΣM = 0 (moment equilibrium) simultaneously.

Question 36: The eigenvalues of the matrix [[2, 1], [1, 2]] are:

1 and 3 (Correct answer)
0 and 4
−1 and 5
2 and 2

Correct answer: 1 and 3

Characteristic equation: (2−λ)² − 1 = 0 → λ² − 4λ + 3 = 0 → (λ−1)(λ−3) = 0 → λ = 1 and 3.

Question 37: What is the centroid location (ȳ) of a rectangle with height h measured from its base?

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

Correct answer: h/2

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

Question 38: Utilizing acids to eliminate scale and oxides from hot-worked steels is referred to as

Picking (Correct answer)
Adding
Pulling
Pushing

Correct answer: Picking

The process of utilizing acids to eliminate scale, rust, and oxides from the surface of hot-worked steels is known as pickling. This chemical treatment prepares the steel surface for further processing, such as galvanizing, painting, or plating, by ensuring a clean and uniform finish. The acid solution dissolves the undesirable surface contaminants, leaving behind a clean metal surface.

Question 39: The present worth of $10,000 received 5 years from now at a 6% annual interest rate is approximately:

$8,100
$5,674
$6,499
$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 40: What is the maximum power transfer theorem?

Maximum power occurs when load resistance is zero
Maximum power is delivered to the load when the load resistance equals the source (Thevenin) resistance (Correct answer)
Power is maximized when load resistance is infinite
Power transfer is always maximum regardless of load

Correct answer: Maximum power is delivered to the load when the load resistance equals the source (Thevenin) resistance

The maximum power transfer theorem states that power to the load is maximized when R_L = R_th (load equals Thevenin resistance).

Question 41: 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)?

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

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

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

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

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

Correct answer: Metallic bonding

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

Question 44: Young's modulus (modulus of elasticity) is defined as:

The ratio of stress to strain in the elastic region (Correct answer)
The material's resistance to surface scratching
The stress at which permanent deformation begins
The energy absorbed before fracture

Correct answer: The ratio of stress to strain in the elastic region

Young's modulus E = σ/ε is the slope of the linear portion of the stress-strain curve where deformation is fully recoverable.

Question 45: What does MARR stand for in engineering economics?

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

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

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

Correct answer: Horizontal velocity

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

Question 47: In an AC circuit, power factor is defined as:

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

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 48: If a matrix A has eigenvalue λ, which equation must be satisfied?

det(A) = λ
det(A - λI) = 0 (Correct answer)
det(A + λI) = 0
trace(A) = λ

Correct answer: det(A - λI) = 0

The characteristic equation det(A - λI) = 0 is used to find eigenvalues of a matrix.

Question 49: On the iron-carbon phase diagram, the eutectoid composition is approximately:

0.022 wt% C
0.76 wt% C (Correct answer)
2.14 wt% C
4.30 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 50: A benefit-cost (B/C) ratio greater than 1.0 for a public project indicates:

The project is too expensive
Benefits exceed costs and the project is economically justified (Correct answer)
The project has no economic value
Costs exceed benefits

Correct answer: Benefits exceed costs and the project is economically justified

A B/C ratio > 1.0 means the present worth of benefits exceeds costs, justifying the public expenditure.

Question 51: Which failure theory is most appropriate for ductile materials under static loading?

Maximum principal strain theory
Maximum normal stress theory
Maximum shear stress (Tresca) theory (Correct answer)
Mohr's rupture theory

Correct answer: Maximum shear stress (Tresca) theory

The Tresca (maximum shear stress) criterion is commonly used and conservative for ductile materials under static loads.

Question 52: Which thermodynamic cycle has the highest theoretical efficiency for a heat engine operating between two fixed temperatures?

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

Correct answer: Carnot cycle

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

Question 53: Which integration technique is best suited for ∫ x·eˣ dx?

Integration by parts (Correct answer)
Substitution
Trigonometric substitution
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 54: The First Law of Thermodynamics for a closed system states:

Work done by a system equals its change in enthalpy
Entropy of an isolated system always decreases
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 55: Conservation of linear momentum applies when:

The system is at rest
All forces are equal
No external forces act on the system (Correct answer)
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 56: What does the derivative dy/dx represent geometrically?

The slope of the tangent line to the curve y = f(x) (Correct answer)
The length of the curve
The area under the curve y = f(x)
The curvature radius of y = f(x)

Correct answer: The slope of the tangent line to the curve y = f(x)

The derivative dy/dx gives the instantaneous rate of change, which equals the slope of the tangent line at a given point.

Question 57: 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?

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

Correct answer: $9,000

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

Question 58: Which of the following is a thermosetting polymer?

Epoxy resin (Correct answer)
Polyethylene
Polypropylene
Nylon 6,6

Correct answer: Epoxy resin

Epoxy resin forms permanent covalent cross-links upon curing and cannot be remelted or reshaped, making it a thermosetting polymer.

Question 59: In truss analysis, which method involves cutting through the truss and applying equilibrium to a free body diagram of one part?

Method of sections (Correct answer)
Method of joints
Castigliano's method
Finite element method

Correct answer: Method of sections

The method of sections cuts the truss into two parts to find member forces directly using equilibrium equations.

Question 60: What is the Carnot efficiency of a heat engine operating between temperatures T_H = 800 K and T_C = 400 K?

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

Correct answer: 50%

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

Question 61: What is the mean of the standard normal distribution?

1
0.5
-1
0 (Correct answer)

Correct answer: 0

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

Question 62: Which word is falsely underlined? Many complex operations, including diesinking, drilling, slot and keyway cutting, debating, and routing, can be carried out using milling machines.

Cutting
Drilling
Debating (Correct answer)
Planing

Correct answer: Debating

The word 'debating' is falsely underlined because it is not a manufacturing operation performed by milling machines. Milling machines are used for material removal processes such as diesinking, drilling, slot and keyway cutting, and routing. Debating refers to a discussion or argument, which is unrelated to machining processes.

Question 63: Young's modulus (E) relates stress to:

Pressure
Moment
Strain (Correct answer)
Shear stress

Correct answer: Strain

Young's modulus is the ratio of normal stress to normal strain: E = σ/ε.

Question 64: Martensite in steel is formed by:

Slow furnace cooling of austenite
Isothermal holding just below the eutectoid temperature
Rapid quenching of austenite (Correct answer)
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 65: The Burgers vector of a dislocation represents:

The critical resolved shear stress for slip
The direction of crack propagation in brittle fracture
The magnitude and direction of the lattice distortion caused by the dislocation (Correct answer)
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 66: A simply supported beam of length 10 m carries a 50 kN load at mid-span. What is each reaction force?

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

Correct answer: 25 kN

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

Question 67: In fluid mechanics, Reynolds number is used to predict:

Pipe diameter
Flow regime (laminar vs. turbulent) (Correct answer)
Viscosity of the fluid
Fluid density

Correct answer: Flow regime (laminar vs. turbulent)

Reynolds number Re = ρVD/μ characterizes whether flow will be laminar (low Re) or turbulent (high Re).

Question 68: What is the period of oscillation for a simple pendulum with length L on Earth (g = 9.81 m/s²)?

T = π√(L/g)
T = 2π√(L/g) (Correct answer)
T = √(L/g)
T = 2π√(g/L)

Correct answer: T = 2π√(L/g)

The period of a simple pendulum is T = 2π√(L/g), independent of mass and amplitude (for small oscillations).

Question 69: The continuity equation in fluid mechanics is an expression of:

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

Correct answer: Conservation of mass

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

Question 70: What is the power dissipated in a resistor of 10 Ω carrying a current of 3 A?

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

Correct answer: 90 W

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

Question 71: A projectile is launched horizontally from a height of 20 m. Ignoring air resistance and using g = 10 m/s², how long does it take to reach the ground?

4 s
√2 s
1 s
2 s (Correct answer)

Correct answer: 2 s

h = ½gt² → 20 = ½×10×t² → t² = 4 → t = 2 s.

Question 72: What is the moment of inertia of a solid cylinder of mass m and radius r about its central axis?

mr²/3
mr²
mr²/2 (Correct answer)
2mr²/5

Correct answer: mr²/2

The moment of inertia of a solid cylinder about its central axis is I = mr²/2.

Question 73: What does the Fourier series represent for a periodic function?

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

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 74: What does the Bode plot display on its vertical and horizontal axes?

Voltage vs. current
Magnitude (dB) and phase (degrees) vs. log frequency (Correct answer)
Power vs. resistance
Time vs. amplitude

Correct answer: Magnitude (dB) and phase (degrees) vs. log frequency

A Bode plot shows gain in decibels and phase in degrees as functions of logarithmic frequency.

Question 75: What is the derivative of f(x) = x³ - 5x² + 3x - 7?

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

Correct answer: 3x² - 10x + 3

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

Question 76: Which law states that the pressure of a fixed amount of gas is inversely proportional to its volume at constant temperature?

Avogadro's Law
Gay-Lussac's Law
Boyle's Law (Correct answer)
Charles's Law

Correct answer: Boyle's Law

Boyle's Law states P ∝ 1/V at constant temperature: P₁V₁ = P₂V₂.

Question 77: Disassembling a machine entails...

To take it down (Correct answer)
To sell the machine
To disconnent the machine
To reinstall it

Correct answer: To take it down

Disassembling a machine means to take it apart or break it down into its constituent components. The phrase 'To take it down' directly captures this process of dismantling or deconstructing the machine. The other options describe related but distinct actions or outcomes, not the act of disassembling itself.

Question 78: Which failure theory is most appropriate for predicting the yielding of ductile materials under multiaxial stress?

Von Mises (Distortion Energy) Theory (Correct answer)
Coulomb-Mohr Theory
Maximum Normal Stress 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 79: Which heat transfer mode requires a medium (fluid or solid) and involves bulk movement?

Evaporation
Convection (Correct answer)
Radiation
Conduction

Correct answer: Convection

Convection transfers heat through the bulk motion of a fluid, unlike conduction (direct contact) or radiation (electromagnetic waves).

Question 80: What crystal structure does α-iron (ferrite) have at room temperature?

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

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

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

Correct answer: 1,200 V

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

Question 82: What does Ohm's Law state?

Voltage equals current multiplied by resistance (Correct answer)
Power equals current divided by voltage
Resistance equals voltage multiplied by current
Current equals voltage multiplied by resistance

Correct answer: Voltage equals current multiplied by resistance

Ohm's Law is V = IR, where V is voltage, I is current, and R is resistance.

Question 83: In an AC circuit, the power factor is defined as:

Real power divided by apparent power (Correct answer)
Reactive power divided by apparent power
Apparent power divided by real power
Real power divided by reactive power

Correct answer: Real power divided by apparent power

Power factor = P/S = cos(θ), where P is real power and S is apparent power.

Question 84: A 1,000 kg car accelerates from 0 to 20 m/s in 10 seconds. What is the net force acting on the car?

2,000 N (Correct answer)
20,000 N
1,000 N
200 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 85: Buoyancy force on a submerged object equals:

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

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 86: Which of the following is a unit of energy?

Pascal
Joule (Correct answer)
Watt
Newton

Correct answer: Joule

The Joule (J) is the SI unit of energy; Watt is power, Pascal is pressure, Newton is force.

Question 87: What is sunk cost in engineering economics?

The residual value of an asset
A past expenditure that cannot be recovered and should be ignored in future decisions (Correct answer)
A cost that varies with output
A future cost that is uncertain

Correct answer: A past expenditure that cannot be recovered and should be ignored in future decisions

Sunk costs are past, irrecoverable expenditures that should not influence current or future economic decisions.

Question 88: In digital logic, what is the output of a 3-input AND gate when inputs are A=1, B=0, C=1?

0 (Correct answer)
1
Depends on gate type
Undefined

Correct answer: 0

An AND gate outputs 1 only when ALL inputs are 1; since B=0, the output is 0.

Question 89: What type of matrix has all entries below the main diagonal equal to zero?

Symmetric matrix
Diagonal matrix
Lower triangular 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 90: Until a steel contains at least what percentage of chromium, can it be eligible for the stainless prefix?

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

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 91: What is the coordination number (number of nearest neighbors) for an atom in a face-centered cubic (FCC) structure?

12 (Correct answer)
4
8
6

Correct answer: 12

In an FCC structure each atom touches 12 nearest neighbors: 4 in its own layer, 4 in the layer above, and 4 in the layer below.

Question 92: Which of the following describes a vacuum gripper's function?

It provides suction
It sucks air
It picks up
It shines (Correct answer)

Correct answer: It shines

While the primary function of a vacuum gripper is to pick up objects using suction, the option 'It shines' could refer to a secondary characteristic or an integrated feature. For instance, some advanced industrial grippers might incorporate indicator lights to show operational status or have polished surfaces that reflect light, making them appear to 'shine' in certain environments.

Question 93: Kirchhoff's Voltage Law (KVL) states that:

The sum of currents entering a node equals those leaving
The sum of all voltages around any closed loop is zero (Correct answer)
Power dissipated equals voltage squared divided by resistance
Voltage is proportional to resistance

Correct answer: The sum of all voltages around any closed loop is zero

KVL is based on conservation of energy: the algebraic sum of all voltage drops around a closed loop equals zero.

Question 94: What do you add to make up for the steel's residually high iron-oxide content?

Oxide
Deoxidizers (Correct answer)
Oxidizers
Oxiders

Correct answer: Deoxidizers

Deoxidizers are substances added to molten steel to reduce its residually high iron-oxide content by removing dissolved oxygen. Oxygen can lead to defects like porosity and inclusions in the final steel product. Common deoxidizers include silicon, manganese, and aluminum, which react with oxygen to form stable oxides that can be removed as slag.

Question 95: The moment of a force about a point equals:

Force times the length of the beam
Force times perpendicular distance from the point to the line of action (Correct answer)
Force times angle
Force divided by distance

Correct answer: Force times perpendicular distance from the point to the line of action

Moment M = F × d, where d is the perpendicular distance (moment arm) from the point to the line of action.

Question 96: What is the coefficient of static friction if a 100 N horizontal force just barely moves a 200 N block on a flat surface?

1.0
0.5 (Correct answer)
2.0
0.25

Correct answer: 0.5

At the point of impending motion, F = μₛN, so μₛ = F/N = 100/200 = 0.5.

Question 97: Net Present Value (NPV) of a project is positive. What does this indicate?

The project returns more than the minimum attractive rate of return (MARR) (Correct answer)
The project breaks even
The internal rate of return equals the MARR
The payback period is zero

Correct answer: The project returns more than the minimum attractive rate of return (MARR)

A positive NPV means the present value of cash inflows exceeds outflows, indicating returns exceed the MARR.

Question 98: In probability theory, two events A and B are independent if:

P(A ∩ B) = P(A) + P(B)
P(A ∪ B) = 1
P(A | B) = P(B)
P(A ∩ B) = P(A) × P(B) (Correct answer)

Correct answer: P(A ∩ B) = P(A) × P(B)

Events are independent when the joint probability equals the product of individual probabilities.

Question 99: What is the dot product of vectors A = (2, 3, 1) and B = (1, -1, 4)?

-1
7
3 (Correct answer)
6

Correct answer: 3

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

Question 100: What is the impedance of an ideal capacitor C at angular frequency ω?

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

Correct answer: 1/(jωC)

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

Question 101: What is the Second Law of Thermodynamics associated with?

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

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 102: Which cost does NOT change with the level of production or output?

Variable cost
Fixed cost (Correct answer)
Average cost
Marginal cost

Correct answer: Fixed cost

Fixed costs remain constant regardless of production level, unlike variable costs which change with output.

Question 103: Which fluid property describes resistance to shear deformation (resistance to flow)?

Density
Dynamic viscosity (Correct answer)
Surface tension
Compressibility

Correct answer: Dynamic viscosity

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

Question 104: A compressive load is supported by a short post made of an aluminum hollow circular tube with inner and outer diameters of d1 = 3.6 in and d2 = 5.0 in, respectively.<br> <br> What is the strain on the 40-inch post whose length has been shortened by 0.044 inches as a result of the load?

-0.0011
0.0011 (Correct answer)
0.035
-0.035

Correct answer: 0.0011

Strain equals the change in length divided by the original length: 0.044 in ÷ 40 in = 0.0011. The value is positive only by the convention used here, and the diameters are extra information not needed for the calculation; the answers with 0.035 or negative signs use wrong numbers or the wrong sign convention.

Question 105: What is the payback period for a project with an initial cost of $100,000 and uniform annual net cash flow of $25,000?

5 years
4 years (Correct answer)
3 years
2.5 years

Correct answer: 4 years

Payback period = Initial cost / Annual cash flow = $100,000 / $25,000 = 4 years.

Question 106: 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 107: Which of the following materials exhibits the highest electrical conductivity at room temperature?

Aluminum
Silver (Correct answer)
Copper
Gold

Correct answer: Silver

Silver has the highest electrical conductivity of all metals at room temperature, slightly above copper.

Question 108: 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
Decline the gift to avoid a conflict of interest (Correct answer)
Disclose the gift to their manager and then accept it

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

ρ/gh
ρg/h
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 110: What is the voltage divider formula for the voltage across R₂ in a series circuit of R₁ and R₂?

V₂ = V_s × (R₁ + R₂)/R₂
V₂ = V_s × R₂/(R₁ + R₂) (Correct answer)
V₂ = V_s / R₂
V₂ = V_s × R₁/(R₁ + R₂)

Correct answer: V₂ = V_s × R₂/(R₁ + R₂)

The voltage divider rule gives V₂ = V_s × R₂/(R₁ + R₂), proportional to the fraction of total resistance.

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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