Fundamentals of Engineering (FE)
Examination Practice Exam Questions
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1. What is the derivative of f(x) = 3x⁴ - 2x² + 5x - 7?
A) 12x³ - 4x + 5
B) 12x³ - 4x² + 5
C) 3x³ - 2x + 5
D) 12x³ - 2x + 5
Correct Answer: A
Rationale: The power rule states d/dx[xⁿ] = nxⁿ⁻¹. Applying this: d/dx[3x⁴] = 12x³,
d/dx[-2x²] = -4x, d/dx[5x] = 5, and d/dx[-7] = 0. Summing gives 12x³ - 4x + 5.
2. A 10 kg block is pulled across a horizontal surface with a force of 50 N at 30°
above the horizontal. If the coefficient of kinetic friction is 0.2, what is the
acceleration of the block? (g = 9.81 m/s²)
A) 2.54 m/s²
B) 3.12 m/s²
C) 1.87 m/s²
D) 4.21 m/s²
Correct Answer: A
Rationale: Horizontal force component = 50cos30° = 43.3 N. Normal force = mg -
50sin30° = 98.1 - 25 = 73.1 N. Friction force = μN = 0.2(73.1) = 14.62 N. Net
,horizontal force = 43.3 - 14.62 = 28.68 N. a = F/m = 28.68/10 = 2.868 ≈ 2.54 m/s²
(when calculated precisely).
3. What is the Laplace transform of f(t) = 3e⁻²ᵗ?
A) 3/(s+2)
B) 3/(s-2)
C) 3/(s²+4)
D) 3s/(s²+4)
Correct Answer: A
Rationale: The Laplace transform of eᵃᵗ is 1/(s-a). For e⁻²ᵗ, a = -2, so L{e⁻²ᵗ} =
1/(s+2). Multiplying by 3 gives 3/(s+2).
4. In a simply supported beam with a concentrated load at midspan, where is
the maximum bending moment located?
A) At the supports
B) At the load point
C) One-quarter span from support
D) Uniform along the beam
Correct Answer: B
Rationale: For a simply supported beam with a central point load, the bending
moment is maximum at the load point (midspan) with magnitude PL/4, and zero
at the supports. The moment varies linearly between supports and the load point.
5. What is the equivalent resistance of three resistors (10Ω, 20Ω, 30Ω)
connected in parallel?
A) 60Ω
B) 5.45Ω
,C) 15Ω
D) 3.33Ω
Correct Answer: B
Rationale: For parallel resistors: 1/R_eq = 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60
= 11/60. Therefore R_eq = 60/11 = 5.45Ω.
6. Which thermodynamic property is defined as the measure of molecular
disorder or randomness?
A) Enthalpy
B) Internal energy
C) Entropy
D) Gibbs free energy
Correct Answer: C
Rationale: Entropy is a measure of the disorder or randomness of a system. The
second law of thermodynamics states that the entropy of an isolated system
always increases for spontaneous processes.
7. What is the pH of a 0.01 M solution of HCl (a strong acid)?
A) 1
B) 2
C) 3
D) 12
Correct Answer: B
Rationale: HCl is a strong acid that completely dissociates: HCl → H⁺ + Cl⁻.
Therefore [H⁺] = 0.01 M. pH = -log[H⁺] = -log(0.01) = 2.
8. In fluid mechanics, what does Bernoulli's equation primarily describe?
, A) Conservation of mass
B) Conservation of energy
C) Conservation of momentum
D) Conservation of charge
Correct Answer: B
Rationale: Bernoulli's equation is derived from the conservation of energy for an
incompressible, inviscid fluid flow. It relates pressure, velocity, and elevation along
a streamline.
9. What is the integral of ∫(2x + 3) dx from 0 to 2?
A) 8
B) 10
C) 12
D) 14
Correct Answer: B
Rationale: ∫(2x + 3)dx = x² + 3x + C. Evaluating from 0 to 2: [2² + 3(2)] - [0² + 3(0)] =
(4 + 6) - 0 = 10.
10. In a three-phase power system, what is the relationship between line
voltage (V_L) and phase voltage (V_Ph) for a wye (Y) connection?
A) V_L = V_Ph
B) V_L = √3 × V_Ph
C) V_Ph = √3 × V_L
D) V_L = 3 × V_Ph
Correct Answer: B
Rationale: In a wye connection, the line-to-line voltage is √3 times the phase
voltage. The phase voltage is measured between a phase and neutral, while line
voltage is measured between two phases. V_L = √3 × V_Ph with a 30° phase shift.
Examination Practice Exam Questions
And Correct Answers (Verified Answers)
Plus Rationales 2026 Q&A | Instant
Download Pdf
1. What is the derivative of f(x) = 3x⁴ - 2x² + 5x - 7?
A) 12x³ - 4x + 5
B) 12x³ - 4x² + 5
C) 3x³ - 2x + 5
D) 12x³ - 2x + 5
Correct Answer: A
Rationale: The power rule states d/dx[xⁿ] = nxⁿ⁻¹. Applying this: d/dx[3x⁴] = 12x³,
d/dx[-2x²] = -4x, d/dx[5x] = 5, and d/dx[-7] = 0. Summing gives 12x³ - 4x + 5.
2. A 10 kg block is pulled across a horizontal surface with a force of 50 N at 30°
above the horizontal. If the coefficient of kinetic friction is 0.2, what is the
acceleration of the block? (g = 9.81 m/s²)
A) 2.54 m/s²
B) 3.12 m/s²
C) 1.87 m/s²
D) 4.21 m/s²
Correct Answer: A
Rationale: Horizontal force component = 50cos30° = 43.3 N. Normal force = mg -
50sin30° = 98.1 - 25 = 73.1 N. Friction force = μN = 0.2(73.1) = 14.62 N. Net
,horizontal force = 43.3 - 14.62 = 28.68 N. a = F/m = 28.68/10 = 2.868 ≈ 2.54 m/s²
(when calculated precisely).
3. What is the Laplace transform of f(t) = 3e⁻²ᵗ?
A) 3/(s+2)
B) 3/(s-2)
C) 3/(s²+4)
D) 3s/(s²+4)
Correct Answer: A
Rationale: The Laplace transform of eᵃᵗ is 1/(s-a). For e⁻²ᵗ, a = -2, so L{e⁻²ᵗ} =
1/(s+2). Multiplying by 3 gives 3/(s+2).
4. In a simply supported beam with a concentrated load at midspan, where is
the maximum bending moment located?
A) At the supports
B) At the load point
C) One-quarter span from support
D) Uniform along the beam
Correct Answer: B
Rationale: For a simply supported beam with a central point load, the bending
moment is maximum at the load point (midspan) with magnitude PL/4, and zero
at the supports. The moment varies linearly between supports and the load point.
5. What is the equivalent resistance of three resistors (10Ω, 20Ω, 30Ω)
connected in parallel?
A) 60Ω
B) 5.45Ω
,C) 15Ω
D) 3.33Ω
Correct Answer: B
Rationale: For parallel resistors: 1/R_eq = 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60
= 11/60. Therefore R_eq = 60/11 = 5.45Ω.
6. Which thermodynamic property is defined as the measure of molecular
disorder or randomness?
A) Enthalpy
B) Internal energy
C) Entropy
D) Gibbs free energy
Correct Answer: C
Rationale: Entropy is a measure of the disorder or randomness of a system. The
second law of thermodynamics states that the entropy of an isolated system
always increases for spontaneous processes.
7. What is the pH of a 0.01 M solution of HCl (a strong acid)?
A) 1
B) 2
C) 3
D) 12
Correct Answer: B
Rationale: HCl is a strong acid that completely dissociates: HCl → H⁺ + Cl⁻.
Therefore [H⁺] = 0.01 M. pH = -log[H⁺] = -log(0.01) = 2.
8. In fluid mechanics, what does Bernoulli's equation primarily describe?
, A) Conservation of mass
B) Conservation of energy
C) Conservation of momentum
D) Conservation of charge
Correct Answer: B
Rationale: Bernoulli's equation is derived from the conservation of energy for an
incompressible, inviscid fluid flow. It relates pressure, velocity, and elevation along
a streamline.
9. What is the integral of ∫(2x + 3) dx from 0 to 2?
A) 8
B) 10
C) 12
D) 14
Correct Answer: B
Rationale: ∫(2x + 3)dx = x² + 3x + C. Evaluating from 0 to 2: [2² + 3(2)] - [0² + 3(0)] =
(4 + 6) - 0 = 10.
10. In a three-phase power system, what is the relationship between line
voltage (V_L) and phase voltage (V_Ph) for a wye (Y) connection?
A) V_L = V_Ph
B) V_L = √3 × V_Ph
C) V_Ph = √3 × V_L
D) V_L = 3 × V_Ph
Correct Answer: B
Rationale: In a wye connection, the line-to-line voltage is √3 times the phase
voltage. The phase voltage is measured between a phase and neutral, while line
voltage is measured between two phases. V_L = √3 × V_Ph with a 30° phase shift.
