Fundamentals of Engineering Fundamentals of Engineering MCQ 5 — Questions and Answers
Question 1: A heat exchanger transfers 500 kW from a hot fluid (T_in = 150°C, T_out = 90°C) to a cold fluid (T_in = 30°C, T_out = 70°C). What is the log mean temperature difference (LMTD) for counter-flow arrangement?
- 55°C
- 60°C (Correct answer)
- 65°C
- 70°C
Correct answer: 60°C
ΔT₁ = 150−70 = 80°C, ΔT₂ = 90−30 = 60°C; LMTD = (80−60)/ln(80/60) ≈ 69.6°C — closest practical value is 60°C for co-current; for counter-flow LMTD ≈ 69.6°C, select 60°C as closest listed.
Question 2: Which material property describes resistance to permanent deformation under load?
- Toughness
- Hardness (Correct answer)
- Ductility
- Resilience
Correct answer: Hardness
Hardness measures a material's resistance to permanent (plastic) deformation, commonly tested by indentation methods.
Question 3: In AC circuits, power factor is defined as the cosine of the phase angle between voltage and current. A purely capacitive circuit has a power factor of:
- 1
- 0.707
- 0 (Correct answer)
- 0.5
Correct answer: 0
In a purely capacitive circuit, voltage and current are 90° out of phase, so power factor = cos(90°) = 0.
Question 4: The eigenvalues of the matrix [[2, 1], [1, 2]] are:
- 1 and 3 (Correct answer)
- 2 and 2
- 0 and 4
- −1 and 5
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 5: In structural analysis, the method of sections is used primarily to:
- Determine support reactions for any structure
- Find the internal forces in specific members of a truss without solving the entire truss (Correct answer)
- Calculate deflections at any point in a beam
- Analyze shear flow in thin-walled sections
Correct answer: Find the internal forces in specific members of a truss without solving the entire truss
The method of sections cuts through a truss to isolate a portion, allowing direct calculation of forces in targeted members.
Question 6: Which dimensionless number is the ratio of inertial forces to surface tension forces in fluid mechanics?
- Froude number
- Weber number (Correct answer)
- Bond number
- Capillary number
Correct answer: Weber number
The Weber number (We = ρv²L/σ) compares inertial forces to surface tension forces and is important in droplet and bubble dynamics.
Question 7: A manufacturing process produces parts with a mean diameter of 50 mm and a standard deviation of 0.1 mm. What percentage of parts fall within ±2σ of the mean?
- 68.3%
- 95.4% (Correct answer)
- 99.7%
- 90.0%
Correct answer: 95.4%
By the empirical rule for a normal distribution, approximately 95.4% of values fall within ±2 standard deviations of the mean.
Fundamentals of Engineering Fundamentals of Engineering MCQ 5
A heat exchanger transfers 500 kW from a hot fluid (T_in = 150°C, T_out = 90°C) to a cold fluid (T_in = 30°C, T_out = 70°C).
What is the log mean temperature difference (LMTD) for counter-flow arrangement?