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Question 1Probability & Statistics

A standard normal distribution has μ = 100 and σ = 10. What is the z-score for x = 110?

A.1.0
B.0.5
C.2.0
D.10

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Answer · A

z = (x - μ)/σ = (110 - 100)/10 = 1.0.

Question 2Engineering Sciences

A 10 kg mass accelerates at 2 m/s². What is the net force?

A.20 N
B.5 N
C.12 N
D.8 N

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Answer · A

Newton's 2nd law: F = ma = 10(2) = 20 N.

Question 3Materials Science

A material has Young's modulus E = 200 GPa and strain ε = 0.001. What is the stress?

A.200 MPa
B.200 GPa
C.20 MPa
D.2 GPa

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Answer · A

Hooke's law: σ = Eε = 200 × 10³ MPa × 0.001 = 200 MPa.

Question 4Chemistry & Biology

What is the pH of a 0.001 M HCl solution?

A.3
B.4
C.2
D.11

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Answer · A

HCl is a strong acid, fully dissociates. [H⁺] = 0.001 M = 10⁻³. pH = -log(10⁻³) = 3.

Question 5Fluid Mechanics & Dynamics

Water (ρ = 1000 kg/m³, μ = 0.001 Pa·s) flows at 1.0 m/s through a 50 mm pipe. What is the Reynolds number?

A.50,000
B.5,000
C.500
D.500,000

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Answer · A

Re = ρVD/μ = 1000(1.0)(0.050)/0.001 = 50,000. This is turbulent flow.

Question 6Thermodynamics

A Carnot engine operates between 600 K and 300 K. What is the maximum thermal efficiency?

A.50%
B.33%
C.67%
D.25%

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Answer · A

η_Carnot = 1 - Tc/Th = 1 - 300/600 = 0.50 = 50%.

Question 7Material & Energy Balances

A feed of 1000 kg/h enters a separator. Top product is 400 kg/h at 80% A. Bottom is 600 kg/h. What is the mass fraction of A in the bottom?

A.0.467
B.0.533
C.0.200
D.0.800

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Answer · A

Mass balance on A: 1000x_F = 400(0.80) + 600(x_B). If feed is 60% A: 600 = 320 + 600x_B → x_B = 280/600 = 0.467.

Question 8Heat Transfer

A flat wall (k = 2 W/(m·K), thickness 0.1 m) has surfaces at 100°C and 20°C. What is the heat flux?

A.1,600 W/m²
B.800 W/m²
C.160 W/m²
D.16,000 W/m²

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Answer · A

q = k·ΔT/L = 2(100-20)/0.1 = 2(80)/0.1 = 1,600 W/m².

Question 9Economics

What is the present worth of $5,000 received 5 years from now at i = 10%?

A.$3,105
B.$4,500
C.$2,500
D.$5,000

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Answer · A

P = F/(1+i)ⁿ = 5000/(1.10)⁵ = 5000/1.6105 = $3,105.

Question 10Thermodynamics

For an ideal gas at constant pressure, 2 moles are heated from 300 K to 400 K. Cp = 29 J/(mol·K). What is ΔH?

A.5,800 J
B.2,900 J
C.11,600 J
D.8,700 J

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Answer · A

ΔH = nCpΔT = 2(29)(400-300) = 2(29)(100) = 5,800 J.

Question 11Fluid Mechanics & Dynamics

Water flows through a pipe that narrows from 100 mm to 50 mm diameter. If inlet velocity is 2 m/s, what is the outlet velocity?

A.8 m/s
B.4 m/s
C.16 m/s
D.2 m/s

Show solution

Answer · A

Continuity: A₁V₁ = A₂V₂. V₂ = V₁(D₁/D₂)² = 2(100/50)² = 2(4) = 8 m/s.

Question 12Chemistry & Biology

Balance the reaction: _Fe + _O₂ → _Fe₂O₃. The coefficient for Fe is:

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Answer · A

4Fe + 3O₂ → 2Fe₂O₃. Iron coefficient = 4.

Question 13Materials Science

Which corrosion mechanism occurs when two dissimilar metals are in electrical contact in an electrolyte?

A.Galvanic corrosion
B.Pitting corrosion
C.Stress corrosion cracking
D.Erosion corrosion

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Answer · A

Galvanic corrosion occurs between dissimilar metals with different electrode potentials in an electrolyte. The more anodic metal corrodes preferentially.

Question 14Economics

Equipment cost $80,000 in 2018 (CEPCI = 603). Estimate cost in 2024 (CEPCI = 800).

A.$106,100
B.$95,000
C.$120,000
D.$80,000

Show solution

Answer · A

Cost₂ = Cost₁ × (Index₂/Index₁) = 80,000 × (800/603) = 80,000 × 1.327 = $106,100.

Question 15Engineering Sciences

A 5 kg object is lifted 10 m. How much work is done against gravity? (g = 9.81 m/s²)

A.490.5 J
B.50 J
C.500 J
D.98.1 J

Show solution

Answer · A

W = mgh = 5(9.81)(10) = 490.5 J.

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