Practice city guilds model questions vol1 engineering 2023 Past Questions

Question 1 View Details

A cylindrical water tank has a total surface area (including top and bottom) of \(2000\) cm\(^2\) and a capacity of \(5000\) cm\(^3\). Determine the radius of the tank in centimetres, correct to two decimal places.

A. 13.87 cm

B. 15.22 cm

Correct C. 14.44 cm

D. 12.55 cm

Correct Answer: C

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Question 2 View Details

In a workshop risk‑assessment three hazards A, B and C are identified. Their consequence scores are 4, 3 and 5 respectively (higher means more severe). The probability scores (on a 1-5 scale) satisfy \(p_{B}=p_{A}+1\) and \(p_{C}=p_{A}-2\). The overall risk rating, defined as \(\sum (\text{consequence}\times\text{probability})\), is 29. Determine the probability scores for A, B and C and state which hazard requires the highest control priority (use the highest individual risk product; if tied, choose the hazard with the larger consequence).

Correct A. p_A = 3, p_B = 4, p_C = 1; hazard A has the highest priority

B. p_A = 3, p_B = 5, p_C = 2; hazard B has the highest priority

C. p_A = 4, p_B = 5, p_C = 2; hazard B has the highest priority

D. p_A = 2, p_B = 3, p_C = 0; hazard B has the highest priority

Correct Answer: A

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Question 3 View Details

A metal part requires a cylindrical hole of diameter \(20\) mm and depth \(50\) mm. Two machining options are considered:\n\n1. Drilling with a twist drill: cutting speed \(30\) m·min\(^{-1}\), feed \(0.15\) mm·rev\(^{-1}\), tool life \(45\) min.\n2. Boring with a single‑point tool: cutting speed \(20\) m·min\(^{-1}\), feed \(0.10\) mm·rev\(^{-1}\), tool life \(60\) min.\n\nThe machine spindle speed cannot exceed \(1500\) rev·min\(^{-1}\). Each tool change takes \(2\) min. For a production run of \(100\) holes, determine which process gives the lower total machining time (including tool changes) and the corresponding total cost if the drilling cost is \(\text{₦}150\) per minute and the boring cost is \(\text{₦}200\) per minute.

A. Drilling; total time 80 min, total cost ₦12000

B. Boring; total time 70 min, total cost ₦14000

Correct C. Drilling; total time 72 min, total cost ₦10800

D. Boring; total time 84 min, total cost ₦16800

Correct Answer: C

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Question 4 View Details

A simply supported rectangular steel beam spans \(6\) m and carries a uniformly distributed load of \(20\) kN·m\(^{-1}\). The beam width is \(150\) mm and the height \(h\) mm is to be chosen. The allowable bending stress for the steel is \(150\) MPa. Using the bending formula \(\sigma = \dfrac{M y}{I}\) with \(I=\dfrac{b h^{3}}{12}\) and \(y=\dfrac{h}{2}\), determine the minimum integer height \(h\) (in mm) that satisfies the stress limit.

Correct A. 155 mm

B. 160 mm

C. 165 mm

D. 150 mm

Correct Answer: A

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Question 5 View Details

A DC circuit consists of a 12 V battery, a resistor \(R_{1}\) in series with a parallel combination of \(R_{2}\) and \(R_{3}\). The total current drawn from the battery is 2 A and the voltage across \(R_{3}\) is 3 V. It is known that \(R_{1}=2R_{2}\). Find the values of \(R_{1}, R_{2}\) and \(R_{3}\) in ohms.

A. R1 = 4.5 Ω, R2 = 2.25 Ω, R3 = 2.25 Ω

B. R1 = 6 Ω, R2 = 3 Ω, R3 = 6 Ω

C. R1 = 3 Ω, R2 = 1.5 Ω, R3 = 3 Ω

Correct D. R1 = 4.5 Ω, R2 = 2.25 Ω, R3 = 4.5 Ω

Correct Answer: D

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Question 6 View Details

In a multiview drawing of a part, the scale is \(1:50\). In the front view the distance between two aligned holes measures \(3\ \text{cm}\), while in the top view the same distance measures \(4\ \text{cm}\). The holes lie in a plane that is common to the front and top views (i.e., there is no offset in the side direction). Determine the true distance between the holes in the actual part (in millimetres).

A. 300

Correct B. 250

C. 200

D. 225

Correct Answer: B

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Question 7 View Details

A gear train consists of four gears. Gear A has 20 teeth and drives gear B with 40 teeth. Gears B and C are mounted on the same shaft; gear C has 30 teeth and drives gear D with 60 teeth. An input torque of \(10\ \text{N·m}\) is applied to gear A, which rotates at \(1200\ \text{rpm}\). Each mesh operates at 90 % efficiency. Find the output speed (rpm) and torque (N·m) at gear D.

A. 240 rpm, 27 N·m

B. 300 rpm, 27 N·m

Correct C. 300 rpm, 32.4 N·m

D. 360 rpm, 36 N·m

Correct Answer: C

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Question 8 View Details

A solid steel rod 2 m long has a circular cross‑section of diameter \(20\ \text{mm}\). It is subjected to an axial load of \(30\ \text{kN}\) and, due to an eccentric load, a bending moment of \(0.05\ \text{kNm}\). The steel has a yield strength of \(250\ \text{MPa}\). Using the von Mises criterion, determine whether the rod will fail. (Give the von Mises stress in MPa and state if it is safe.)

Correct A. Safe (von Mises stress ≈ 146 MPa)

B. Unsafe (von Mises stress ≈ 260 MPa)

C. Safe (von Mises stress ≈ 120 MPa)

D. Unsafe (von Mises stress ≈ 140 MPa)

Correct Answer: A

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Question 9 View Details

Solve the differential equation \(\frac{dy}{dx}=3y\) with the initial condition \(y(0)=2\). Find the value of \(y\) at \(x=1\).

A. 6e^{3}

B. e^{3}

Correct C. 2e^{3}

D. 2e^{2}

Correct Answer: C

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Question 10 View Details

In the circuit shown, a 12 V source is in series with a resistor \(R_{1}=4\ \Omega\). The node after \(R_{1}\) splits into a parallel branch containing a known resistor \(R_{2}=12\ \Omega\) and an unknown resistor \(R_{x}\). The voltage measured across the parallel branch is \(8\ \text{V}\). Determine the resistance \(R_{x}\) (in ohms).

A. 48

B. 16

C. 6

Correct D. 24

Correct Answer: D

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Question 11 View Details

A machine's output speed varies linearly with the applied voltage. When the voltage is \(120\ \text{V}\), the speed is \(300\ \text{rpm}\). When the voltage is \(150\ \text{V}\), the speed is \(375\ \text{rpm}\). Assuming the relationship remains linear, what voltage is required to obtain a speed of \(420\ \text{rpm}\)?

A. 180 V

B. 160 V

Correct C. 168 V

D. 176 V

Correct Answer: C

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Question 12 View Details

An engineering workshop has a floor area of \(250\ \text{m}^2\) and stores flammable liquids. Safety regulations require that at least \(80\%\) of the floor area be protected by ABC‑type powder fire extinguishers, each of which can effectively cover \(30\ \text{m}^2\). In addition, one CO\(_2\) extinguisher must be provided for electrical fire protection. If an ABC extinguisher costs \(\₦45{,}000\) and a CO\(_2\) extinguisher costs \(\₦60{,}000\), determine the minimum total cost for the required fire‑extinguishing equipment.

A. ₦340,000

B. ₦465,000

Correct C. ₦375,000

D. ₦330,000

Correct Answer: C

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Question 13 View Details

An equipment component has a constant failure rate of \(\lambda = 0.0002\ \text{h}^{-1}\) (exponential distribution). The cost of replacing the component is \(\₦20{,}000\) and the cost incurred for each hour of equipment downtime is \(\₦5{,}000\). If a preventive replacement is scheduled every \(T\) hours, the average cost per hour is given by\n\[\nC(T)=\frac{20{,}000}{T}+5{,}000 \times 2 \times \bigl(1-e^{-\lambda T}\bigr),\n\]\nwhere the factor \(2\) represents an average downtime of two hours per failure. Determine the value of \(T\) (in hours, to the nearest whole hour) that minimizes the average cost per hour.

A. 108 h

B. 95 h

Correct C. 101 h

D. 115 h

Correct Answer: C

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Question 14 View Details

In a multiview drawing of a straight pipe, the front (elevation) view shows a projected length of \(150\ \text{mm}\) and the top (plan) view shows a projected length of \(200\ \text{mm}\). Assuming the pipe lies in a single plane and the two views are orthogonal projections, calculate the true length of the pipe in millimetres.

A. 300 mm

Correct B. 250 mm

C. 350 mm

D. 200 mm

Correct Answer: B

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Question 15 View Details

An alloy is composed of \(60\%\) iron and \(40\%\) carbon by mass. The densities are \(\rho_{\text{Fe}} = 7.87\ \text{g/cm}^3\) and \(\rho_{\text{C}} = 2.26\ \text{g/cm}^3\). Determine the volume fraction of carbon in the alloy, expressed as a percentage to one decimal place.

A. 64.0 %

B. 58.2 %

C. 71.5 %

Correct D. 69.8 %

Correct Answer: D

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Question 16 View Details

A composite material is made by mixing material A and material B. Material A has a density of \(2.5\ \text{g/cm}^3\) and a Young's modulus of \(70\ \text{GPa}\). Material B has a density of \(8.0\ \text{g/cm}^3\) and a Young's modulus of \(200\ \text{GPa}\). The resulting composite has an overall density of \(3.5\ \text{g/cm}^3\) and an overall Young's modulus of \(93.6\ \text{GPa}\). Assuming the rule of mixtures applies linearly to both density and modulus, determine the volume fraction of material A in the composite. Then, for a block of the composite with a volume of \(0.20\ \text{m}^3\), calculate the mass of material A contained in the block. Give your answer in kilograms (to two decimal places).

A. 500.00 kg

B. 350.00 kg

C. 450.00 kg

Correct D. 409.09 kg

Correct Answer: D

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Question 17 View Details

An electric motor drives a gear train as follows: Gear A (diameter \(100\ \text{mm}\)) is mounted on the motor shaft rotating at \(1500\ \text{rpm}\) and delivering a torque of \(10\ \text{N·m}\). Gear A meshes with Gear B (diameter \(250\ \text{mm}\)). Gear B is fixed on the same shaft as Gear C (diameter \(80\ \text{mm}\)), which in turn meshes with Gear D (diameter \(200\ \text{mm}\)) attached to the load. Each gear mesh operates at an efficiency of \(95\%\). Determine the torque delivered to the load (Gear D) in newton‑metres, correct to two decimal places.

A. 70.00 N·m

B. 45.00 N·m

C. 62.50 N·m

Correct D. 56.41 N·m

Correct Answer: D

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Question 18 View Details

A simply supported rectangular steel beam \(6\ \text{m}\) long has a uniform distributed load of \(8\ \text{kN/m}\) over its entire span and a point load of \(20\ \text{kN}\) located \(2\ \text{m}\) from the left support. The beam cross‑section is \(150\ \text{mm}\) wide and \(300\ \text{mm}\) deep. Assuming linear elastic behaviour, calculate the maximum bending stress in the beam in megapascals (MPa), rounded to one decimal place.

A. 22.5 MPa

B. 31.4 MPa

C. 28.9 MPa

Correct D. 26.1 MPa

Correct Answer: D

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Question 19 View Details

A balanced three‑phase Y‑connected load is supplied from a \(400\ \text{V}\) line‑to‑line source at \(50\ \text{Hz}\). The total real power consumed is \(30\ \text{kW}\) and the total reactive power is \(40\ \text{kVAR}\). Determine (a) the apparent power per phase in volt‑amperes, (b) the magnitude of the per‑phase impedance in ohms, and (c) the resistance of each phase in ohms. Give numerical answers to two decimal places where appropriate.

A. a) 16600.00 VA; b) 3.50 Ω; c) 2.20 Ω

B. a) 18000.00 VA; b) 2.80 Ω; c) 1.70 Ω

C. a) 15000.00 VA; b) 4.00 Ω; c) 2.10 Ω

Correct D. a) 16666.67 VA; b) 3.20 Ω; c) 1.92 Ω

Correct Answer: D

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Question 20 View Details

A steel rod is to be used as a tension member. The steel has a yield strength of \(250\ \text{MPa}\). The design tensile load is \(100\ \text{kN}\) and a factor of safety of \(2.5\) is required. Determine the minimum cross‑sectional area of the rod in square millimetres, rounded to the nearest whole number.

A. 1250 mm^2

B. 1500 mm^2

Correct C. 1000 mm^2

D. 800 mm^2

Correct Answer: C

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Question 21 View Details

A critical system consists of two components in series. Component 1 is maintained preventively every 200 h and its reliability over the interval is constant at \(R_{1}=0.98\). Component 2 is subject to exponential degradation: immediately after a preventive maintenance its reliability is \(0.99\) and thereafter it follows \(R_{2}(t)=0.99\,e^{-0.0005 t}\) where \(t\) is the time (in hours) since the last maintenance. The whole system undergoes a preventive maintenance every 300 h, which restores component 2 to the initial reliability of \(0.99\). Determine the system reliability at the end of the 300‑hour interval.

Correct A. 0.835

B. 0.801

C. 0.842

D. 0.823

Correct Answer: A

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Question 22 View Details

A surveyor measures the height of a building using two different methods. In method A a theodolite measures the distance \(d=150.0\,\text{m}\) with an uncertainty of \(\pm0.1\,\text{m}\) and the vertical angle \(\theta=30.0^{\circ}\) with an uncertainty of \(\pm0.02^{\circ}\). The height is computed as \(h=d\tan\theta\). In method B a laser range‑finder gives the distance \(d'=150.2\,\text{m}\) with an uncertainty of \(\pm0.05\,\text{m}\) and an inclinometer measures the angle \(\theta'=30.5^{\circ}\) with an uncertainty of \(\pm0.05^{\circ}\). Using linear error propagation, determine which method yields the smaller maximum possible absolute error in the calculated height and state that error (in metres, rounded to three decimal places).

Correct A. 0.128

B. 0.115

C. 0.162

D. 0.140

Correct Answer: A

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Question 23 View Details

The volume of an irregular stone is measured by water displacement. The initial water volume is \(V_{1}=250.0\,\text{mL}\) with an uncertainty of \(\pm0.2\,\text{mL}\) and the final volume after immersion is \(V_{2}=310.5\,\text{mL}\) with the same uncertainty. The stone's mass is measured as \(m=0.162\,\text{kg}\) with an uncertainty of \(\pm0.001\,\text{kg}\). The material density is known to be \(\rho=2.70\,\text{g\,cm}^{-3}\) with an uncertainty of \(\pm0.02\,\text{g\,cm}^{-3}\).\ Calculate the percentage relative error of the volume obtained by water displacement and that obtained by the density method (i.e., \(V=m/\rho\)). State which method provides the more reliable (smaller) relative error, giving the percentages to two decimal places.

A. Displacement method: 0.47 %; Density method: 1.10 %; Displacement is more reliable

Correct B. Displacement method: 0.47 %; Density method: 0.96 %; Displacement is more reliable

C. Displacement method: 0.55 %; Density method: 0.96 %; Density is more reliable

D. Displacement method: 0.60 %; Density method: 0.80 %; Density is more reliable

Correct Answer: B

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Question 24 View Details

A solid steel rod of diameter \(20\,\text{mm}\) is subjected to an axial tensile load of \(30\,\text{kN}\) and a bending moment of \(5\,\text{kN·mm}\). The material has a yield strength of \(250\,\text{MPa}\) and an ultimate strength of \(400\,\text{MPa}\). Using the von Mises criterion, determine the factor of safety based on yield strength and state whether the rod is safe under the combined loading.

A. 3.10 (safe)

B. 2.60 (unsafe)

Correct C. 2.60 (safe)

D. 2.20 (unsafe)

Correct Answer: C

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Question 25 View Details

Solve for \(x\) in the logarithmic equation \(\log_{3}\bigl(x^{2}-4x+7\bigr)=2\). Give all real solutions.

A. 2\pm\sqrt{5}

Correct B. 2\pm\sqrt{6}

C. 2\pm\sqrt{8}

D. -2\pm\sqrt{6}

Correct Answer: B

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