Practice city guilds model questions vol1 engineering 2024 Past Questions

Question 1 View Details

In orthographic projection, a line AB makes an angle $ \theta $ with the horizontal plane. Its projection on the top view measures 160 mm and its projection on the front view measures 120 mm. Determine the true length of AB (in mm) and the angle $ \theta $ (in degrees, to one decimal place).

A. 160 mm, 60.0°

B. 180 mm, 45.0°

C. 220 mm, 30.0°

Correct D. 200 mm, 36.9°

Correct Answer: D

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Question 2 View Details

The linear system $ x + 2y = 3 $ $ kx + 4y = 6 $ has infinitely many solutions. Find the value of the parameter $ k $.

A. 3

B. 0

C. 1

Correct D. 2

Correct Answer: D

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Question 3 View Details

A rectangular block has dimensions 150 mm × 80 mm × 60 mm at 25 °C. Its coefficients of linear expansion are $ \alpha_x = 10 \times 10^{-6}\,^{\circ}\!C^{-1} $, $ \alpha_y = 12 \times 10^{-6}\,^{\circ}\!C^{-1} $ and $ \alpha_z = 8 \times 10^{-6}\,^{\circ}\!C^{-1} $ along the respective edges. The block is uniformly heated to 75 °C. (a) Calculate the new dimensions of the block. (b) Determine the new volume (in mm³, to the nearest mm³) and the percentage increase in volume (to two decimal places).

A. 150.75 mm, 80.48 mm, 60.24 mm; volume = 730,853 mm³; increase = 1.51%

Correct B. 150.075 mm, 80.048 mm, 60.024 mm; volume = 721,081 mm³; increase = 0.15%

C. 150.060 mm, 80.038 mm, 60.019 mm; volume = 720,858 mm³; increase = 0.12%

D. 150.075 mm, 80.048 mm, 60.024 mm; volume = 720,500 mm³; increase = 0.07%

Correct Answer: B

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Question 4 View Details

A 12 V source is connected in series with a 4 Ω resistor $ R_1 $. Across the terminals after $ R_1 $ there is a parallel network consisting of an unknown resistor $ R_2 $ in parallel with a 6 Ω resistor. A load resistor $ R_L = 8 \;\Omega $ is connected across this parallel network. Find the value of $ R_2 $ (in Ω) that maximizes the power dissipated in $ R_L $.

A. 14

Correct B. 12

C. 10

D. 8

Correct Answer: B

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Question 5 View Details

A solid uniform cylinder of mass 10 kg and radius 0.20 m rolls without slipping down a straight incline. The coefficient of rolling friction is $ \mu_r = 0.02 $. Determine the smallest angle $ \theta $ (in degrees, to one decimal place) of the incline for which the cylinder accelerates down the plane with magnitude $ 2.0 \;\text{m s}^{-2} $.

Correct A. 12.9°

B. 14.3°

C. 9.8°

D. 10.5°

Correct Answer: A

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Question 6 View Details

A block‑and‑tackle system is used to lift a load of 500 N. The system has three supporting rope sections (i.e., a mechanical advantage of 3). Each movable pulley operates with an efficiency of 90 % due to friction. Assuming the efficiencies of the three pulleys are independent, determine the minimum input force that must be applied to the rope to lift the load.

A. 185.2 N

Correct B. 228.7 N

C. 205.8 N

D. 166.7 N

Correct Answer: B

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Question 7 View Details

An irregular metal block is measured by water displacement. When fully immersed, the water level rises by 250 mL. The block's length and width are 5 cm and 8 cm respectively, so its height can be found from the displaced volume. The metal's density at 20 °C is 7.85 g cm⁻³ and its linear expansion coefficient is $12\times10^{-6}\ \text{°C}^{-1}$. The laboratory temperature during measurement is 30 °C. The metal is sold at ₦150 per kilogram for the first 2 kg and ₦120 per kilogram for any additional weight. A tax of 12 % is applied to the net amount. Calculate the total amount payable (in naira) for the block.

A. ₦294.38

B. ₦323.82

C. ₦403.20

Correct D. ₦329.58

Correct Answer: D

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Question 8 View Details

A component made of mild steel requires a cylindrical hole of diameter 20 mm and depth 50 mm with a surface roughness of $Ra\le 0.8\ \mu\text{m}$ and a dimensional tolerance of $\pm0.02$ mm. Two machining routes are considered for a batch of 200 parts: (a) drilling the hole followed by reaming, (b) CNC boring. The following data are supplied: - Drilling cycle time per hole: 15 s; tool‑change time: 5 s; drill tool cost per use: $0.20; drill tool life: 100 parts, replacement cost $5. - Reaming cycle time: 10 s; tool‑change time: 5 s; reamer cost per use: $0.30; reamer life: 100 parts, replacement cost $5. - CNC boring cycle time: 30 s; tool‑change time: 5 s; boring tool cost per use: $0.45; boring tool life: 200 parts (no replacement cost). - Labour cost: $0.05 per second. Determine which route gives the lower total cost (labour + tool + replacement) and state the total cost for each route and the saving achieved by the preferred route.

A. CNC boring; total cost $460; saving $0

B. Drilling & reaming; total cost $440; saving $0

Correct C. CNC boring; total cost $440; saving $20

D. Drilling & reaming; total cost $460; saving $0

Correct Answer: C

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Question 9 View Details

In a workshop, a grinding machine produces a noise level of 95 dB(A) at the operator's ear. The permissible exposure limit (PEL) for an 8‑hour shift is 85 dB(A). According to the safety table, for every 5 dB increase above the PEL the required attenuation doubles from a baseline of 10 dB at 90 dB. Assuming a 50 % derating is applied to the Noise Reduction Rating (NRR) of earplugs, determine the minimum NRR (in dB) that the earplugs must have to protect the operator. Also state the maximum continuous exposure time allowed when using earplugs with that NRR.

A. Minimum NRR = 35 dB; maximum exposure = 8 hours

Correct B. Minimum NRR = 40 dB; maximum exposure = 8 hours

C. Minimum NRR = 45 dB; maximum exposure = 8 hours

D. Minimum NRR = 40 dB; maximum exposure = 6 hours

Correct Answer: B

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Question 10 View Details

A workshop operates three identical induction heating units, each rated at 2 kW, 240 V, 50 Hz with a power factor of 0.85 lagging. The units are connected in parallel to a three‑phase 415 V, 50 Hz supply. The electricity tariff is: first 500 kWh at ₦15 kWh⁻¹, next 500 kWh at ₦12 kWh⁻¹, thereafter ₦10 kWh⁻¹. The units run 6 hours per day, 5 days a week. (a) Calculate the weekly energy cost if the supply is billed on apparent energy (kVAh) using the given power factor. (b) If a power‑factor correction bank improves the overall PF to 0.95, recalculate the weekly energy cost. (c) Determine the weekly saving obtained by the correction.

A. Without correction ₦3176.47; with correction ₦3000.00; weekly saving ₦176.47

Correct B. Without correction ₦3176.47; with correction ₦2842.11; weekly saving ₦334.36

C. Without correction ₦3220.00; with correction ₦2890.55; weekly saving ₦329.45

D. Without correction ₦3105.12; with correction ₦2780.00; weekly saving ₦325.12

Correct Answer: B

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Question 11 View Details

A system of linear equations is given by $2x + 3y = 7$ and $4x - y = 5$. Solve for $x$.

Correct A. 11/7

B. 13/7

C. 11/5

D. 9/7

Correct Answer: A

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Question 12 View Details

A steel rod of length $2.00\,\text{m}$ and cross‑sectional area $1.20 \times 10^{-4}\,\text{m}^2$ is subjected to a tensile load. The rod elongates by $0.50\,\text{mm}$. Given Young's modulus $E = 200\,\text{GPa}$ and a yield stress of $250\,\text{MPa}$, determine (a) the tensile load in newtons, (b) the stress in the rod, and (c) whether the rod is safe against yielding.

Correct A. 6000 N, safe

B. 7000 N, safe

C. 6000 N, unsafe

D. 5000 N, safe

Correct Answer: A

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Question 13 View Details

An irregular metal block has a mass of $150.0\,\text{g}$ in air. When immersed in water at $20^{\circ}\text{C}$ its apparent loss of weight is $45.0\,\text{g}$. The density of water at $20^{\circ}\text{C}$ is $0.9982\,\text{g cm}^{-3}$ and at $25^{\circ}\text{C}$ is $0.9970\,\text{g cm}^{-3}$. (a) Determine the volume of the block. (b) Using the volume, calculate the true density of the metal. (c) State whether this density agrees with that of aluminium ($2.70\,\text{g cm}^{-3}$) within $\pm0.05\,\text{g cm}^{-3}$.

A. Volume ≈45.1 cm³, density ≈2.70 g/cm³, agrees

B. Volume ≈50.0 cm³, density ≈3.00 g/cm³, does not agree

Correct C. Volume ≈45.1 cm³, density ≈3.33 g/cm³, does not agree

D. Volume ≈33.2 cm³, density ≈4.52 g/cm³, does not agree

Correct Answer: C

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Question 14 View Details

A motor delivers $5.0\,\text{kW}$ at $1500$ rpm. It drives a two‑stage gear train. The first stage has a gear ratio of 3:1 (driver:driven) and the second stage a ratio of 2:1. The overall efficiency of the gear train is 90 %. (a) Find the angular speed (in rpm) and torque (in N·m) of the final gear. (b) A pulley of radius $0.20\,\text{m}$ is mounted on the final gear and lifts a load vertically at constant speed. Assuming no slip, determine the maximum mass (in kg) that can be lifted.

A. 300 rpm, 150 N·m, 75 kg

B. 250 rpm, 200 N·m, 70 kg

Correct C. 250 rpm, 172 N·m, 88 kg

D. 200 rpm, 190 N·m, 95 kg

Correct Answer: C

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Question 15 View Details

If $x + \frac{1}{x} = 3$, find the value of $x^{2} + \frac{1}{x^{2}}$.

A. 5

B. 8

Correct C. 7

D. 9

Correct Answer: C

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Question 16 View Details

In a circuit, a resistor $R_1 = 40\ \Omega$ is connected in series with a parallel network of resistors $R_2$ and $R_3$. The total resistance measured across the circuit is $120\ \Omega$. It is known that $R_2$ is twice the resistance of $R_3$. The circuit is supplied by a $240\ \text{V}$ source. Determine the current flowing through resistor $R_2$.

A. \frac{3}{4}\ \text{A}

B. \frac{1}{2}\ \text{A}

Correct C. \frac{2}{3}\ \text{A}

D. \frac{5}{6}\ \text{A}

Correct Answer: C

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Question 17 View Details

A workshop stores a flammable liquid (flash point 30\,\degree C) in eight identical containers, each holding 15\,L. Regulations require that for every 10\,L of such liquid, at least 2\,kg of a Class\,B fire extinguisher be readily available within 5\,m. The workshop currently has three 6\,kg extinguishers. A ventilation system reduces the fire‑load by 20\%. Determine whether the workshop meets the safety requirement, and if not, how many additional 6\,kg extinguishers are needed.

A. 0

B. 3

C. 2

Correct D. 1

Correct Answer: D

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Question 18 View Details

A particle moves along a straight line with displacement (in metres) given by $s(t)=4t^{2}-12t+9$, where $t$ is time in seconds. Find the time at which the particle is momentarily at rest and state its displacement at that instant.

A. t = 2\\ \text{s},\\ s = -3\\ \text{m}

B. t = \\frac{3}{2}\\ \text{s},\\ s = 5\\ \text{m}

Correct C. t = \frac{3}{2}\ \text{s},\ s = 0\ \text{m}

D. t = 1\\ \text{s},\\ s = 1\\ \text{m}

Correct Answer: C

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Question 19 View Details

A system consists of two components A and B arranged in series. Component A has a mean time between failures (MTBF) of 200\,h and a mean time to repair (MTTR) of 5\,h; component B has MTBF = 300\,h and MTTR = 8\,h. The system availability is the product of the availabilities of the two components. Management can either (i) reduce the MTTR of component A by 2\,h or (ii) reduce the MTTR of component B by 2\,h. Assuming all other parameters remain unchanged, which option yields the greater increase in system availability? Compute the new system availability for each option and state the preferred option.

A. Option (i) is better; new availability = \\frac{15000}{15600} \\approx 0.9615 (increase \\approx 0.0115).

B. Option (ii) is better; new availability = \\frac{15000}{15631} \\approx 0.9597 (increase \\approx 0.0097).

Correct C. Option (i) is better; new availability = \frac{15000}{15631} \approx 0.9597 (increase ≈ 0.0097).

D. Option (i) is better; new availability = \\frac{14900}{15631} \\approx 0.9535 (increase \\approx 0.0035).

Correct Answer: C

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Question 20 View Details

A solid circular steel shaft transmits 12\,kW of power at 1500\,rpm and is subjected to a bending moment of 800\,N·m due to a gear. The material has an allowable tensile stress of 250\,MPa and an allowable shear stress of 40\,MPa, with a required factor of safety of 2. Using the von\,Mises criterion, determine the minimum shaft diameter (in mm) that will safely carry the combined loading.

A. 52\ \text{mm}

B. 38\ \text{mm}

Correct C. 41\ \text{mm}

D. 45\ \text{mm}

Correct Answer: C

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Question 21 View Details

Two rods A and B are fixed in parallel between two plates and carry a tensile load of 10 kN. Rod A has Young's modulus $E_{A}=200$ GPa and cross‑sectional area $A_{A}=20$ mm$^2$. Rod B has unknown modulus $E_{B}$ and area $A_{B}=30$ mm$^2$. The measured total extension of the assembly under load is $0.5$ mm.\n\n(a) Determine $E_{B}$ in GPa (to two decimal places).\n\n(b) If the extension must not exceed $0.4$ mm and the area of rod A cannot be changed, what minimum additional area (mm$^2$, nearest integer) must be added to rod B while keeping $E_{B}$ unchanged?

A. E_B = 480.00 GPa; additional area = 12 mm^2

B. E_B = 533.33 GPa; additional area = 8 mm^2

Correct C. E_B = 533.33 GPa; additional area = 9 mm^2

D. E_B = 600.00 GPa; additional area = 7 mm^2

Correct Answer: C

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Question 22 View Details

A workshop floor measures 120 m$^2$ with a ceiling height of 3 m. The space stores wood, oil and electrical equipment. Safety code requires fire‑extinguishers as follows: Class A (wood) - 2 L per 30 m$^2$; Class B (oil) - 1 L per 30 m$^2$; Class C (electrical) - 1 L per 30 m$^2$. Extinguishers are available in the sizes: 2 L Class A (cost ₦12 000 each), 1 L Class B (cost ₦8 000 each), 1 L Class C (cost ₦9 000 each). The total number of extinguishers may not exceed 10 because of space limits.\n\nDetermine the minimum numbers of each dedicated extinguisher type required and the total cost. If the 10‑extinguisher limit is exceeded, suggest an alternative using multi‑class 2 L extinguishers (cost ₦15 000 each, each covering all three classes) that satisfies the safety requirements with the lowest possible cost. State the final numbers of each extinguisher type and the total expense.

A. 4 multi‑class 2 L extinguishers; total cost = ₦70 000

B. 5 multi‑class 2 L extinguishers; total cost = ₦75 000

C. 3 multi‑class 2 L extinguishers; total cost = ₦45 000

Correct D. 4 multi‑class 2 L extinguishers; total cost = ₦60 000

Correct Answer: D

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Question 23 View Details

A machine operates 8 hours per day, 250 days a year (total $H = 2000$ h). It has two critical components, A and B, each subject to a constant failure rate (exponential distribution).\n\nComponent A: failure rate $\lambda_{A}=0.001$ h$^{-1}$, preventive‑maintenance (PM) cost $C_{PM,A}=₦5\,000$ per PM, failure cost $C_{F}=₦20\,000$ per unplanned failure.\nComponent B: failure rate $\lambda_{B}=0.0005$ h$^{-1}$, PM cost $C_{PM,B}=₦3\,000$.\n\nPM is performed at a fixed interval $\tau$ (hours) for each component, resetting its age to zero. The expected number of failures per year for a component with interval $\tau$ is \[ N_{F}=\frac{H}{\tau}\bigl(1-e^{-\lambda\tau}\bigr). \]\nThe total annual cost for a component is \[ C(\tau)=\frac{H}{\tau}C_{PM}+N_{F}C_{F}. \]\nDetermine the optimal PM interval (in whole hours) for each component that minimises its annual cost, assuming the interval cannot exceed the annual operating time (2000 h). Also give the minimum annual cost for each component (rounded to the nearest naira).

Correct A. Component A: τ = 2000 h, annual cost ≈ ₦22 300; Component B: τ = 2000 h, annual cost ≈ ₦15 600

B. Component A: τ = 2000 h, annual cost ≈ ₦23 500; Component B: τ = 2000 h, annual cost ≈ ₦16 200

C. Component A: τ = 1000 h, annual cost ≈ ₦23 800; Component B: τ = 1000 h, annual cost ≈ ₦16 200

D. Component A: τ = 1500 h, annual cost ≈ ₦22 800; Component B: τ = 1500 h, annual cost ≈ ₦15 900

Correct Answer: A

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Question 24 View Details

A small hydro‑electric plant drops water from a height of 50 m at a flow rate of 20 L s$^{-1}$. Assuming water density $\rho = 1000$ kg m$^{-3}$ and gravitational acceleration $g = 9.81$ m s$^{-2}$,\n\n(a) Calculate the theoretical power output in kilowatts.\n(b) If the turbine‑generator efficiency is 85 %, what is the actual usable power (kW)?

A. Theoretical power = 8.20 kW; actual usable power = 6.97 kW

B. Theoretical power = 9.81 kW; actual usable power = 7.85 kW

C. Theoretical power = 10.5 kW; actual usable power = 8.9 kW

Correct D. Theoretical power = 9.81 kW; actual usable power = 8.34 kW

Correct Answer: D

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Question 25 View Details

In a turning operation a carbide tool removes material at a required rate of 1 200 mm$^3$ min$^{-1}$. The cutting speed is $V_c = 30$ m min$^{-1}$ and the feed per revolution is $f = 0.2$ mm rev$^{-1}$.\n\n(a) Determine the depth of cut $a$ (mm) needed to achieve the required material‑removal rate.\n(b) With a tool nose radius $r = 0.8$ mm, calculate the theoretical surface roughness $R_a$ using $R_a = \dfrac{f^{2}}{32r}$. Give $a$ to one decimal place and $R_a$ in micrometres (µm) to two decimal places.

A. a = 0.3 mm; R_a = 2.00 µm

B. a = 0.4 mm; R_a = 3.12 µm

C. a = 0.1 mm; R_a = 0.78 µm

Correct D. a = 0.2 mm; R_a = 1.56 µm

Correct Answer: D

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