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Bac Séries F Côte d'Ivoire - independent subject practice study materials
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Bac Séries F Côte d'Ivoire - independent subject practice practice questions

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Question 1Manufacturing, machining models and metrology

In a turning operation on a cylindrical steel workpiece of diameter D = 50 mm, the cutting speed is specified as Vc = 120 m/min. What is the required spindle rotational speed N in revolutions per minute (rpm)?

  1. N ≈ 764 rpm Correct answer.
  2. N ≈ 450 rpm
  3. N ≈ 1200 rpm
  4. N ≈ 2400 rpm

Explanation

The cutting speed formula in turning is Vc = (π · D · N) / 1000, where Vc is in m/min and D is in mm. Solving for rotational speed N: N = (1000 · Vc) / (π · D) = (1000 · 120) / (π · 50) = 120000 / 157.08 ≈ 763.94 rpm, which rounds to approximately 764 rpm.

Question 2Manufacturing, machining models and metrology

In CNC machining programming using ISO standard G-codes, which instruction is used to command linear interpolation at a programmed feed rate?

  1. G00
  2. G01 Correct answer.
  3. G02
  4. G03

Explanation

G01 specifies linear interpolation at a controlled cutting feed rate (F). In contrast, G00 is rapid positioning (non-cutting traverse), G02 is clockwise circular interpolation, and G03 is counterclockwise circular interpolation.

Question 3Manufacturing, machining models and metrology

A face milling cutter with a diameter D = 80 mm has z = 6 teeth. If the cutting speed is Vc = 150 m/min and the feed per tooth is fz = 0.12 mm/tooth, calculate the table feed rate Vf in mm/min.

  1. Vf ≈ 108 mm/min
  2. Vf ≈ 430 mm/min Correct answer.
  3. Vf ≈ 716 mm/min
  4. Vf ≈ 1250 mm/min

Explanation

First calculate spindle speed N: N = (1000 · Vc) / (π · D) = (1000 · 150) / (π · 80) = 150000 / 251.33 ≈ 596.83 rpm. The table feed speed Vf is given by Vf = fz · z · N = 0.12 mm/tooth · 6 teeth · 596.83 rpm = 0.72 · 596.83 ≈ 429.72 mm/min ≈ 430 mm/min.

Question 4Manufacturing, machining models and metrology

In metal casting, what is the primary function of a riser (masselotte)?

  1. To vent gases and steam trapped inside the mold cavity during pouring
  2. To supply molten reservoir metal to compensate for volumetric shrinkage during solidification Correct answer.
  3. To support the sand core inside the mold cavity
  4. To filter slag and oxides from the incoming molten metal stream

Explanation

A riser (masselotte in French foundry terminology) acts as a thermal and liquid reservoir. It solidifies last (following Chvorinov's rule) and feeds molten metal into the casting to compensate for liquid-to-solid volumetric shrinkage, preventing shrinkage cavities (retassures).

Question 5Manufacturing, machining models and metrology

[Mechanical Engineering] An ISO tolerance fit between a 50 mm nominal diameter bore and shaft is designated as 50 H7/g6. The hole tolerance H7 is 0 to +25 μm, and the shaft tolerance g6 is -9 to -25 μm. What type of fit does this represent, and what is the maximum clearance J_max?

  1. Interference fit (ajustement avec serrage); J_max = -50 μm
  2. Transition fit (ajustement incertain); J_max = +16 μm
  3. Clearance fit (ajustement avec jeu); J_max = +50 μm (+0.050 mm) Correct answer.
  4. Clearance fit (ajustement avec jeu); J_max = +25 μm (+0.025 mm)

Explanation

The maximum hole size is D_max = 50.000 + 0.025 = 50.025 mm, and the minimum hole size is D_min = 50.000 mm. The maximum shaft size is d_max = 50.000 − 0.009 = 49.991 mm, and the minimum shaft size is d_min = 50.000 − 0.025 = 49.975 mm. Because D_min (50.000 mm) > d_max (49.991 mm), minimum clearance is J_min = +9 μm > 0, ensuring a clearance fit. The maximum clearance is J_max = D_max − d_min = 50.025 − 49.975 = +0.050 mm = +50 μm.

Question 6Statics, strength and mechanical transmission

In a biological or chemical laboratory, which piece of safety equipment provides personal protection by containing and exhausting hazardous airborne toxic vapors, acid fumes, and volatile organic solvents away from the user via ducted negative pressure?

  1. Chemical fume hood (sorbonne de laboratoire) Correct answer.
  2. Class II Biological Safety Cabinet (laminar flow cabinet for product protection)
  3. Dry heat drying oven (étuve)
  4. Emergency eye wash station (rince-œil)

Explanation

A chemical fume hood (sorbonne) captures, contains, and exhausts chemical fumes, vapors, and dusts through an exhaust duct to the building exterior, protecting the operator from toxic inhalation hazards.

Question 7Statics, strength and mechanical transmission

A charged particle with charge q = +1.6 × 10^-19 C enters a uniform magnetic field B = 0.50 T with velocity v = 2.0 × 10^6 m/s perpendicular to the field lines. What is the magnitude of the magnetic Lorentz force acting on the particle?

  1. F = 1.6 × 10^-13 N Correct answer.
  2. F = 3.2 × 10^-13 N
  3. F = 0.8 × 10^-13 N
  4. F = 6.4 × 10^-14 N

Explanation

The magnetic force on a moving charge is F = |q| · v · B · sin(θ). For θ = 90° (sin 90° = 1): F = (1.6 × 10^-19 C) · (2.0 × 10^6 m/s) · (0.50 T) = 1.6 × 10^-13 N.

Question 8Statics, strength and mechanical transmission

A vertical open water storage tank in Yamoussoukro has a water depth of h = 8.0 m. Taking water density ρ = 1000 kg/m^3 and gravitational acceleration g = 9.81 m/s^2, what is the hydrostatic relative gauge pressure p_gauge at the bottom of the tank?

  1. p_gauge = 78.48 kPa (0.785 bar) Correct answer.
  2. p_gauge = 178.48 kPa
  3. p_gauge = 8.0 kPa
  4. p_gauge = 784.8 kPa

Explanation

The fundamental hydrostatic relation for gauge pressure is p_gauge = ρ · g · h = 1000 kg/m^3 · 9.81 m/s^2 · 8.0 m = 78480 Pa = 78.48 kPa (approx 0.785 bar).

Question 9Statics, strength and mechanical transmission

Water (incompressible fluid) flows through a horizontal pipe that narrows from diameter D1 = 100 mm to D2 = 50 mm. If the flow velocity in the first section is v1 = 1.5 m/s, what is the flow velocity v2 in the constricted section?

  1. v2 = 6.0 m/s Correct answer.
  2. v2 = 3.0 m/s
  3. v2 = 0.75 m/s
  4. v2 = 12.0 m/s

Explanation

By the continuity equation for incompressible flow: Q = S1 · v1 = S2 · v2. The cross-sectional area is S = (π · D^2) / 4. Thus, v2 = v1 · (D1 / D2)^2 = 1.5 · (100 / 50)^2 = 1.5 · 2^2 = 1.5 · 4 = 6.0 m/s.

Question 10Statics, strength and mechanical transmission

In Bernoulli's equation for steady, incompressible, frictionless streamline flow of a fluid with density ρ: p + 1/2 · ρ · v^2 + ρ · g · z = constant. What physical principle does this equation represent?

  1. Conservation of mechanical energy for a flowing fluid element Correct answer.
  2. Conservation of electrical charge in a moving medium
  3. Conservation of linear momentum during inelastic collision
  4. Second law of thermodynamics for irreversible throttling

Explanation

Bernoulli's equation is a statement of the conservation of mechanical energy per unit volume for an ideal fluid, summing static pressure energy (p), kinetic energy (1/2·ρ·v^2), and gravitational potential energy (ρ·g·z).

Question 11Statics, strength and mechanical transmission

A hydraulic press has a small pump piston of area A1 = 5 cm^2 and a large ram piston of area A2 = 250 cm^2. If an operator applies a force of F1 = 120 N to the small piston, what lifting force F2 is developed at the large piston (assuming no friction)?

  1. F2 = 6000 N (6.0 kN) Correct answer.
  2. F2 = 1200 N
  3. F2 = 30000 N
  4. F2 = 24 N

Explanation

According to Pascal's principle, pressure is transmitted undiminished: p = F1 / A1 = F2 / A2. Therefore, F2 = F1 · (A2 / A1) = 120 N · (250 cm^2 / 5 cm^2) = 120 · 50 = 6000 N (6.0 kN).

Question 12Statics, strength and mechanical transmission

A Venturi meter is installed in a horizontal water pipe (ρ = 1000 kg/m^3). The pressure drop between the upstream pipe section (v1 ≈ 1.0 m/s) and the throat (v2) is measured as Δp = p1 - p2 = 6000 Pa. Using Bernoulli's equation, calculate the throat velocity v2.

  1. v2 ≈ 3.61 m/s Correct answer.
  2. v2 ≈ 2.45 m/s
  3. v2 ≈ 6.00 m/s
  4. v2 ≈ 12.0 m/s

Explanation

For a horizontal pipe (z1 = z2): p1 - p2 = 1/2 · ρ · (v2^2 - v1^2) => Δp = 500 · (v2^2 - 1.0^2) => 6000 / 500 = v2^2 - 1 => 12 = v2^2 - 1 => v2^2 = 13 => v2 = √13 ≈ 3.6056 m/s ≈ 3.61 m/s.

Question 13Statics, strength and mechanical transmission

Read the following excerpt from an industrial equipment operating manual: 'Before commissioning the hydraulic power unit, ensure that the reservoir is filled to the nominal level, bleed all air from the actuator lines, and verify that the pressure relief valve is set to 160 bar.' What does the term 'commissioning' mean in this context?

  1. The process of inspecting, testing, and bringing a newly installed machine into active operational service Correct answer.
  2. Decommissioning and disposing of broken equipment
  3. Calculating financial sales commissions for the purchasing department
  4. Ordering spare parts from an international supplier catalog

Explanation

In engineering and industrial project management, 'commissioning' (mise en service) refers to the rigorous process of verifying, calibrating, functionally testing, and formally starting up newly installed equipment before handing it over for routine production.

Question 14Electrical circuits, machines and digital logic

A 4-pole, 3-phase induction motor is connected to a 50 Hz power supply. At full load, its rotor rotates at nr = 1440 rpm. What is the slip g of the motor?

  1. g = 4.0% (0.04) Correct answer.
  2. g = 6.0% (0.06)
  3. g = 2.0% (0.02)
  4. g = 8.0% (0.08)

Explanation

The synchronous speed is ns = (60 · f) / p, where p is the number of pole pairs (p = 4 poles / 2 = 2). Thus, ns = (60 · 50) / 2 = 1500 rpm. The slip is g = (ns - nr) / ns = (1500 - 1440) / 1500 = 60 / 1500 = 0.04 or 4.0%.

Question 15Electrical circuits, machines and digital logic

During star-delta (Y-Δ) starting of a three-phase asynchronous motor, how do the starting line current I_start and starting torque T_start compare to direct-on-line (DOL) starting in delta connection?

  1. Both starting current and starting torque are divided by 3 (reduced to 33%) Correct answer.
  2. Starting current is divided by 3, but torque remains unchanged
  3. Starting current is divided by √3, and torque is divided by 3
  4. Both starting current and starting torque are divided by √3

Explanation

In star connection, phase voltage is U/√3 instead of U. Phase current is divided by √3, and line current is equal to phase current (unlike delta where I_line = √3 · I_phase). Thus, I_start,Y = (1/3) · I_start,Δ. Since torque is proportional to the square of the applied voltage (T ∝ V^2), T_start,Y = (1/√3)^2 · T_start,Δ = (1/3) · T_start,Δ.

Question 16Electrical circuits, machines and digital logic

A single-phase transformer has N1 = 1200 primary turns and N2 = 120 secondary turns. It is connected to a primary voltage of U1 = 230 V (50 Hz). Assuming an ideal transformer, calculate the secondary no-load voltage U20 and the transformation ratio m.

  1. m = 0.10, U20 = 23 V Correct answer.
  2. m = 10.0, U20 = 2300 V
  3. m = 0.10, U20 = 115 V
  4. m = 0.50, U20 = 46 V

Explanation

The transformation ratio is m = N2 / N1 = 120 / 1200 = 0.10. The secondary no-load voltage is U20 = m · U1 = 0.10 · 230 V = 23 V.

Question 17Electrical circuits, machines and digital logic

In a 3-phase synchronous generator operating on an interconnected 50 Hz grid, how many poles must the rotor have if the turbine drives the shaft at nr = 3000 rpm?

  1. 2 poles (1 pole pair, p = 1) Correct answer.
  2. 4 poles (2 pole pairs, p = 2)
  3. 6 poles (3 pole pairs, p = 3)
  4. 8 poles (4 pole pairs, p = 4)

Explanation

The electrical frequency is related to rotational speed by f = (p · n) / 60. Solving for pole pairs p: p = (60 · f) / n = (60 · 50) / 3000 = 3000 / 3000 = 1 pole pair. Therefore, the rotor has 2 poles (p = 1).

Question 18Electrical circuits, machines and digital logic

In the open-circuit test (essai à vide) of a power transformer at rated primary voltage, what primary quantity is primarily measured to determine core losses?

  1. Active power P0, which represents ferromagnetic iron losses (hysteresis and eddy currents) Correct answer.
  2. Reactive power Q0, which represents full-load winding Joule losses
  3. Short-circuit impedance Zcc
  4. Secondary full-load copper losses Pj2

Explanation

During the open-circuit test with I2 = 0, the primary current I0 is very small (typically 2-5% of rated current), making primary copper losses negligible. Thus, the measured active power P0 corresponds directly to core iron losses Pfer (hysteresis + eddy currents).

Question 19Electrical circuits, machines and digital logic

A DC electrical circuit consists of a voltage source E = 24 V connected to three resistors in series: R1 = 12 Ω, R2 = 18 Ω, and R3 = 30 Ω. What is the current I flowing in the circuit and the voltage drop U2 across resistor R2?

  1. I = 0.40 A, U2 = 7.2 V Correct answer.
  2. I = 0.80 A, U2 = 14.4 V
  3. I = 0.40 A, U2 = 12.0 V
  4. I = 2.0 A, U2 = 24.0 V

Explanation

The equivalent series resistance is Req = R1 + R2 + R3 = 12 + 18 + 30 = 60 Ω. The circuit current is I = E / Req = 24 V / 60 Ω = 0.40 A. The voltage across R2 is U2 = R2 · I = 18 Ω · 0.40 A = 7.2 V.

Question 20Electrical circuits, machines and digital logic

In a single-phase AC installation operating at U = 230 V (50 Hz), an inductive load consumes an active power P = 4.6 kW with a lagging power factor of cos(φ) = 0.80. Calculate the apparent power S and the reactive power Q absorbed by the load.

  1. S = 5.75 kVA, Q = 3.45 kvar Correct answer.
  2. S = 3.68 kVA, Q = 2.76 kvar
  3. S = 5.75 kVA, Q = 4.60 kvar
  4. S = 4.60 kVA, Q = 1.15 kvar

Explanation

Apparent power is S = P / cos(φ) = 4.6 kW / 0.80 = 5.75 kVA. For cos(φ) = 0.80, sin(φ) = √(1 - 0.80^2) = 0.60. Reactive power is Q = S · sin(φ) = 5.75 · 0.60 = 3.45 kvar (or Q = √(S^2 - P^2) = √(5.75^2 - 4.6^2) = √(33.0625 - 21.16) = √11.9025 = 3.45 kvar).

Question 21Electrical circuits, machines and digital logic

An industrial plant draws P = 100 kW with an uncompensated power factor of cos(φ1) = 0.707 (tan(φ1) = 1.0) from a 400 V, 50 Hz three-phase supply. To raise the power factor to cos(φ2) = 0.95 (tan(φ2) = 0.329), what reactive power Qc must the power factor correction capacitor bank supply?

  1. Qc = 67.1 kvar Correct answer.
  2. Qc = 100.0 kvar
  3. Qc = 32.9 kvar
  4. Qc = 132.9 kvar

Explanation

The required reactive power compensation is given by Boucherot's theorem: Qc = P · [tan(φ1) - tan(φ2)] = 100 kW · [1.0 - 0.329] = 100 · 0.671 = 67.1 kvar.

Question 22Electrical circuits, machines and digital logic

In a balanced star-connected three-phase system, what is the mathematical relationship between the line-to-line voltage U and the single-phase phase-to-neutral voltage V?

  1. U = √3 · V with U leading V by 30° Correct answer.
  2. U = V / √3
  3. U = 3 · V
  4. U = V

Explanation

In a star (Y) connection, the line-to-line voltage is the phasor difference between two phase voltages: U12 = V1 - V2. The magnitude relationship is U = √3 · V (e.g., 400 V = √3 · 230 V), and line voltage leads phase voltage by π/6 (30°).

Question 23Electrical circuits, machines and digital logic

Using the two-wattmeter method (méthode des deux wattmètres) on a balanced 3-phase, 3-wire inductive load, the wattmeter readings are W1 = 6000 W and W2 = 2000 W. What is the total active power P and total reactive power Q consumed by the load?

  1. P = 8000 W, Q = 6928 var Correct answer.
  2. P = 4000 W, Q = 4000 var
  3. P = 8000 W, Q = 4000 var
  4. P = 6000 W, Q = 3464 var

Explanation

In the two-wattmeter method for balanced loads: Total active power P = W1 + W2 = 6000 + 2000 = 8000 W. Total reactive power Q = √3 · (W1 - W2) = √3 · (6000 - 2000) = 1.73205 · 4000 = 6928.2 var.

Question 24Electrical circuits, machines and digital logic

In a series RLC circuit connected to an AC voltage source of frequency f, what condition defines electrical resonance?

  1. Inductive reactance equals capacitive reactance (XL = XC, so L·ω = 1/(C·ω)) Correct answer.
  2. Circuit impedance is maximized and current is zero
  3. Voltage across the capacitor is zero
  4. Phase angle φ between voltage and current is 90°

Explanation

Series resonance occurs when XL = XC => L·ω0 = 1 / (C·ω0) => ω0 = 1 / √(LC). At this frequency, the net reactance X = XL - XC = 0, the circuit impedance is purely resistive and at its minimum (Z = R), and current is at its maximum in phase with voltage (cos(φ) = 1).

Question 25Electrical circuits, machines and digital logic

A pure inductor L = 0.318 H (where L ≈ 1/π H) is connected across a sinusoidal voltage u(t) = 325 sin(100π t) V (f = 50 Hz). What is its inductive reactance XL and the RMS current I through the inductor?

  1. XL = 100 Ω, I_rms = 2.30 A Correct answer.
  2. XL = 50 Ω, I_rms = 4.60 A
  3. XL = 100 Ω, I_rms = 3.25 A
  4. XL = 314 Ω, I_rms = 0.73 A

Explanation

The angular frequency is ω = 2·π·f = 100π ≈ 314.16 rad/s. Inductive reactance is XL = L · ω = 0.318 · 314.16 = 100.0 Ω. The RMS voltage is U_rms = U_max / √2 = 325 / 1.414 ≈ 230 V. The RMS current is I_rms = U_rms / XL = 230 V / 100 Ω = 2.30 A.

Question 26Electrical circuits, machines and digital logic

A straight conductor of active length L = 0.40 m carrying a direct current I = 15 A is placed perpendicularly in a uniform magnetic field of flux density B = 0.80 T. What is the magnitude of the Laplace electromagnetic force acting on the conductor?

  1. F = 4.8 N Correct answer.
  2. F = 6.0 N
  3. F = 0.48 N
  4. F = 12.0 N

Explanation

The Laplace force on a current-carrying conductor in a magnetic field is F = I · L · B · sin(θ). Since the conductor is perpendicular to the field (θ = 90°, sin(90°) = 1): F = 15 A · 0.40 m · 0.80 T · 1 = 4.8 N.

Question 27Electrical circuits, machines and digital logic

According to fire safety regulations in industrial facilities, what class of fire involves energized electrical equipment (such as switchboards, transformers, and electric motors)?

  1. Class E / Electrical fire (Class C in European ISO EN 2 standard is flammable gases; CO2 or dry powder extinguishers are used for electrical hazards) Correct answer.
  2. Class A (solid cellulosic materials: wood, paper)
  3. Class B (flammable liquids: oils, solvents, petrol)
  4. Class D (combustible metals: magnesium, sodium)

Explanation

Fires involving energized electrical equipment require non-conductive extinguishing agents (such as CO2 or specialized dielectric dry powder) to prevent electric shock to firefighters. Water jets must never be used on live electrical gear.

Question 28Measurement, feedback, PLC and automation

In GRAFCET syntax, which graphical construct is used to represent an AND divergence (divergence en ET / simultaneous sequence branching)?

  1. A single transition followed by a double horizontal bar branching into multiple simultaneous steps Correct answer.
  2. A single horizontal line followed by multiple independent transitions with mutually exclusive conditions
  3. A single step branching into multiple transitions without horizontal lines
  4. A closed circular loop without transitions

Explanation

In GRAFCET, simultaneous branching (divergence en ET) is represented by a single transition followed by a double horizontal line. When the preceding transition is validated and its receptivity is true, all subsequent steps below the double line become active simultaneously.

Question 29Measurement, feedback, PLC and automation

What are the two mandatory conditions that must be simultaneously satisfied for a GRAFCET transition to be cleared (franchissement d'une transition)?

  1. All immediately preceding steps must be ACTIVE, and the associated transition RECEPTIVITY must be TRUE Correct answer.
  2. The downstream steps must be active, and emergency stop must be pressed
  3. The PLC scan cycle must be paused, and all inputs must be high
  4. All preceding steps must be inactive, and a timer must have expired

Explanation

According to the fundamental rules of GRAFCET: (1) A transition is enabled (validée) if and only if all immediately preceding steps are active. (2) A transition is fired/cleared (franchie) when it is enabled AND its associated condition (réceptivité) evaluates to logical TRUE (1).

Question 30Measurement, feedback, PLC and automation

In GRAFCET notation, what is the meaning of the time-delayed receptivity designation 't1 / X4 / 5s'?

  1. The transition receptivity becomes TRUE exactly 5 seconds after step 4 (X4) becomes active Correct answer.
  2. Step 4 remains active for only 5 seconds and then permanently deactivates the entire chart
  3. The timer resets step 4 to step 1 after 5 seconds
  4. The transition condition is checked every 5 seconds indefinitely

Explanation

The notation 't1 / X4 / 5s' designates a time-delayed condition: a timer t1 starts when step 4 is activated (X4 = 1). The condition is FALSE from 0 to 5 s and becomes TRUE (logical 1) when 5 seconds have elapsed while step 4 remains continuously active.

Question 31Measurement, feedback, PLC and automation

In a Programmable Logic Controller (PLC / API), what is the correct chronological sequence of operations performed during each repetitive CPU scan cycle (cycle d'automate)?

  1. 1. Read physical inputs to input image table -> 2. Execute user program logic -> 3. Update physical outputs from output image table -> 4. System diagnostics and housekeeping Correct answer.
  2. 1. Execute user program logic -> 2. Read physical inputs -> 3. Power down CPU -> 4. Write outputs
  3. 1. Update physical outputs -> 2. Wait for operator button -> 3. Read inputs -> 4. Clear memory
  4. 1. Read inputs -> 2. Update physical outputs immediately -> 3. Execute user program

Explanation

The standard PLC operating cycle executes cyclically: (1) Input Scan: physical input terminal states are read and copied into internal input process image memory; (2) Program Scan: the user program executes sequentially from first to last rung; (3) Output Scan: resulting values in the output image table are written to physical output modules; (4) Housekeeping & Communications.

Question 32Measurement, feedback, PLC and automation

In PLC hardware architectures, what is the primary role of optocouplers (photocoupleurs) located inside digital input interface modules?

  1. To provide galvanic electrical isolation between high-voltage field sensor wiring (e.g., 24 VDC / 230 VAC) and sensitive low-voltage CPU microelectronics (5 VDC) Correct answer.
  2. To amplify electrical output power to directly drive 3-phase hydraulic pumps
  3. To convert AC frequency directly into mechanical torque
  4. To provide non-volatile flash storage for ladder programs

Explanation

Optocouplers use an internal LED and phototransistor to transmit digital signals via light, providing complete galvanic isolation (typically 1.5 kV to 4 kV). This prevents electrical noise, voltage spikes, and ground loops from field devices from destroying sensitive CPU microprocessors.

Question 33Measurement, feedback, PLC and automation

A double-acting pneumatic cylinder has a piston diameter D = 80 mm and rod diameter d = 25 mm. If compressed air is supplied at gauge pressure p = 6.0 bar (0.60 MPa = 60 N/cm^2), calculate the theoretical pushing (outstroke) force F_push.

  1. F_push ≈ 3016 N (3.02 kN) Correct answer.
  2. F_push ≈ 2721 N (2.72 kN)
  3. F_push ≈ 12064 N
  4. F_push ≈ 480 N

Explanation

The full piston surface area during outstroke (pushing) is A_push = (π · D^2) / 4 = (π · 8.0^2) / 4 = 50.265 cm^2 = 5.0265 × 10^-3 m^2. Pushing force is F_push = p · A_push = (0.60 × 10^6 N/m^2) · (5.0265 × 10^-3 m^2) = 3015.9 N ≈ 3016 N (3.02 kN).

Question 34Measurement, feedback, PLC and automation

In an industrial pneumatic control circuit, which type of directional control valve (distributeur pneumatique) is standardly used to command the forward and backward strokes of a double-acting cylinder?

  1. 5/2-way valve (distributeur 5 orifices, 2 positions) Correct answer.
  2. 2/2-way valve (distributeur 2 orifices, 2 positions)
  3. 3/2-way normally closed valve
  4. Check valve (clapet anti-retour simple)

Explanation

A 5/2-way directional control valve has 5 ports (1 supply, 2 working ports to the cylinder chambers, and 2 exhausts) and 2 switching positions. It can pressurize one cylinder chamber while exhausting the opposite chamber simultaneously, making it the standard valve for double-acting cylinders.

Question 35Measurement, feedback, PLC and automation

Which type of proximity sensor operates on the principle of Eddy current damping of a high-frequency electromagnetic field and is capable of detecting ONLY metallic target objects?

  1. Inductive proximity sensor (détecteur de proximité inductif) Correct answer.
  2. Capacitive proximity sensor (détecteur capacitif)
  3. Photoelectric diffuse sensor (cellule photoélectrique réflex)
  4. Ultrasonic proximity sensor (capteur à ultrautos)

Explanation

Inductive proximity sensors generate an oscillating electromagnetic field via an LC coil circuit. When a conductive metallic object enters the field, eddy currents are induced in the metal, causing energy loss and damping oscillator amplitude, triggering detection. They only detect metals.

Question 36Engineering models, drawings, evidence and project decisions

In mechanical design and ISO tolerancing, a shaft-hole fit is designated as 40 H7/g6. What type of fit does this represent?

  1. Clearance fit (ajustement avec jeu) Correct answer.
  2. Interference fit (ajustement avec serrage)
  3. Transition fit (ajustement incertain)
  4. Shrink fit with hydraulic expansion

Explanation

In ISO limits and fits, 'H' indicates a hole with lower deviation EI = 0. The letter 'g' for a shaft represents an upper deviation es < 0 (the shaft is always smaller than the nominal size 40 mm). Therefore, minimum clearance = EI - es = 0 - (negative) > 0, ensuring a guaranteed clearance fit (ajustement avec jeu).

Question 37Engineering models, drawings, evidence and project decisions

During orthogonal metal cutting, the chip thickness before cut is a = 0.25 mm and the cut chip thickness is ac = 0.50 mm. What is the chip compression ratio (cutting ratio rc)?

  1. rc = 0.50 Correct answer.
  2. rc = 2.00
  3. rc = 0.25
  4. rc = 1.25

Explanation

The cutting ratio (or chip compression ratio rc) is defined as rc = a / ac (uncut chip thickness divided by deformed chip thickness) = 0.25 / 0.50 = 0.50. (The chip thickening ratio λc = 1/rc = 2.0).

Question 38Engineering models, drawings, evidence and project decisions

According to the Nyquist-Shannon sampling theorem, what is the minimum sampling frequency required to completely reconstruct a bandlimited continuous signal with a maximum frequency component of fmax = 8 kHz?

  1. fs ≥ 16 kHz Correct answer.
  2. fs ≥ 8 kHz
  3. fs ≥ 4 kHz
  4. fs ≥ 32 kHz

Explanation

The Nyquist-Shannon sampling theorem states that to prevent aliasing and allow perfect reconstruction of a signal, the sampling frequency fs must be at least twice the maximum frequency present in the signal: fs ≥ 2 · fmax = 2 · 8 kHz = 16 kHz.

Question 39Engineering models, drawings, evidence and project decisions

In optical leveling (nivellement direct), a backsight reading (lecture arrière) on point A is Lar = 1.650 m. Point A has a known elevation of ZA = +25.400 m. If the foresight reading (lecture avant) on point B is Lav = 0.950 m, what is the elevation ZB of point B?

  1. ZB = +26.100 m Correct answer.
  2. ZB = +24.700 m
  3. ZB = +27.050 m
  4. ZB = +23.750 m

Explanation

The instrument line of sight elevation is Hplane = ZA + Lar = 25.400 m + 1.650 m = 27.050 m. The elevation of point B is ZB = Hplane - Lav = 27.050 m - 0.950 m = +26.100 m. Alternatively, ΔZ = Lar - Lav = 1.650 - 0.950 = +0.700 m; ZB = 25.400 + 0.700 = 26.100 m.

Question 40Engineering models, drawings, evidence and project decisions

In a volumetric acid-base titration, a 20.0 mL sample of hydrochloric acid (HCl) of unknown molarity CA is titrated to equivalence with 0.100 mol/L sodium hydroxide (NaOH). The burette equivalence volume is VE = 16.4 mL. What is CA?

  1. CA = 0.082 mol/L Correct answer.
  2. CA = 0.122 mol/L
  3. CA = 0.164 mol/L
  4. CA = 0.041 mol/L

Explanation

For the stoichiometric reaction HCl + NaOH → NaCl + H2O, n(acid) = n(base) at equivalence, so CA · VA = CB · VE. Thus, CA = (CB · VE) / VA = (0.100 mol/L · 16.4 mL) / 20.0 mL = 1.64 / 20.0 = 0.082 mol/L.

Question 41Engineering models, drawings, evidence and project decisions

In thin-layer chromatography (TLC), a solute spot migrates a distance of d_spot = 3.6 cm from the origin line, while the solvent front migrates d_front = 9.0 cm. What is the retention factor (Rf) of this compound?

  1. Rf = 0.40 Correct answer.
  2. Rf = 2.50
  3. Rf = 0.25
  4. Rf = 0.60

Explanation

The retention factor Rf in planar chromatography is defined as Rf = d_spot / d_front = 3.6 cm / 9.0 cm = 0.40. Rf is a dimensionless ratio between 0 and 1.

Question 42Engineering models, drawings, evidence and project decisions

What standard temperature and minimum exposure time parameters are required in a saturated steam autoclave to achieve complete sterilization of microbiological culture media?

  1. 121 °C at 1 bar (100 kPa) relative steam pressure for 15 to 20 minutes Correct answer.
  2. 100 °C at atmospheric pressure for 5 minutes
  3. 70 °C for 30 minutes (Pasteurization)
  4. 180 °C dry heat for 10 seconds

Explanation

Standard autoclave sterilization requires saturated steam under pressure at 121 °C (approximately 1 bar gauge pressure / 15 psi) for 15 to 20 minutes to kill all vegetative bacteria, fungi, viruses, and highly heat-resistant bacterial endospores (such as Geobacillus stearothermophilus).

Question 43Engineering models, drawings, evidence and project decisions

In microbiology, what type of culture medium contains specific inhibitory agents (such as bile salts, antibiotics, or dyes) that suppress the growth of unwanted microorganisms while permitting the target organism to grow?

  1. Selective medium (milieu sélectif) Correct answer.
  2. Enriched non-selective medium (milieu enrichi)
  3. Synthetic minimal medium (milieu synthétique minimal)
  4. Reducing anaerobic medium (milieu réducteur)

Explanation

A selective medium contains chemical agents that inhibit the growth of certain microbial groups while allowing the growth of the target microorganism (e.g., MacConkey agar selects for Gram-negative bacteria by inhibiting Gram-positive bacteria with bile salts and crystal violet).

Question 44Engineering models, drawings, evidence and project decisions

In chemical analysis, 50.0 mL of a 0.50 mol/L stock solution of copper sulfate (CuSO4) is diluted with distilled water in a volumetric flask to a final volume of 250.0 mL. What is the molar concentration of the resulting diluted solution?

  1. 0.10 mol/L Correct answer.
  2. 0.25 mol/L
  3. 0.05 mol/L
  4. 0.01 mol/L

Explanation

Using the dilution equation C1 · V1 = C2 · V2: C2 = (C1 · V1) / V2 = (0.50 mol/L · 50.0 mL) / 250.0 mL = 25.0 / 250.0 = 0.10 mol/L.

Question 45Engineering models, drawings, evidence and project decisions

In ISO technical engineering drawing (European projection method / First-angle projection), where is the Left View (vue de gauche) standardly positioned relative to the Front View (vue de face)?

  1. Positioned to the RIGHT of the Front View Correct answer.
  2. Positioned to the LEFT of the Front View
  3. Positioned directly ABOVE the Front View
  4. Positioned directly BELOW the Front View

Explanation

In European first-angle projection (symbole du tronc de cône), the observer looks at the left side of the object and projects the image onto the plane behind it, which places the Left View (vue de gauche) to the RIGHT of the Front View. (Conversely, the Top View is placed below the Front View).

Question 46Engineering models, drawings, evidence and project decisions

On a technical mechanical blueprint, a surface finish is marked with a standard root symbol accompanied by the designation 'Ra = 0.8 µm'. What does Ra represent?

  1. Arithmetical mean roughness value (écart moyen arithmétique du profil de rugosité) Correct answer.
  2. Maximum peak-to-valley profile height (hauteur totale Rz)
  3. Rockwell A surface hardness value
  4. Radius of curvature of the machined fillet

Explanation

Ra is the globally standardized parameter for surface roughness according to ISO 4287. It represents the arithmetical mean deviation of the assessed profile heights from the mean line over the evaluation length.

Question 47Engineering models, drawings, evidence and project decisions

In ISO geometric dimensioning and tolerancing (GD&T), what geometric characteristic is symbolized by two parallel slanted lines at an angle (//)?

  1. Parallelism tolerance (tolérance d'orientation: parallélisme) Correct answer.
  2. Perpendicularity tolerance (perpendicularité ⊥)
  3. Concentricity tolerance (concentricité ◎)
  4. Flatness form tolerance (planéité ⏢)

Explanation

In ISO 1101 GD&T symbology, two parallel diagonal lines (//) represent the parallelism orientation tolerance, specifying that the toleranced feature surface or axis must lie within two parallel planes or a cylinder parallel to a datum.

Question 48Engineering models, drawings, evidence and project decisions

In occupational risk prevention (sécurité au travail), what is the highest level in the standardized Hierarchy of Controls for workplace hazards?

  1. Elimination of the hazard at the source (Élimination du danger) Correct answer.
  2. Personal Protective Equipment (PPE / EPI)
  3. Administrative warning signs and training procedures
  4. Engineering barriers and safety guards

Explanation

The standardized hierarchy of hazard control ranks interventions from most effective to least effective: 1. Elimination (physically remove hazard) -> 2. Substitution -> 3. Engineering controls (guards/isolation) -> 4. Administrative controls (procedures/signs) -> 5. PPE (least reliable as sole protection).

Question 49Engineering models, drawings, evidence and project decisions

In an English industrial maintenance manual, what is the exact definition of 'Preventive Maintenance' compared to 'Corrective Maintenance'?

  1. Maintenance performed at predetermined intervals or according to prescribed criteria to reduce the probability of failure before a breakdown occurs Correct answer.
  2. Maintenance carried out exclusively after fault recognition to restore an asset to a state where it can perform its required function
  3. Emergency repairs performed under hazardous breakdown conditions
  4. The complete demolition and permanent scrapping of industrial assets

Explanation

Preventive maintenance is scheduled proactive maintenance conducted before failure occurs (systematic inspections, lubrication, filter replacements) to decrease equipment degradation. Corrective maintenance is reactive repair performed after a breakdown has occurred.

Question 50Engineering models, drawings, evidence and project decisions

In industrial design, what does the acronym 'CAD / CAM' (French: CAO / FAO) stand for in technical English?

  1. Computer-Aided Design / Computer-Aided Manufacturing Correct answer.
  2. Central Automation Device / Control Actuator Module
  3. Continuous Alternating Current / Digital Current Assessment
  4. Casting Alloy Distribution / Chemical Analysis Method

Explanation

CAD stands for Computer-Aided Design (software used to create 2D/3D digital geometric models of components, CAO in French). CAM stands for Computer-Aided Manufacturing (software that generates CNC machine toolpaths from CAD models, FAO in French).