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GCAA CAR-66 B2 Exam study materials
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GCAA CAR-66 B2 Exam practice questions

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Question 1Mathematics

A rectangular aircraft panel measures 0.75 m by 1.2 m. What is its area in square metres?

  1. 0.80 m²
  2. 1.95 m²
  3. 0.90 m² Correct answer.
  4. 0.45 m²

Explanation

Area of a rectangle is length multiplied by width, so 0.75 × 1.2 = 0.90 m². Multiplying the decimals gives 0.9, and the unit is square metres because two lengths are multiplied.

Question 2Mathematics

What is the value of 2^5 × 2^3 expressed as a single power of 2?

  1. 2^15
  2. 2^2
  3. 4^8
  4. 2^8 Correct answer.

Explanation

When multiplying powers with the same base, the exponents are added: 2^5 × 2^3 = 2^(5+3) = 2^8. The base stays the same and only the indices combine.

Question 3Mathematics

A torque wrench is set to 45 N·m. Expressed in basic SI base units, which combination is equivalent?

  1. N/m
  2. kg·m/s²
  3. kg·m²/s
  4. kg·m²/s² Correct answer.

Explanation

One newton is kg·m/s², and torque is force times distance, so N·m becomes kg·m²/s². This is dimensionally the same as a joule, though torque and energy are physically distinct quantities.

Question 4Mathematics

A quantity is given as 4.80 × 10^4 metres. How is this written in ordinary decimal notation?

  1. 4800 m
  2. 480000 m
  3. 0.00048 m
  4. 48000 m Correct answer.

Explanation

The exponent 4 on the base 10 means the decimal point moves four places to the right, giving 48 000. The digits 4, 8 and 0 are retained from the coefficient.

Question 5Mathematics

In a right-angled triangle the two shorter sides are 3 cm and 4 cm. What is the length of the hypotenuse?

  1. 5 cm Correct answer.
  2. 25 cm
  3. 12 cm
  4. 7 cm

Explanation

By Pythagoras' theorem the hypotenuse squared equals 3² + 4² = 9 + 16 = 25, so the hypotenuse is the square root of 25, which is 5 cm.

Question 6Mathematics

An aircraft component has a mass of 12.5 kg. What is this mass in grams, expressed in standard form?

  1. 1.25 × 10^4 g Correct answer.
  2. 1.25 × 10^2 g
  3. 1.25 × 10^5 g
  4. 1.25 × 10^3 g

Explanation

There are 1000 grams in a kilogram, so 12.5 kg = 12 500 g. In standard form this is 1.25 × 10^4 g, since the decimal point moves four places.

Question 7Mathematics

A batch of 250 rivets contains 15 that are out of tolerance. What percentage of the batch is defective?

  1. 6.0 % Correct answer.
  2. 4.0 %
  3. 16.7 %
  4. 15 %

Explanation

Percentage defective equals (15 / 250) × 100. Since 15/250 = 0.06, the percentage is 6.0 %.

Question 8Mathematics

Solve for x in the equation 3x − 7 = 2x + 5.

  1. x = 4
  2. x = 2
  3. x = 12 Correct answer.
  4. x = −12

Explanation

Subtract 2x from both sides to get x − 7 = 5, then add 7 to both sides to obtain x = 12. Each step preserves equality by applying the same operation to both sides.

Question 9Mathematics

A right-angled triangle has an opposite side of 6 cm and a hypotenuse of 10 cm. What is the sine of the angle opposite the 6 cm side?

  1. 0.75
  2. 0.8
  3. 1.67
  4. 0.6 Correct answer.

Explanation

Sine of an angle in a right triangle equals the opposite side divided by the hypotenuse, so sin θ = 6/10 = 0.6. The value must lie between 0 and 1 for an acute angle.

Question 10Mathematics

Convert 5/8 into a decimal.

  1. 1.6
  2. 0.625 Correct answer.
  3. 0.58
  4. 0.85

Explanation

Dividing the numerator by the denominator gives 5 ÷ 8 = 0.625. The result is less than one because the numerator is smaller than the denominator.

Question 11Mathematics

A wire of length 2.0 m is cut into pieces each 0.16 m long. How many complete pieces can be obtained?

  1. 10
  2. 8
  3. 13
  4. 12 Correct answer.

Explanation

Dividing the total length by the piece length gives 2.0 ÷ 0.16 = 12.5. Since only complete pieces count, the answer is 12 pieces with a short remainder left over.

Question 12Mathematics

A quantity doubles every 30 minutes. Starting from 5 units, what is the quantity after 2 hours?

  1. 20 units
  2. 40 units
  3. 160 units
  4. 80 units Correct answer.

Explanation

Two hours contains four 30-minute intervals, so the quantity is multiplied by 2 four times: 5 × 2^4 = 5 × 16 = 80 units.

Question 13Mathematics

A right-angled triangle has an adjacent side of 8 cm and a hypotenuse of 10 cm. What is the cosine of the angle between them, and what is the angle to the nearest degree?

  1. 0.80 and 53°
  2. 0.60 and 53°
  3. 0.80 and 37° Correct answer.
  4. 0.75 and 41°

Explanation

Cosine equals adjacent over hypotenuse, so cos θ = 8/10 = 0.80. The inverse cosine of 0.80 is approximately 36.9°, which rounds to 37°.

Question 14Mathematics

The resistance of a conductor is given by R = ρL/A. If the length L is doubled and the cross-sectional area A is halved, by what factor does the resistance change?

  1. It increases by a factor of 2
  2. It increases by a factor of 4 Correct answer.
  3. It decreases by a factor of 2
  4. It remains unchanged

Explanation

Resistance is proportional to length and inversely proportional to area. Doubling L doubles R, and halving A doubles R again, so the combined factor is 2 × 2 = 4.

Question 15Mathematics

A component's failure probability follows the relationship P = 1 − e^(−kt). If k = 0.02 per hour, what is the value of P after t = 50 hours, to two decimal places?

  1. 0.37
  2. 0.02
  3. 1.00
  4. 0.63 Correct answer.

Explanation

The exponent is −0.02 × 50 = −1, and e^(−1) ≈ 0.368. Therefore P = 1 − 0.368 = 0.632, which rounds to 0.63.

Question 16Mathematics

Two vectors act at a point: a force of 6 N due east and a force of 8 N due north. What is the magnitude of the resultant force?

  1. 2 N
  2. 14 N
  3. 48 N
  4. 10 N Correct answer.

Explanation

Perpendicular vectors combine by Pythagoras: the resultant magnitude is the square root of 6² + 8² = 36 + 64 = 100, which is 10 N.

Question 17Physics

A body moves in a straight line at constant velocity. Which statement about the forces acting on it is correct?

  1. A net force acts opposite to the direction of motion
  2. The net force increases steadily with time
  3. The net force acting on the body is zero Correct answer.
  4. A constant net force acts in the direction of motion

Explanation

By Newton's first law, a body continues at constant velocity only when the resultant force on it is zero. Constant velocity means both speed and direction are unchanged, so acceleration is zero. Any non-zero net force would produce acceleration.

Question 18Physics

A mass of 2 kg is accelerated uniformly from rest to 10 m/s in 5 s. What is the resultant force acting on it?

  1. 20 N
  2. 50 N
  3. 4 N Correct answer.
  4. 10 N

Explanation

Acceleration equals change in velocity divided by time: (10 - 0)/5 = 2 m/s². Force equals mass times acceleration: 2 kg × 2 m/s² = 4 N.

Question 19Physics

Which quantity is a scalar?

  1. Work Correct answer.
  2. Displacement
  3. Acceleration
  4. Velocity

Explanation

A scalar has magnitude only, whereas a vector has both magnitude and direction. Work is the product of force and displacement in the direction of the force and is fully described by magnitude and sign.

Question 20Physics

A force of 50 N is applied to a lever at a perpendicular distance of 0.4 m from the fulcrum. What moment does it produce?

  1. 12.5 N·m
  2. 50.4 N·m
  3. 125 N·m
  4. 20 N·m Correct answer.

Explanation

The moment of a force about a point equals force multiplied by the perpendicular distance from the point to the line of action. Here 50 N × 0.4 m = 20 N·m.

Question 21Physics

In the SI system, the unit of pressure is the pascal. Which combination of base units is equivalent to one pascal?

  1. kg/(m·s²) Correct answer.
  2. kg/(m²·s)
  3. kg·m²/s²
  4. kg·m/s²

Explanation

Pressure is force per unit area. A newton is kg·m/s², and dividing by area in m² gives kg/(m·s²).

Question 22Physics

An object of weight 300 N is immersed fully in a liquid and displaces 0.02 m³ of liquid of density 800 kg/m³. Taking g as 10 m/s², what is the upthrust?

  1. 160 N Correct answer.
  2. 1600 N
  3. 16 N
  4. 240 N

Explanation

Upthrust equals the weight of fluid displaced: density × volume × g = 800 × 0.02 × 10 = 160 N. The weight of the object itself does not enter this calculation.

Question 23Physics

A hydraulic press has a small piston of area 0.001 m² and a large piston of area 0.05 m². If a force of 200 N is applied to the small piston, what force is produced at the large piston (assuming ideal conditions)?

  1. 10000 N Correct answer.
  2. 100 N
  3. 4000 N
  4. 4 N

Explanation

Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished, so P = F₁/A₁ = F₂/A₂. Thus F₂ = 200 × (0.05/0.001) = 10 000 N.

Question 24Physics

A block of mass 5 kg rests on a horizontal surface. The coefficient of static friction is 0.4 and g is 10 m/s². What is the minimum horizontal force needed to just start the block moving?

  1. 20 N Correct answer.
  2. 50 N
  3. 12.5 N
  4. 2 N

Explanation

The limiting static friction equals μ times the normal reaction, which here equals the weight, 5 × 10 = 50 N. Thus F = 0.4 × 50 = 20 N.

Question 25Physics

A car travels 150 m in 10 s while accelerating uniformly from 10 m/s. What is its final velocity?

  1. 15 m/s
  2. 30 m/s
  3. 25 m/s
  4. 20 m/s Correct answer.

Explanation

For uniform acceleration, distance equals average velocity times time, so average velocity = 150/10 = 15 m/s. The average of initial and final velocities is 15 m/s, giving final velocity = 2×15 − 10 = 20 m/s.

Question 26Physics

A body moves in a circle at constant speed. Which statement about its acceleration is correct?

  1. It is directed away from the centre of the circle
  2. It is directed along the tangent to the circle
  3. It is directed towards the centre of the circle Correct answer.
  4. It is zero because the speed is constant

Explanation

In uniform circular motion the speed is constant but the direction of velocity changes continuously. This change in velocity is directed towards the centre, producing centripetal acceleration of magnitude v²/r.

Question 27Physics

A body of mass 4 kg moving at 6 m/s collides and couples with a stationary body of mass 2 kg. What is their common velocity after the collision?

  1. 3 m/s
  2. 6 m/s
  3. 2 m/s
  4. 4 m/s Correct answer.

Explanation

By conservation of linear momentum, total momentum before equals total momentum after: 4 × 6 = (4 + 2) × v. Solving gives v = 24/6 = 4 m/s.

Question 28Physics

A machine raises a load of 500 N through 2 m using an effort that does 1200 J of work. What is its efficiency?

  1. 120 %
  2. 60 %
  3. 41.7 %
  4. 83.3 % Correct answer.

Explanation

Useful work output equals load × distance = 500 × 2 = 1000 J. Efficiency is useful output divided by input, 1000/1200 = 0.833, or 83.3 %.

Question 29Physics

A mass on a spring undergoes simple harmonic motion. At the point of maximum displacement from equilibrium, which statement is correct?

  1. Kinetic energy is maximum and acceleration is maximum
  2. Kinetic energy is zero and acceleration is maximum Correct answer.
  3. Kinetic energy is maximum and acceleration is zero
  4. Kinetic energy is zero and acceleration is zero

Explanation

At maximum displacement the velocity is momentarily zero, so kinetic energy is zero. The restoring force, and hence acceleration, is proportional to displacement and therefore maximum there.

Question 30Physics

A gas in a cylinder is compressed slowly while its temperature is held constant. Which statement describes the behaviour of the gas?

  1. Its pressure falls as its volume falls
  2. Its pressure stays unchanged because the temperature is constant
  3. Its pressure rises in direct proportion to its volume
  4. Its pressure rises in inverse proportion to its volume Correct answer.

Explanation

Boyle's law applies to a fixed mass of gas at constant temperature: pressure is inversely proportional to volume. Compressing the gas therefore raises its pressure.

Question 31Physics

An ideal gas is heated at constant volume. Which statement best explains the rise in pressure?

  1. The average kinetic energy of the molecules increases, so collisions with the walls are more forceful and frequent Correct answer.
  2. The molecules move more slowly but collide more often with the walls
  3. The number of molecules in the container increases
  4. The molecules become larger, so they collide more often with the walls

Explanation

Temperature is a measure of the average kinetic energy of the molecules. At constant volume, heating raises molecular speed, increasing both the rate and the momentum change of wall collisions, so pressure rises.

Question 32Physics

A block of density 600 kg/m³ floats in water of density 1000 kg/m³. What fraction of its volume is submerged?

  1. 0.6 Correct answer.
  2. 0.4
  3. 0.67
  4. 1.0

Explanation

A floating body displaces its own weight of fluid, so the submerged fraction equals the ratio of body density to fluid density: 600/1000 = 0.6.

Question 33Electrical Fundamentals

Two resistors of 6 ohms and 3 ohms are connected in parallel. What is the equivalent resistance of the combination?

  1. 4.5 ohms
  2. 9 ohms
  3. 2 ohms Correct answer.
  4. 1.5 ohms

Explanation

For two resistors in parallel the product-over-sum rule gives (6 x 3)/(6 + 3) = 18/9 = 2 ohms. The equivalent resistance of a parallel network is always smaller than the smallest branch resistance.

Question 34Electrical Fundamentals

Which statement correctly describes the relationship between current, voltage and resistance in a linear resistive circuit?

  1. Current is inversely proportional to voltage and directly proportional to resistance.
  2. Current is directly proportional to both voltage and resistance.
  3. Current is independent of resistance when voltage is constant.
  4. Current is directly proportional to voltage and inversely proportional to resistance. Correct answer.

Explanation

Ohm's law states I = V/R, so for a fixed resistance the current rises with voltage, and for a fixed voltage the current falls as resistance rises. This direct/inverse pairing defines a linear resistive element.

Question 35Electrical Fundamentals

A capacitor of 10 microfarads is charged to 50 volts. How much energy is stored in the capacitor?

  1. 0.5 joules
  2. 0.25 joules
  3. 0.0125 joules Correct answer.
  4. 0.0005 joules

Explanation

Stored energy is W = 1/2 C V squared. Substituting gives 0.5 x 10e-6 x 2500 = 0.0125 joules.

Question 36Electrical Fundamentals

What is the time constant of a series circuit containing a 100 kilohm resistor and a 10 microfarad capacitor?

  1. 0.1 second
  2. 1000 seconds
  3. 1 second Correct answer.
  4. 10 seconds

Explanation

The RC time constant is the product of resistance and capacitance: 100e3 x 10e-6 = 1 second. It is the time for the capacitor voltage to change by about 63 percent of the step value.

Question 37Electrical Fundamentals

An alternating current completes 400 full cycles in 8 seconds. What is its frequency?

  1. 0.02 hertz
  2. 400 hertz
  3. 3200 hertz
  4. 50 hertz Correct answer.

Explanation

Frequency is cycles per second, so 400 cycles divided by 8 seconds equals 50 hertz. One hertz corresponds to one complete cycle each second.

Question 38Electrical Fundamentals

In a purely inductive AC circuit, how does the current behave relative to the applied voltage?

  1. The current is in phase with the voltage.
  2. The current lags the voltage by 180 degrees.
  3. The current leads the voltage by 90 degrees.
  4. The current lags the voltage by 90 degrees. Correct answer.

Explanation

An inductor opposes changes in current, so the current reaches its peak a quarter cycle after the voltage, giving a 90 degree lag. This phase relationship is expressed by the inductive reactance being positive imaginary.

Question 39Electrical Fundamentals

What is the reactance of a 50 millihenry inductor at a frequency of 400 hertz?

  1. Approximately 800 ohms
  2. Approximately 20 ohms
  3. Approximately 31 ohms
  4. Approximately 126 ohms Correct answer.

Explanation

Inductive reactance is X = 2 pi f L. Substituting gives 2 x 3.1416 x 400 x 0.05, which is about 126 ohms.

Question 40Electrical Fundamentals

In a series RLC circuit at resonance, which condition holds?

  1. The total impedance equals the sum of all three element values.
  2. Inductive reactance is twice the capacitive reactance.
  3. The circuit draws zero current from the source.
  4. Inductive reactance equals capacitive reactance and they cancel. Correct answer.

Explanation

At resonance the inductive and capacitive reactances are equal in magnitude and opposite in sign, so they cancel and the impedance reduces to the resistance. Current is then at a maximum for a given source voltage.

Question 41Electrical Fundamentals

What is the RMS value of a sinusoidal voltage with a peak value of 340 volts?

  1. Approximately 170 volts
  2. Approximately 480 volts
  3. Approximately 240 volts Correct answer.
  4. Approximately 680 volts

Explanation

The RMS value of a sine wave is the peak divided by the square root of two, so 340/1.414 is about 240 volts. RMS is the equivalent steady value that produces the same heating effect.

Question 42Electrical Fundamentals

Which material is classed as a semiconductor because its conductivity lies between that of conductors and insulators?

  1. Glass
  2. Rubber
  3. Copper
  4. Silicon Correct answer.

Explanation

Silicon has four valence electrons and a moderate energy gap, so its conductivity lies between metals and insulators and can be controlled by doping. Copper, glass and rubber are respectively a conductor and two insulators.

Question 43Electrical Fundamentals

A diode is forward biased in a circuit. Which description of its behaviour is correct?

  1. It behaves as a capacitor at all voltages.
  2. It conducts once the forward voltage exceeds the barrier potential. Correct answer.
  3. It conducts equally in both directions.
  4. It blocks current until the reverse voltage is exceeded.

Explanation

A forward-biased PN junction conducts when the applied voltage overcomes the barrier potential, roughly 0.7 volts for silicon. Below that level only a small leakage current flows.

Question 44Electrical Fundamentals

What is the purpose of a freewheeling diode connected across an inductive load switched by a transistor?

  1. To provide a path for the collapsing inductive current and protect the switch. Correct answer.
  2. To raise the supply voltage during switching.
  3. To convert the DC supply into an AC waveform.
  4. To increase the switching speed of the transistor.

Explanation

When the switch opens, the inductor tries to maintain its current and generates a large voltage spike. The freewheeling diode clamps this by giving the stored energy a circulating path, protecting the transistor.

Question 45Electrical Fundamentals

A transformer has 500 turns on the primary and 50 turns on the secondary. With 230 volts applied to the primary, what is the secondary voltage under no load?

  1. 11.5 volts
  2. 2300 volts
  3. 23 volts Correct answer.
  4. 230 volts

Explanation

The turns ratio is 500 to 50, a step-down factor of ten. The secondary voltage is therefore 230 divided by ten, giving 23 volts.

Question 46Electrical Fundamentals

Which statement about a transformer operating on AC is correct?

  1. It works equally well on steady direct current.
  2. It transfers energy by mutual induction between windings. Correct answer.
  3. It changes the frequency of the supply.
  4. It transfers energy by direct conduction between windings.

Explanation

A changing primary current produces a changing magnetic flux that links the secondary winding and induces a voltage there by mutual induction. This requires a changing flux, which is why a steady DC supply does not sustain transformation.

Question 47Electrical Fundamentals

A 12 volt battery supplies a 4 ohm load. What power is dissipated in the load?

  1. 36 watts Correct answer.
  2. 48 watts
  3. 192 watts
  4. 3 watts

Explanation

Power can be found as V squared divided by R, giving 144/4 = 36 watts. Equivalently the current is 3 amperes and P = V x I = 12 x 3 = 36 watts.

Question 48Electrical Fundamentals

In a three-phase star-connected supply with a line voltage of 400 volts, what is the phase voltage?

  1. Approximately 231 volts Correct answer.
  2. Approximately 400 volts
  3. Approximately 133 volts
  4. Approximately 693 volts

Explanation

In a star connection the phase voltage is the line voltage divided by the square root of three, so 400/1.732 is about 231 volts. The line current equals the phase current in this configuration.

Question 49Electronic Fundamentals

In a semiconductor diode, the depletion region is formed by which mechanism?

  1. Diffusion of majority carriers across the junction leaving fixed ionised atoms Correct answer.
  2. Drift of minority carriers under an external forward bias
  3. Thermal generation of electron-hole pairs in the bulk material
  4. Recombination of carriers at the metal contact surfaces

Explanation

At the junction, majority carriers diffuse across and recombine, leaving behind fixed ionised donor and acceptor atoms that create the depletion region and its built-in potential barrier. Drift and recombination at contacts do not create the depletion zone.

Question 50Electronic Fundamentals

A silicon diode is forward biased. Approximately what forward voltage drop is expected across it under normal conduction?

  1. 5.0 V
  2. 0.7 V Correct answer.
  3. 1.2 V
  4. 0.3 V

Explanation

A conducting silicon pn-junction diode exhibits a forward drop of about 0.6 to 0.7 V. Germanium diodes are lower at roughly 0.3 V, and higher values apply to other device types.