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Part-66 Module 1 study materials
Part-66 Module 1 study resources

Part-66 Module 1 practice questions

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Question 1Mathematics

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

  1. 2^8 Correct answer.
  2. 2^15
  3. 2^56
  4. 2^2

Explanation

When multiplying powers with the same base, add the exponents: 2^5 × 2^3 = 2^(5+3) = 2^8. The base stays unchanged.

Question 2Mathematics

A component is 0.0375 m long. Expressed in standard form (scientific notation), this is:

  1. 3.75 × 10^3 m
  2. 3.75 × 10^-2 m Correct answer.
  3. 3.75 × 10^-1 m
  4. 3.75 × 10^2 m

Explanation

Standard form writes a number as a value between 1 and 10 multiplied by a power of 10. Moving the decimal point two places right to get 3.75 means the power is 10^-2.

Question 3Mathematics

A rectangular panel measures 1.2 m by 0.75 m. What is its area?

  1. 1.95 m²
  2. 9.0 m²
  3. 0.90 m² Correct answer.
  4. 0.09 m²

Explanation

Area of a rectangle is length × width: 1.2 × 0.75 = 0.90 m². The units are square metres because two lengths are multiplied.

Question 4Mathematics

Convert 5/8 to a decimal.

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

Explanation

Dividing the numerator by the denominator gives 5 ÷ 8 = 0.625. A fraction always represents this division.

Question 5Mathematics

What is the mean of the values 12, 15, 9, 20 and 14?

  1. 12
  2. 17
  3. 15
  4. 14 Correct answer.

Explanation

The mean is the sum of the values divided by how many there are: (12+15+9+20+14) = 70, and 70 ÷ 5 = 14.

Question 6Mathematics

A right-angled triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?

  1. 10 cm Correct answer.
  2. 48 cm
  3. 14 cm
  4. 12 cm

Explanation

By Pythagoras' theorem the hypotenuse squared equals the sum of the squares of the other two sides: 6² + 8² = 36 + 64 = 100, so the hypotenuse is √100 = 10 cm.

Question 7Mathematics

Solve for x: 3x − 7 = 2x + 5.

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

Explanation

Subtract 2x from both sides to get x − 7 = 5, then add 7 to both sides to get x = 12. Each step keeps the equation balanced.

Question 8Mathematics

A quantity grows by 4% each year. By what factor is it multiplied over one year?

  1. 4.0
  2. 0.04
  3. 1.4
  4. 1.04 Correct answer.

Explanation

A percentage increase is applied by multiplying by (1 + rate) where the rate is expressed as a decimal. A 4% increase gives a multiplier of 1 + 0.04 = 1.04.

Question 9Mathematics

Using the formula s = ut + ½at², find s when u = 3, t = 4 and a = 2.

  1. 28 Correct answer.
  2. 36
  3. 20
  4. 40

Explanation

Substitute the values: ut = 3 × 4 = 12, and ½at² = ½ × 2 × 4² = 16. Adding gives s = 12 + 16 = 28.

Question 10Mathematics

Two similar components have lengths in the ratio 2:5. What is the ratio of their surface areas?

  1. 2:5
  2. 8:125
  3. 4:10
  4. 4:25 Correct answer.

Explanation

For similar shapes, lengths scale by the ratio k, so areas scale by k². Squaring 2:5 gives 4:25.

Question 11Mathematics

A right-angled triangle has an opposite side of 5 cm and a hypotenuse of 13 cm. What is the sine of the angle?

  1. 12/13
  2. 5/12
  3. 5/13 Correct answer.
  4. 13/5

Explanation

Sine is the ratio of the opposite side to the hypotenuse: sin θ = opposite/hypotenuse = 5/13. The adjacent side is not used for sine.

Question 12Mathematics

The number 0.000046 written in standard form is:

  1. 4.6 × 10^-5 Correct answer.
  2. 4.6 × 10^-4
  3. 4.6 × 10^5
  4. 46 × 10^-6

Explanation

To reach a mantissa between 1 and 10, the decimal point moves five places right, so the exponent is −5. This gives 4.6 × 10^-5.

Question 13Mathematics

Simplify (2x³)(3x²).

  1. 5x⁵
  2. 6x⁶
  3. 6x^1
  4. 6x⁵ Correct answer.

Explanation

Multiply the coefficients (2 × 3 = 6) and add the exponents of like bases (3 + 2 = 5), giving 6x⁵.

Question 14Mathematics

A circle has a radius of 7 cm. Using π ≈ 22/7, what is its circumference?

  1. 154 cm
  2. 88 cm
  3. 22 cm
  4. 44 cm Correct answer.

Explanation

Circumference = 2πr = 2 × (22/7) × 7 = 44 cm. The radius of 7 cancels neatly with the denominator of the approximation.

Question 15Mathematics

The probability of an event is 0.35. What is the probability of it not occurring?

  1. 0.7
  2. 0.65 Correct answer.
  3. 0.5
  4. 0.35

Explanation

The probabilities of an event occurring and not occurring must sum to 1. Therefore the complement is 1 − 0.35 = 0.65.

Question 16Mathematics

A right-angled triangle has an opposite side of 5 cm and an adjacent side of 12 cm. What is the tangent of the angle?

  1. 5/13
  2. 5/12 Correct answer.
  3. 12/5
  4. 13/12

Explanation

Tangent is the ratio of the opposite side to the adjacent side: tan θ = opposite/adjacent = 5/12. The hypotenuse is not part of the tangent ratio.

Question 17Mathematics

If y is inversely proportional to x and y = 8 when x = 3, what is y when x = 12?

  1. 2 Correct answer.
  2. 32
  3. 4
  4. 0.5

Explanation

Inverse proportion means xy = constant. Here the constant is 8 × 3 = 24, so when x = 12, y = 24 ÷ 12 = 2.

Question 18Physics

Which SI base quantity is measured in newtons?

  1. Pressure
  2. Force Correct answer.
  3. Mass
  4. Energy

Explanation

The newton is the SI derived unit of force, defined as the force giving a 1 kg mass an acceleration of 1 m/s². Mass is measured in kilograms and energy in joules.

Question 19Physics

An aircraft accelerates uniformly from rest to 80 m/s in 20 s. What is its acceleration?

  1. 4 m/s² Correct answer.
  2. 2 m/s²
  3. 8 m/s²
  4. 16 m/s²

Explanation

Acceleration is the change in velocity divided by the time taken: (80 − 0)/20 = 4 m/s². Uniform acceleration means this value is constant throughout.

Question 20Physics

A body moves at constant velocity. What is true of the forces acting on it?

  1. They are zero in total Correct answer.
  2. They are all equal in size
  3. They increase with speed
  4. They act in one direction

Explanation

Constant velocity means zero acceleration, so by Newton's second law the resultant force must be zero. Individual forces may be large provided they cancel.

Question 21Physics

What is the approximate value of the acceleration due to gravity at the Earth's surface?

  1. 9.8 m/s² Correct answer.
  2. 1.6 m/s²
  3. 19.6 m/s²
  4. 3.8 m/s²

Explanation

Standard gravity at the Earth's surface is about 9.81 m/s², often rounded to 9.8 m/s². This value is used to convert mass to weight.

Question 22Physics

Which quantity is a scalar?

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

Explanation

A scalar has magnitude only, and speed is defined purely by magnitude. Velocity, displacement and acceleration all carry direction as well.

Question 23Physics

A mass of 25 kg is raised through a vertical height of 4 m. Taking g as 10 m/s², how much gravitational potential energy does it gain?

  1. 1000 J Correct answer.
  2. 250 J
  3. 100 J
  4. 2500 J

Explanation

Gravitational potential energy equals mgh, so 25 × 10 × 4 = 1000 J. The height must be measured vertically for this relationship to apply.

Question 24Physics

A force of 60 N acts at 60° to the horizontal. What is the horizontal component of the force?

  1. 30 N Correct answer.
  2. 52 N
  3. 42 N
  4. 60 N

Explanation

The horizontal component is F cos θ = 60 × cos 60° = 60 × 0.5 = 30 N. The vertical component would be F sin θ.

Question 25Physics

A moment of 240 N·m is produced by a force applied perpendicular to a lever arm of 1.6 m. What is the force?

  1. 150 N Correct answer.
  2. 96 N
  3. 120 N
  4. 384 N

Explanation

Moment equals force times perpendicular distance, so F = 240/1.6 = 150 N. The force must act at right angles to the arm for this direct relationship.

Question 26Physics

A body of mass 4 kg experiences a resultant force of 12 N. What is its acceleration?

  1. 3 m/s² Correct answer.
  2. 16 m/s²
  3. 48 m/s²
  4. 0.33 m/s²

Explanation

Newton's second law gives a = F/m = 12/4 = 3 m/s². The resultant force, not any single applied force, must be used.

Question 27Physics

A machine does 3000 J of useful work while consuming 5000 J of energy input. What is its efficiency?

  1. 67%
  2. 60% Correct answer.
  3. 167%
  4. 40%

Explanation

Efficiency is useful output divided by total input, expressed as a percentage: (3000/5000) × 100 = 60%. Efficiency cannot exceed 100% for a real machine.

Question 28Physics

In a hydraulic system, a small piston of area 0.01 m² is pushed with 200 N. What pressure is transmitted to the fluid?

  1. 2000 Pa
  2. 200000 Pa
  3. 2 Pa
  4. 20000 Pa Correct answer.

Explanation

Pressure equals force divided by area: 200/0.01 = 20 000 Pa. Pascal's principle states this pressure is transmitted undiminished throughout the enclosed fluid.

Question 29Physics

A block of volume 0.002 m³ is fully submerged in a fluid of density 1000 kg/m³. Taking g as 10 m/s², what upthrust acts on it?

  1. 200 N
  2. 10 N
  3. 20 N Correct answer.
  4. 2 N

Explanation

Upthrust equals the weight of displaced fluid: ρVg = 1000 × 0.002 × 10 = 20 N. This is Archimedes' principle applied to a fully submerged body.

Question 30Physics

Which statement describes the relationship between absolute temperature and the average kinetic energy of gas molecules?

  1. Kinetic energy is independent of temperature
  2. Kinetic energy is proportional to absolute temperature Correct answer.
  3. Kinetic energy rises only when pressure rises
  4. Kinetic energy doubles when volume halves

Explanation

The kinetic theory of gases shows average translational kinetic energy is directly proportional to absolute temperature. Pressure and volume changes matter only as they affect temperature.

Question 31Physics

A gas is heated at constant pressure so that its absolute temperature rises from 300 K to 450 K. If the initial volume was 2.0 m³, what is the final volume?

  1. 1.33 m³
  2. 3.0 m³ Correct answer.
  3. 4.5 m³
  4. 2.67 m³

Explanation

Charles' law gives V₂ = V₁T₂/T₁ = 2.0 × 450/300 = 3.0 m³. Volume varies directly with absolute temperature at constant pressure.

Question 32Physics

Two parallel forces of 40 N and 60 N act in opposite directions at the ends of a 2 m bar. What is the magnitude of the resultant couple and its effect?

  1. A couple of 100 N·m causing rotation
  2. A couple of 200 N·m causing rotation
  3. A couple of 40 N·m causing rotation Correct answer.
  4. No couple, only a net force of 20 N

Explanation

A couple consists of two equal, opposite, parallel forces, but here they are unequal, so a pure couple does not strictly form. Taking the perpendicular distance as 2 m, the moment of the pair about the bar is (60 − 40) × 2 = 40 N·m, tending to rotate it.

Question 33Physics

A projectile is launched horizontally at 30 m/s from a height of 45 m. Taking g as 10 m/s² and ignoring air resistance, how far horizontally does it travel before landing?

  1. 45 m
  2. 90 m Correct answer.
  3. 135 m
  4. 60 m

Explanation

Vertical fall time follows s = ½gt², giving t = √(2×45/10) = 3 s. Horizontal distance is then 30 × 3 = 90 m, since horizontal velocity is unchanged.

Question 34Physics

A 2 kg mass moving at 6 m/s collides head-on with a stationary 4 kg mass and they stick together. What is their common velocity after impact?

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

Explanation

Conservation of momentum gives total momentum 2 × 6 = 12 kg·m/s, shared by the combined 6 kg mass. The common velocity is 12/6 = 2 m/s in the original direction.

Question 35Electrical Fundamentals

A resistor has a colour code of brown, black, red, gold. What is its nominal value and tolerance?

  1. 1 kΩ ±5% Correct answer.
  2. 1.2 kΩ ±5%
  3. 100 Ω ±5%
  4. 10 Ω ±10%

Explanation

Brown = 1, black = 0, red = multiplier ×100, giving 10 × 100 = 1000 Ω. Gold denotes a tolerance of ±5%.

Question 36Electrical Fundamentals

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

  1. 9 Ω
  2. 18 Ω
  3. 4.5 Ω
  4. 2 Ω Correct answer.

Explanation

For two resistors in parallel, R = (R1 × R2)/(R1 + R2) = (6 × 3)/(6 + 3) = 18/9 = 2 Ω. The equivalent is always smaller than the smallest branch resistance.

Question 37Electrical Fundamentals

What is the unit of electrical capacitance?

  1. Henry
  2. Farad Correct answer.
  3. Ohm
  4. Weber

Explanation

Capacitance is measured in farads, where one farad stores one coulomb per volt. The henry measures inductance and the ohm measures resistance.

Question 38Electrical Fundamentals

In a purely capacitive AC circuit, how does the current relate to the applied voltage?

  1. Current lags voltage by 90°
  2. Current leads voltage by 45°
  3. Current is in phase with voltage
  4. Current leads voltage by 90° Correct answer.

Explanation

In a capacitor the current reaches its peak before the voltage does, so current leads voltage by a quarter cycle (90°). This is remembered by the mnemonic CIV.

Question 39Electrical Fundamentals

A 12 V battery supplies a current of 0.5 A to a lamp. What power is dissipated by the lamp?

  1. 6 W Correct answer.
  2. 12.5 W
  3. 24 W
  4. 0.04 W

Explanation

Power equals voltage multiplied by current: P = V × I = 12 × 0.5 = 6 W. This relationship holds for any resistive load.

Question 40Electrical Fundamentals

Which material is classed as a semiconductor?

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

Explanation

Silicon has four valence electrons and its conductivity lies between that of conductors and insulators, making it a semiconductor. Copper is a conductor, while rubber and mica are insulators.

Question 41Electrical Fundamentals

Three capacitors of 3 µF each are connected in series. What is the total capacitance?

  1. 6 µF
  2. 9 µF
  3. 3 µF
  4. 1 µF Correct answer.

Explanation

Capacitors in series combine like resistors in parallel: 1/C = 1/3 + 1/3 + 1/3 = 1, so C = 1 µF. The total is always less than the smallest individual capacitor.

Question 42Electrical Fundamentals

A transformer has 500 primary turns and 50 secondary turns. If the primary is supplied at 230 V, what is the secondary voltage (ideal transformer)?

  1. 11.5 V
  2. 23 V Correct answer.
  3. 2300 V
  4. 115 V

Explanation

The turns ratio is 500:50, or 10:1 step-down. Secondary voltage = 230 × (50/500) = 23 V.

Question 43Electrical Fundamentals

What is the RMS value of a sinusoidal voltage whose peak value is 100 V?

  1. 70.7 V Correct answer.
  2. 63.7 V
  3. 50 V
  4. 100 V

Explanation

For a sine wave, RMS = peak/√2 = 100/1.414 ≈ 70.7 V. RMS is the value that produces the same heating effect as an equivalent DC voltage.

Question 44Electrical Fundamentals

Which statement describes the magnetic field around a straight current-carrying conductor?

  1. It forms concentric circles around the conductor Correct answer.
  2. It is uniform and parallel to the conductor
  3. It is zero outside the conductor
  4. It runs radially outward from the conductor

Explanation

The field lines form concentric circles around the conductor, with direction given by the right-hand grip rule. Field strength decreases with distance from the conductor.

Question 45Electrical Fundamentals

A coil has an inductance of 4 H and carries a current that changes at 2 A per second. What is the induced EMF?

  1. 8 V Correct answer.
  2. 6 V
  3. 2 V
  4. 0.5 V

Explanation

Faraday's law gives EMF = L × (dI/dt) = 4 × 2 = 8 V. The induced EMF opposes the change in current according to Lenz's law.

Question 46Electrical Fundamentals

A 24 V supply is connected across a 12 Ω resistor. What current flows?

  1. 0.5 A
  2. 36 A
  3. 288 A
  4. 2 A Correct answer.

Explanation

Ohm's law gives I = V/R = 24/12 = 2 A. Current is directly proportional to voltage and inversely proportional to resistance.

Question 47Electrical Fundamentals

In a series circuit containing a resistor and an inductor, which statement about the total impedance is correct?

  1. It equals the vector sum of R and XL Correct answer.
  2. It equals the product of R and XL
  3. It equals the difference between R and XL
  4. It equals the arithmetic sum of R and XL

Explanation

Resistance and inductive reactance are 90° out of phase, so they add as vectors: Z = √(R² + XL²). The result is always less than the arithmetic sum.

Question 48Electrical Fundamentals

What is the purpose of a diode in a rectifier circuit?

  1. To allow current in one direction only Correct answer.
  2. To step up the AC voltage
  3. To smooth the output ripple
  4. To store charge between half cycles

Explanation

A diode conducts in forward bias and blocks reverse current, so it converts AC into unidirectional current. Smoothing is done by a capacitor, not the diode.

Question 49Electrical Fundamentals

A conductor of length 0.5 m carries 10 A at right angles to a magnetic field of flux density 0.4 T. What force acts on the conductor?

  1. 2 N Correct answer.
  2. 0.2 N
  3. 4 N
  4. 20 N

Explanation

The force is given by F = B × I × L × sin θ, with sin 90° = 1. Thus F = 0.4 × 10 × 0.5 = 2 N.

Question 50Electrical Fundamentals

A 100 µF capacitor is charged to 50 V. How much energy is stored?

  1. 5 J
  2. 2.5 J
  3. 0.25 J
  4. 0.125 J Correct answer.

Explanation

Energy stored is E = ½CV² = 0.5 × 100×10⁻⁶ × 50² = 0.125 J. The capacitance must be converted to farads before calculating.