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HSC Engineering Studies practice questions

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Question 1Engineering Studies

Which property best describes the ability of a material to be drawn into thin wire without fracturing?

  1. Brittleness
  2. Elasticity
  3. Ductility Correct answer.
  4. Hardness

Explanation

Ductility is the capacity of a material to undergo significant plastic deformation in tension before rupture, which allows it to be formed into wire. Metals such as copper and mild steel are ductile because their crystal structure permits slip of dislocations. The other properties describe resistance to indentation, lack of plastic deformation, and recoverable deformation respectively.

Question 2Engineering Studies

A simply supported beam carries a single concentrated point load at midspan. Where does the maximum bending moment occur?

  1. At the supports
  2. At the quarter points
  3. It is uniform along the beam
  4. At midspan under the load Correct answer.

Explanation

For a simply supported beam with a central point load, the shear force changes sign at midspan and the bending moment diagram is triangular, peaking directly beneath the load. The moment is zero at both supports because they cannot resist rotation. Hence the greatest bending moment, and the greatest bending stress, occurs at midspan.

Question 3Engineering Studies

In a four-stroke internal combustion engine, during which stroke does the spark plug ignite the compressed air-fuel mixture?

  1. Exhaust stroke
  2. Power stroke
  3. Compression stroke Correct answer.
  4. Intake stroke

Explanation

The spark is timed to occur near the end of the compression stroke, when the mixture is at high pressure and temperature, so combustion begins just before the piston reaches top dead centre. The rapid pressure rise then drives the piston down during the power stroke. Igniting earlier in the intake stroke would be impossible because the mixture is not yet compressed.

Question 4Engineering Studies

Which type of engineering drawing uses parallel projection lines perpendicular to the viewing plane so that true shape is shown on faces parallel to that plane?

  1. Isometric projection
  2. Orthogonal projection Correct answer.
  3. Perspective projection
  4. Oblique projection

Explanation

Orthogonal (orthographic) projection projects points along lines perpendicular to the picture plane, so any face parallel to that plane appears in true shape and size. This is why orthographic views are used for dimensioned working drawings. Perspective and isometric projections foreshorten dimensions, making direct measurement unreliable.

Question 5Engineering Studies

A force of 50 N acts at 30 degrees above the horizontal. What is the horizontal component of this force?

  1. 28.9 N
  2. 43.3 N Correct answer.
  3. 25.0 N
  4. 50.0 N

Explanation

The horizontal component equals the magnitude multiplied by the cosine of the angle to the horizontal, so 50 times cos 30 degrees equals 50 times 0.866, giving 43.3 N. The vertical component would use the sine function instead. Resolving forces into perpendicular components is the standard first step in equilibrium analysis.

Question 6Engineering Studies

Which heat treatment process involves heating steel above its critical temperature and then cooling it very slowly in the furnace?

  1. Case hardening
  2. Tempering
  3. Quenching
  4. Annealing Correct answer.

Explanation

Annealing heats steel above its critical temperature and then cools it slowly, often by leaving it in the furnace, producing a soft, stress-relieved and ductile structure. Slow cooling allows equilibrium microstructures to form. Quenching and tempering involve rapid cooling and reheating respectively.

Question 7Engineering Studies

In a series circuit containing a 6 ohm and a 3 ohm resistor connected to a 12 V supply, what current flows through the circuit?

  1. 1.33 A Correct answer.
  2. 2.0 A
  3. 4.0 A
  4. 0.75 A

Explanation

In a series circuit the resistances add, giving a total of 9 ohms. Applying Ohm's law, current equals voltage divided by resistance, so 12 divided by 9 gives 1.33 A. This same current flows through both resistors because there is only one path.

Question 8Engineering Studies

Which engineering material is a composite consisting of glass fibres embedded in a polymer matrix?

  1. Cast iron
  2. Mild steel
  3. Aluminium alloy
  4. Fibre-reinforced plastic Correct answer.

Explanation

Fibre-reinforced plastic combines strong stiff glass fibres with a polymer resin matrix that binds and protects them, giving a high strength-to-weight ratio. The fibres carry tensile load while the matrix transfers stress between fibres. The other options are metallic materials, not composites.

Question 9Engineering Studies

A simply supported beam of span 4 m carries a uniformly distributed load of 10 kN/m over its full length. What is the magnitude of the reaction at each support?

  1. 5 kN
  2. 40 kN
  3. 10 kN
  4. 20 kN Correct answer.

Explanation

The total load is the intensity multiplied by the span, giving 10 kN/m times 4 m equals 40 kN. By symmetry of the loading and supports, each reaction carries half the total load, so each is 20 kN. Summing vertical forces confirms the two reactions together balance the 40 kN applied load.

Question 10Engineering Studies

Which statement correctly describes the difference between a brittle material and a ductile material when tested in tension?

  1. A ductile material has a higher Young's modulus than any brittle material
  2. A brittle material absorbs more energy before fracture than a ductile material
  3. A brittle material fractures with little plastic deformation while a ductile material undergoes significant plastic deformation before fracture Correct answer.
  4. A brittle material yields noticeably before fracture while a ductile material does not

Explanation

Brittle materials such as cast iron or glass show elastic behaviour up to fracture with almost no yielding, so their stress-strain curve ends abruptly. Ductile materials such as mild steel yield and stretch plastically, absorbing considerable energy before rupture. Young's modulus depends on stiffness rather than on the extent of plastic deformation.

Question 11Engineering Studies

A block weighing 200 N rests on a horizontal surface. The coefficient of static friction between the block and surface is 0.4. What horizontal force is just sufficient to start the block moving?

  1. 500 N
  2. 40 N
  3. 80 N Correct answer.
  4. 200 N

Explanation

The limiting static friction force equals the coefficient of friction multiplied by the normal reaction. On a horizontal surface the normal reaction equals the weight, 200 N, so the required force is 0.4 times 200, giving 80 N. Any applied force below this value is balanced by friction and the block remains at rest.

Question 12Engineering Studies

Which mechanism converts continuous rotary motion into intermittent rotary motion with a dwell period?

  1. Geneva mechanism Correct answer.
  2. Slider-crank mechanism
  3. Worm and wheel
  4. Rack and pinion

Explanation

The Geneva mechanism uses a driving pin that engages slots in a driven wheel, turning it through discrete increments separated by periods when the wheel is locked and stationary. This produces intermittent motion with dwell, common in indexing tables and film projectors. The other mechanisms give continuous conversion between rotary and linear or continuous rotary motion.

Question 13Engineering Studies

A gear train has a driving gear with 20 teeth meshing with a driven gear of 60 teeth. If the driving gear rotates at 900 rpm, what is the rotational speed of the driven gear?

  1. 1800 rpm
  2. 2700 rpm
  3. 450 rpm
  4. 300 rpm Correct answer.

Explanation

The speed ratio equals the ratio of teeth, so the driven gear turns more slowly by the factor 20 divided by 60, which is one third. Multiplying 900 rpm by one third gives 300 rpm. The torque is increased by the same factor of three, consistent with conservation of power in an ideal train.

Question 14Engineering Studies

Which statement best explains why a fuse is connected in series with a circuit?

  1. So that it can share the circuit current and reduce the load on components
  2. So that it can divide the supply voltage equally among components
  3. So that the entire circuit current passes through it and it melts to break the circuit on overload Correct answer.
  4. So that it provides an alternative low-resistance path around the load

Explanation

A fuse must carry the full circuit current so that an excessive current melts its element and opens the circuit, protecting wiring and components. Connecting it in series guarantees all current passes through it. A parallel connection would let current bypass the fuse and defeat the protection.

Question 15Engineering Studies

In an orthogonal drawing, a feature appears as a circle in the front view. What shape will the same feature appear as in a side view taken perpendicular to the front view?

  1. An ellipse
  2. A circle of the same diameter
  3. A triangle
  4. A rectangle whose height equals the circle diameter Correct answer.

Explanation

A cylindrical feature viewed along its axis appears as a circle, while a view perpendicular to that axis shows its rectangular outline. The rectangle's height equals the cylinder diameter and its width equals the cylinder length. This relationship between adjacent orthographic views is fundamental to interpreting engineering drawings.

Question 16Engineering Studies

Which of the following best describes the purpose of a riser in a metal casting mould?

  1. To supply molten metal to compensate for shrinkage as the casting solidifies Correct answer.
  2. To provide the entry point for molten metal into the mould
  3. To allow gases to escape from the mould cavity
  4. To form the internal cavity of the casting

Explanation

A riser, or feeder, is a reservoir of molten metal that feeds the solidifying casting so that shrinkage cavities form in the riser rather than in the part. It is positioned to solidify after the casting. Vents handle gas escape and the sprue or gate handles metal entry.

Question 17Engineering Studies

A material has a Young's modulus of 200 GPa. A rod of this material with cross-sectional area 100 mm squared is subjected to a tensile force of 20 kN. What is the tensile stress in the rod?

  1. 20 MPa
  2. 2000 MPa
  3. 2 MPa
  4. 200 MPa Correct answer.

Explanation

Stress equals force divided by cross-sectional area. Converting units, 20 kN is 20 000 N and 100 mm squared is 100 times 10 to the power minus six square metres, giving a stress of 200 million pascals, or 200 MPa. Young's modulus is not needed to find stress, only to find strain.

Question 18Engineering Studies

Which type of corrosion occurs when two dissimilar metals are in electrical contact in the presence of an electrolyte?

  1. Crevice corrosion
  2. Galvanic corrosion Correct answer.
  3. Uniform corrosion
  4. Erosion corrosion

Explanation

Galvanic corrosion arises when dissimilar metals form a galvanic cell, with the more active metal becoming the anode and corroding preferentially. The electrolyte provides the ionic path and the direct contact provides the electron path. The greater the difference in electrochemical potential between the metals, the more severe the attack.

Question 19Engineering Studies

A simply supported beam of span 6 m carries a point load of 30 kN at 2 m from the left support. What is the reaction at the right support?

  1. 10 kN Correct answer.
  2. 15 kN
  3. 30 kN
  4. 20 kN

Explanation

Taking moments about the left support, the right reaction multiplied by 6 m equals the load 30 kN multiplied by its 2 m distance, giving 60 kN·m. Dividing by the 6 m span gives a right reaction of 10 kN. The left reaction is then 20 kN, and the two reactions sum to the 30 kN load as required.

Question 20Engineering Studies

Which statement correctly describes the function of a flywheel in a machine?

  1. It converts reciprocating motion into rotary motion
  2. It reduces the total power required to drive the machine
  3. It stores rotational kinetic energy to smooth fluctuations in speed Correct answer.
  4. It increases the maximum torque delivered by the engine

Explanation

A flywheel has a large moment of inertia, so it absorbs energy when the driving torque exceeds demand and releases it when demand exceeds supply, reducing speed fluctuation. It does not create energy or increase the mean power output. Its effect is to smooth cyclic variation in angular velocity.

Question 21Engineering Studies

Which manufacturing process involves forcing heated metal through a die to produce long lengths of constant cross-section?

  1. Rolling
  2. Forging
  3. Deep drawing
  4. Extrusion Correct answer.

Explanation

Extrusion pushes or draws heated metal through a shaped die, so the emerging product has the die's cross-section along its whole length, useful for profiles and tubes. Forging shapes metal by compressive impact or pressure, while rolling reduces thickness between rollers. Deep drawing forms sheet metal into cup shapes.

Question 22Engineering Studies

A beam is subjected to a bending moment that causes tension in its bottom fibres. Where in the cross-section does the maximum bending stress occur?

  1. Uniformly across the whole section
  2. At the outermost fibres furthest from the neutral axis Correct answer.
  3. At the neutral axis
  4. At the centroid of the section

Explanation

Bending stress varies linearly with distance from the neutral axis, following the relationship that stress equals the moment times distance divided by the second moment of area. Therefore the greatest stress occurs at the fibres furthest from the neutral axis, at the top and bottom surfaces. The neutral axis itself carries zero bending stress.

Question 23Engineering Studies

A simply supported beam of span L carries a uniformly distributed load of intensity w. Which expression gives the maximum bending moment?

  1. wL squared divided by 8 Correct answer.
  2. wL divided by 2
  3. wL squared divided by 4
  4. wL squared divided by 2

Explanation

For a simply supported beam under a uniform load, the bending moment diagram is parabolic, with the maximum at midspan equal to w times L squared divided by eight. This follows from each reaction being wL divided by two and taking moments about midspan. The value wL squared divided by four applies to a central point load of magnitude wL.

Question 24Engineering Studies

In a first-angle orthographic projection system, where is the top view placed relative to the front view?

  1. Below the front view Correct answer.
  2. To the left of the front view
  3. To the right of the front view
  4. Above the front view

Explanation

In first-angle projection the object is imagined between the observer and the projection plane, so the view seen from above is projected onto a plane below the object and appears below the front view. This contrasts with third-angle projection, where the top view sits above the front view. Recognising the system is essential to interpreting multi-view drawings correctly.

Question 25Engineering Studies

Two resistors of 6 ohms and 3 ohms are connected in parallel across a 12 V supply. What total current is drawn from the supply?

  1. 4 A
  2. 1.33 A
  3. 2 A
  4. 6 A Correct answer.

Explanation

In parallel each resistor sees the full 12 V, so the branch currents are 12 divided by 6, which is 2 A, and 12 divided by 3, which is 4 A. The supply current is the sum of the branch currents, giving 6 A. Equivalently, the parallel combination is 2 ohms, and 12 V divided by 2 ohms also gives 6 A.

Question 26Engineering Studies

Which property of a material is defined as the ratio of stress to strain within the elastic region?

  1. Yield strength
  2. Toughness
  3. Hardness
  4. Young's modulus Correct answer.

Explanation

Young's modulus is the slope of the linear elastic portion of the stress-strain curve, representing stiffness. Yield strength marks the onset of plastic deformation, toughness is energy absorbed before fracture, and hardness measures resistance to indentation.

Question 27Engineering Studies

In a four-stroke internal combustion engine, during which stroke is the air-fuel mixture drawn into the cylinder?

  1. Exhaust stroke
  2. Power stroke
  3. Intake stroke Correct answer.
  4. Compression stroke

Explanation

The intake stroke begins with the piston at top dead centre and moving downward, creating a low-pressure region that draws the air-fuel mixture through the open intake valve. The compression stroke then compresses the charge, the power stroke follows ignition, and the exhaust stroke expels burned gases.

Question 28Engineering Studies

Which type of engineering drawing uses a single view to show the full shape of an object by projecting it onto a plane?

  1. Orthographic drawing
  2. Pictorial drawing Correct answer.
  3. Assembly drawing
  4. Detail drawing

Explanation

A pictorial drawing presents a three-dimensional representation in a single view, allowing the overall shape to be understood without multiple projections. Orthographic drawings use multiple views, while detail and assembly drawings are types of technical drawings that may use orthographic projection.

Question 29Engineering Studies

Which law states that the current through a conductor is directly proportional to the voltage across it, provided temperature remains constant?

  1. Ohm's law Correct answer.
  2. Kirchhoff's voltage law
  3. Faraday's law
  4. Lenz's law

Explanation

Ohm's law expresses the linear relationship between voltage, current, and resistance (V = IR) under constant temperature. Kirchhoff's laws deal with conservation of charge and energy in circuits, Faraday's law relates changing magnetic flux to induced emf, and Lenz's law gives the direction of induced emf.

Question 30Engineering Studies

Which simple machine consists of a wheel with a groove that rotates about an axle to change the direction of a force?

  1. Pulley Correct answer.
  2. Inclined plane
  3. Lever
  4. Wedge

Explanation

A pulley is a wheel with a grooved rim that rotates about an axle; a rope or cable passing over it can redirect an applied force. Levers, inclined planes, and wedges are other simple machines that do not use a grooved wheel.

Question 31Engineering Studies

Which heat treatment process involves heating steel above its critical temperature and then cooling it rapidly in water or oil?

  1. Quenching Correct answer.
  2. Tempering
  3. Normalising
  4. Annealing

Explanation

Quenching rapidly cools austenitised steel to form martensite, increasing hardness but also brittleness. Annealing and normalising involve slow cooling, while tempering is a reheating process after quenching to reduce brittleness.

Question 32Engineering Studies

Which type of engineering material is composed of two or more distinct phases, such as fibres in a matrix, to obtain properties superior to those of the individual constituents?

  1. Composite Correct answer.
  2. Alloy
  3. Polymer
  4. Ceramic

Explanation

A composite material combines two or more distinct phases, typically a reinforcement (e.g., fibres) and a matrix, to achieve properties not attainable by either alone. Alloys are metallic solid solutions, polymers are long-chain molecules, and ceramics are inorganic non-metallic materials.

Question 33Engineering Studies

Which type of stress is defined as the internal force per unit area acting parallel to the cross-section of a material?

  1. Tensile stress
  2. Compressive stress
  3. Shear stress Correct answer.
  4. Bending stress

Explanation

Shear stress acts parallel to the cross-sectional area, tending to cause sliding of one part of the material over another. Tensile and compressive stresses act perpendicular to the cross-section, and bending stress is a normal stress distribution caused by a bending moment.

Question 34Engineering Studies

A simply supported beam of span 8 m carries a point load of 40 kN at its midspan. What is the magnitude of the reaction at each support?

  1. 10 kN
  2. 40 kN
  3. 80 kN
  4. 20 kN Correct answer.

Explanation

For a symmetrically placed point load at midspan, the reactions at the two supports are equal. Taking moments about one support gives the other reaction as (40 kN × 4 m) / 8 m = 20 kN, and vertical equilibrium gives the same for the first support.

Question 35Engineering Studies

A force of 50 N is applied to a lever at a distance of 0.4 m from the fulcrum. What effort is required at a distance of 0.1 m from the fulcrum to balance the lever?

  1. 12.5 N
  2. 20 N
  3. 50 N
  4. 200 N Correct answer.

Explanation

For a lever in equilibrium, the moments about the fulcrum must balance: effort × effort arm = load × load arm. Thus effort = (50 N × 0.4 m) / 0.1 m = 200 N.

Question 36Engineering Studies

A gear train consists of a driving gear with 15 teeth meshing with a driven gear of 45 teeth. If the driving gear rotates at 1200 rpm, what is the rotational speed of the driven gear?

  1. 1200 rpm
  2. 3600 rpm
  3. 400 rpm Correct answer.
  4. 800 rpm

Explanation

The speed ratio is inversely proportional to the number of teeth: driven speed = driving speed × (driving teeth / driven teeth) = 1200 × (15/45) = 400 rpm. The driven gear rotates more slowly because it has more teeth.

Question 37Engineering Studies

A point load of 60 kN is applied to a simply supported beam of span 5 m at a distance of 2 m from the left support. What is the reaction at the right support?

  1. 60 kN
  2. 12 kN
  3. 24 kN Correct answer.
  4. 36 kN

Explanation

Taking moments about the left support: R_right × 5 m = 60 kN × 2 m, so R_right = 120/5 = 24 kN. The reaction at the left support is then 60 − 24 = 36 kN.

Question 38Engineering Studies

A rod of length 2 m and cross-sectional area 200 mm² is subjected to a tensile force of 40 kN. If the material has a Young's modulus of 200 GPa, what is the elongation of the rod?

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

Explanation

Stress = F/A = 40,000 N / 200 mm² = 200 N/mm² = 200 MPa. Strain = stress/E = 200 MPa / 200,000 MPa = 0.001. Elongation = strain × length = 0.001 × 2000 mm = 2 mm.

Question 39Engineering Studies

Which type of corrosion is characterised by localised attack at the grain boundaries of a metal, often due to improper heat treatment?

  1. Galvanic corrosion
  2. Intergranular corrosion Correct answer.
  3. Pitting corrosion
  4. Erosion corrosion

Explanation

Intergranular corrosion occurs preferentially along grain boundaries, frequently because of sensitisation during welding or heat treatment. Galvanic corrosion requires two dissimilar metals, pitting is highly localised cavity formation, and erosion corrosion involves mechanical wear plus chemical attack.

Question 40Engineering Studies

In a first-angle orthographic projection, where is the top view positioned relative to the front view?

  1. To the right of the front view
  2. Above the front view
  3. To the left of the front view
  4. Below the front view Correct answer.

Explanation

In first-angle projection, the object is placed between the observer and the projection plane, so the view from above is projected onto the plane below the object. Consequently, the top view appears below the front view.

Question 41Engineering Studies

Which manufacturing process involves pulling a metal wire through a die to reduce its cross-sectional area?

  1. Drawing Correct answer.
  2. Forging
  3. Rolling
  4. Extrusion

Explanation

In drawing, a wire or rod is pulled through a die, reducing its diameter and increasing its length. Extrusion pushes material through a die, rolling passes material between rolls, and forging shapes material by compressive forces.

Question 42Engineering Studies

A material has a tensile strength of 500 MPa and a yield strength of 350 MPa. What is the maximum tensile load that a rod of this material with a cross-sectional area of 100 mm² can carry without permanent deformation?

  1. 35 kN Correct answer.
  2. 50 kN
  3. 15 kN
  4. 85 kN

Explanation

Permanent deformation begins when the stress reaches the yield strength. The maximum load without permanent deformation is yield strength × area = 350 N/mm² × 100 mm² = 35,000 N = 35 kN.

Question 43Engineering Studies

Which of the following is a scalar quantity?

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

Explanation

Work is a scalar quantity because it has magnitude but no direction. Force, velocity, and acceleration are vectors, each having both magnitude and direction.

Question 44Engineering Studies

A machine has an actual mechanical advantage of 4 and a velocity ratio of 6. What is its efficiency?

  1. 24%
  2. 150%
  3. 66.7% Correct answer.
  4. 10%

Explanation

Efficiency = (mechanical advantage / velocity ratio) × 100% = (4/6) × 100% ≈ 66.7%. Efficiency cannot exceed 100% for a real machine.

Question 45Engineering Studies

Which type of bearing is designed to support loads acting primarily perpendicular to the shaft axis?

  1. Thrust bearing
  2. Pillow block
  3. Radial bearing Correct answer.
  4. Journal bearing

Explanation

A radial bearing supports loads that act perpendicular to the shaft axis (radial loads). A thrust bearing supports axial loads, while journal and pillow block are specific types of radial bearings but not the general category name.

Question 46Engineering Studies

A simply supported beam of length 4 m carries a uniformly distributed load of 5 kN/m over its entire length. What is the maximum bending moment in the beam?

  1. 5 kN·m
  2. 40 kN·m
  3. 20 kN·m
  4. 10 kN·m Correct answer.

Explanation

The maximum bending moment for a simply supported beam with a uniformly distributed load is wL²/8. Here w = 5 kN/m and L = 4 m, so M_max = 5 × 4² / 8 = 5 × 16 / 8 = 10 kN·m.

Question 47Engineering Studies

A beam of rectangular cross-section has width 50 mm and depth 100 mm. If the maximum bending stress is 120 MPa, what is the maximum bending moment the beam can resist?

  1. 10 kN·m Correct answer.
  2. 5 kN·m
  3. 20 kN·m
  4. 40 kN·m

Explanation

Section modulus Z = bd²/6 = 50 × 100² / 6 = 500,000 / 6 ≈ 83,333 mm³. Maximum moment M = σ × Z = 120 N/mm² × 83,333 mm³ ≈ 10,000,000 N·mm = 10 kN·m.

Question 48Engineering Studies

A shaft transmits 15 kW at a rotational speed of 300 rpm. What is the torque in the shaft?

  1. 955 N·m
  2. 4.77 kN·m
  3. 47.7 N·m
  4. 477 N·m Correct answer.

Explanation

Power P = Tω, where ω = 2πN/60 = 2π × 300 / 60 = 31.42 rad/s. Torque T = P/ω = 15,000 W / 31.42 rad/s ≈ 477 N·m.

Question 49Engineering Studies

A composite material consists of 60% by volume of glass fibres (E = 70 GPa) and 40% by volume of epoxy resin (E = 3 GPa). What is the longitudinal elastic modulus of the composite, assuming the rule of mixtures?

  1. 73 GPa
  2. 21.6 GPa
  3. 36.5 GPa
  4. 43.2 GPa Correct answer.

Explanation

The rule of mixtures for longitudinal modulus gives E_c = V_f E_f + V_m E_m = 0.6 × 70 + 0.4 × 3 = 42 + 1.2 = 43.2 GPa.

Question 50Engineering Studies

A simply supported beam of span 6 m carries a point load of 20 kN at 2 m from the left support and a uniformly distributed load of 4 kN/m over the entire span. What is the reaction at the left support?

  1. 19.33 kN Correct answer.
  2. 12 kN
  3. 22.67 kN
  4. 32 kN

Explanation

Take moments about the right support: R_left × 6 = 20 × 4 + (4 × 6) × 3 = 80 + 72 = 152, so R_left = 152/6 ≈ 25.33 kN? Wait, check: the point load is 2 m from left, so its distance from right is 4 m. UDL total 24 kN acts at 3 m from right. Moments about right: R_left × 6 = 20 × 4 + 24 × 3 = 80 + 72 = 152, R_left = 25.33 kN. That is not among options. Let's re-calculate: If the point load is 2 m from left, then distance from right is 4 m. UDL total = 4 kN/m × 6 m = 24 kN, centroid at 3 m from right. Sum moments about right: R_left × 6 = 20 × 4 + 24 × 3 = 80 + 72 = 152, R_left = 25.33 kN. Not in options. So the question likely intended the point load at 2 m from left, but options are 19.33, 22.67, 12, 32. Let's check if the point load is at 2 m from left, and UDL 4 kN/m, total load = 20 + 24 = 44 kN. Reaction at left = (20×4 + 24×3)/6 = (80+72)/6 = 152/6 = 25.33 kN. Not matching. Maybe the UDL is 4 kN/m over the entire span, but the point load is at 2 m from left. Then reaction at left = (20×4 + 24×3)/6 = 25.33. None. Perhaps the point load is at 2 m from left, and the UDL is 4 kN/m over the entire span, then reaction at left = (20×4 + 24×3)/6 = 25.33. So options are wrong. I need to adjust the question to match the options. Let's choose a different set: If the point load is 20 kN at 2 m from left, and UDL is 4 kN/m over the entire span, the reaction at left is 25.33 kN. To get 19.33 kN, maybe the UDL is 2 kN/m: total UDL = 12 kN, moment about right = 20×4 + 12×3 = 80+36=116, R_left=116/6=19.33 kN. Yes! So if UDL is 2 kN/m, then R_left = 19.33 kN. So I will change the UDL to 2 kN/m. Then options: 19.33 kN correct. 22.67 kN would be reaction at right? Total load = 20 + 12 = 32 kN, R_right = 32 - 19.33 = 12.67 kN. Not 22.67. 22.67 could be if UDL is 4 kN/m and point load at 2 m from left, then R_left = 25.33, R_right = 44-25.33=18.67. Not 22.67. So I'll set the question with UDL 2 kN/m. Then correct answer 19.33 kN. Other options: 22.67 kN (if moments taken incorrectly), 12 kN (total UDL), 32 kN (total load). That works. So final question: A simply supported beam of span 6 m carries a point load of 20 kN at 2 m from the left support and a uniformly distributed load of 2 kN/m over the entire span. What is the reaction at the left support? Options: 19.33 kN, 22.67 kN, 12 kN, 32 kN. Correct index 0. Explanation: Take moments about the right support: R_left × 6 = 20 × 4 + (2 × 6) × 3 = 80 + 36 = 116, so R_left = 116/6 ≈ 19.33 kN. The total load is 20 + 12 = 32 kN, and the right reaction is 12.67 kN.