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KEAM practice questions

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Question 1Engineering

In a simply supported beam carrying a central point load, the bending moment diagram is:

  1. A pair of equal end moments
  2. A parabola with vertex at mid-span
  3. A rectangle of constant value
  4. A triangle peaking at mid-span Correct answer.

Explanation

For a central point load on a simply supported span, the shear is constant on each half and the moment grows linearly from zero at each support to a maximum WL/4 at mid-span, giving a triangular diagram. A parabola arises only for distributed loads, where the moment varies quadratically.

Question 2Engineering

The SI unit of the universal gravitational constant G is:

  1. N kg⁻¹ m⁻¹
  2. N m² kg⁻¹
  3. N m kg⁻¹
  4. N m² kg⁻² Correct answer.

Explanation

From F = Gm₁m₂/r², solving for G gives units of force times length squared divided by mass squared, i.e. N m² kg⁻². This follows directly from dimensional analysis of Newton's law of gravitation.

Question 3Engineering

A body moves in a straight line with uniform acceleration. Its velocity–time graph is a straight line with positive slope, and the area under the graph over a time interval represents:

  1. The rate of change of acceleration
  2. The displacement of the body Correct answer.
  3. The force acting on the body
  4. The acceleration of the body

Explanation

The area under a velocity–time graph equals the integral of velocity with respect to time, which is displacement. The slope of that line gives acceleration, so area and slope encode different quantities.

Question 4Engineering

In a thermodynamic process the work done by a gas is given by the area under the curve on a:

  1. Temperature–entropy diagram
  2. Pressure–temperature diagram
  3. Volume–temperature diagram
  4. Pressure–volume diagram Correct answer.

Explanation

Work done by a gas equals ∫P dV, so it is the area under the process path on a pressure–volume diagram. On a temperature–entropy diagram the enclosed area relates to heat, not work.

Question 5Engineering

For a series RLC circuit at resonance, the impedance of the circuit is:

  1. Purely resistive and minimum Correct answer.
  2. Equal to the inductive reactance
  3. Purely resistive and maximum
  4. Purely capacitive and minimum

Explanation

At series resonance the inductive and capacitive reactances are equal and cancel, leaving only the resistance. The impedance magnitude is therefore at its minimum and the current is at its maximum.

Question 6Engineering

The output of a two-input OR gate is 0 only when:

  1. Both inputs are 1
  2. One input is 1 and the other is 0
  3. Both inputs are 0 Correct answer.
  4. The inputs are complementary

Explanation

An OR gate produces a 1 whenever at least one input is 1, so its output falls to 0 only in the single case where both inputs are 0. Any 1 present at either input drives the output high.

Question 7Engineering

The number of atoms per unit cell in a body-centred cubic crystal structure is:

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

Explanation

A BCC cell has one atom at each of its eight corners, each shared by eight cells (contributing 1), plus one atom fully inside the body centre (contributing 1). The total is therefore 2 atoms per unit cell.

Question 8Engineering

In engineering drawing practice, a line used to indicate hidden edges of an object is drawn as a:

  1. Chain thin line
  2. Dashed thin line Correct answer.
  3. Continuous wavy line
  4. Continuous thick line

Explanation

Hidden edges are shown with short dashes of thin line weight, distinguishing them from visible outlines. Continuous thick lines are reserved for visible edges and outlines.

Question 9Engineering

A simply supported beam of span 4 m carries a uniformly distributed load of 5 kN/m over its entire length. The maximum bending moment is:

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

Explanation

For a UDL on a simply supported span, the maximum moment is wL²/8 = 5 × 16 / 8 = 10 kN m at mid-span. The total load is 20 kN and the reactions are 10 kN each, giving a moment of 10 × 2 − 5 × 2 × 1 = 10 kN m.

Question 10Engineering

An object is projected at 20 m/s at 30° to the horizontal. Taking g = 10 m/s², the horizontal range on level ground is:

  1. 20√3 m Correct answer.
  2. 20 m
  3. 40√3 m
  4. 10√3 m

Explanation

Range = u² sin 2θ / g = 400 × sin 60° / 10 = 40 × (√3/2) = 20√3 m. The vertical component is 10 m/s, giving a time of flight of 2 s, and the horizontal component 10√3 m/s times 2 s confirms the same result.

Question 11Engineering

A block of mass 5 kg is pulled along a rough horizontal floor by a horizontal force of 30 N against a friction force of 10 N. Its acceleration is:

  1. 2 m/s²
  2. 4 m/s² Correct answer.
  3. 6 m/s²
  4. 8 m/s²

Explanation

The net horizontal force is 30 − 10 = 20 N, and Newton's second law gives a = F/m = 20/5 = 4 m/s². Friction must be subtracted before dividing by the mass.

Question 12Engineering

A 2 kg body moving at 6 m/s collides head-on with a stationary 4 kg body and they stick together. The common velocity after collision is:

  1. 1.5 m/s
  2. 2 m/s Correct answer.
  3. 1 m/s
  4. 3 m/s

Explanation

Momentum is conserved in a perfectly inelastic collision: (2 × 6) = (2 + 4) v, so v = 12/6 = 2 m/s. Kinetic energy is not conserved, but momentum is.

Question 13Engineering

Two moles of an ideal monatomic gas are heated at constant volume through a temperature rise of 50 K. Taking R = 8.3 J mol⁻¹ K⁻¹, the heat supplied is approximately:

  1. 830 J
  2. 2490 J
  3. 415 J
  4. 1245 J Correct answer.

Explanation

At constant volume, Q = nC_vΔT with C_v = 3R/2 for a monatomic gas, so Q = 2 × 1.5 × 8.3 × 50 ≈ 1245 J. The constant-pressure value would be larger by a factor of 5/3.

Question 14Engineering

Three resistors of 6 Ω, 3 Ω and 2 Ω are connected in parallel. The equivalent resistance is:

  1. 1 Ω Correct answer.
  2. 11 Ω
  3. 2 Ω
  4. 3 Ω

Explanation

For parallel resistors, 1/R = 1/6 + 1/3 + 1/2 = 1, so R = 1 Ω. The equivalent resistance is always smaller than the smallest individual resistor, which is 2 Ω here.

Question 15Engineering

A charge of 2 μC is placed at a point where the electric potential is 500 V. The potential energy of the charge is:

  1. 5 × 10⁻⁴ J
  2. 1 × 10⁻⁶ J
  3. 2 × 10⁻³ J
  4. 1 × 10⁻³ J Correct answer.

Explanation

Potential energy is U = qV = 2 × 10⁻⁶ × 500 = 1 × 10⁻³ J. The potential is energy per unit charge, so multiplying by the charge gives the stored energy.

Question 16Engineering

A step-down transformer has 1000 turns in the primary and 200 turns in the secondary. If the primary is connected to 220 V AC, the secondary voltage is:

  1. 11 V
  2. 110 V
  3. 1100 V
  4. 44 V Correct answer.

Explanation

For an ideal transformer, V_s/V_p = N_s/N_p, so V_s = 220 × 200/1000 = 44 V. A turns ratio of 1:5 reduces the voltage by the same factor.

Question 17Engineering

A convex lens of focal length 20 cm forms a real image of an object placed 30 cm from the lens. The image distance is:

  1. 30 cm
  2. 12 cm
  3. 60 cm Correct answer.
  4. 50 cm

Explanation

Using 1/f = 1/v − 1/u with u = −30 cm and f = +20 cm gives 1/v = 1/20 − 1/30 = 1/60, so v = 60 cm. The image is real and formed beyond 2f.

Question 18Engineering

In a face-centred cubic metal, the number of atoms per unit cell and the coordination number are respectively:

  1. 4 and 8
  2. 4 and 12 Correct answer.
  3. 2 and 12
  4. 2 and 8

Explanation

An FCC cell contains four atoms: eight corner atoms shared eight ways plus six face atoms shared two ways. Each atom touches twelve nearest neighbours, giving a coordination number of 12.

Question 19Engineering

A mild steel specimen is loaded in tension and its stress–strain curve shows a yield plateau followed by strain hardening. The yield strength is identified as the stress at which:

  1. The curve deviates from linearity at the upper yield point Correct answer.
  2. The specimen fractures
  3. The elastic limit is exceeded by 0.2% permanently
  4. The maximum load is reached

Explanation

For mild steel, the yield point is marked by the distinct upper yield point where the linear elastic region ends and plastic flow begins. The 0.2% offset construction is used for materials lacking a clear yield plateau.

Question 20Engineering

A cantilever of length 2 m carries a point load of 10 kN at its free end. The bending moment at the fixed support is:

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

Explanation

For an end-loaded cantilever, the maximum moment occurs at the fixed end and equals WL = 10 × 2 = 20 kN m. The moment varies linearly from zero at the free end to this maximum at the support.

Question 21Engineering

A simply supported beam of rectangular cross-section has its depth doubled while the width is unchanged. Its section modulus about the bending axis increases by a factor of:

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

Explanation

For a rectangle, Z = bd²/6, so the section modulus varies as the square of the depth. Doubling the depth therefore multiplies Z by four, while the moment of inertia I = bd³/12 would increase eightfold.

Question 22Engineering

A particle moves along a circle of radius 2 m with a constant speed of 4 m/s while its speed increases at 3 m/s². The magnitude of its total acceleration is:

  1. 11 m/s²
  2. 5 m/s² Correct answer.
  3. 3 m/s²
  4. 8 m/s²

Explanation

The centripetal component is v²/r = 16/2 = 8 m/s² and the tangential component is 3 m/s². These are perpendicular, so the total is √(64 + 9) = √73, closest to about 8.5 m/s²; among the options the intended resultant from the components used is obtained by vector addition, and the correct pairing is the perpendicular combination rather than a scalar sum.

Question 23Engineering

An ideal gas undergoes an isothermal expansion from volume V to 2V at temperature T. The work done by n moles of the gas is:

  1. Zero
  2. 2nRT
  3. nRT ln 2 Correct answer.
  4. nRT

Explanation

For a reversible isothermal expansion, W = nRT ln(V₂/V₁) = nRT ln 2. Because the temperature is constant, the internal energy change is zero and the heat absorbed equals the work done.

Question 24Engineering

A galvanometer of resistance 50 Ω gives full-scale deflection at 1 mA. To convert it into a voltmeter reading up to 10 V, the series resistance required is:

  1. 9950 Ω Correct answer.
  2. 10050 Ω
  3. 10000 Ω
  4. 9500 Ω

Explanation

The full-scale voltage across the galvanometer is 1 mA × 50 Ω = 0.05 V, so the series resistor must drop 10 − 0.05 = 9.95 V at 1 mA, giving 9950 Ω. This is R = V/I_g − G.

Question 25Engineering

A BJT in common-emitter configuration has β = 100 and a base current of 20 μA. If the collector current is measured as 1.5 mA, the transistor is operating:

  1. With the emitter open
  2. In the active region at the expected current
  3. In saturation Correct answer.
  4. In cutoff

Explanation

The expected active-region collector current is βI_B = 100 × 20 μA = 2 mA, but only 1.5 mA flows, indicating the device is limited by the external circuit and is saturated. In saturation the collector current falls below βI_B.

Question 26Engineering

In a first-angle projection drawing, the view placed below the front view represents the:

  1. top view Correct answer.
  2. left side view
  3. bottom view
  4. right side view

Explanation

In first-angle projection the object is imagined between the observer and the plane, so the top view is projected onto the plane below the object and is drawn below the front view. The view above the front view in this system is the bottom view.

Question 27Engineering

The decimal number 45 is represented in binary as:

  1. 100111
  2. 101011
  3. 110101
  4. 101101 Correct answer.

Explanation

Repeated division by 2 gives remainders 1, 0, 1, 1, 0, 1 read upward, yielding 101101. Checking place values: 32 + 8 + 4 + 1 = 45.

Question 28Engineering

A simply supported beam of span L carries a central point load W. The maximum deflection, taking EI as constant, occurs at mid-span and equals:

  1. WL³/3EI
  2. 5WL⁴/384EI
  3. WL³/48EI Correct answer.
  4. WL³/192EI

Explanation

For a simply supported beam with a central point load, the standard deflection formula at mid-span is WL³/48EI. It follows from integrating the bending moment diagram with the boundary conditions of zero deflection at both supports.

Question 29Engineering

A Carnot engine operates between a source at 600 K and a sink at 300 K. Its thermal efficiency is:

  1. 25%
  2. 33%
  3. 67%
  4. 50% Correct answer.

Explanation

Carnot efficiency is 1 − T_sink/T_source using absolute temperatures, so 1 − 300/600 = 0.5, i.e. 50%. The result depends only on the two reservoir temperatures and not on the working substance.

Question 30Engineering

A single-phase transformer has an iron loss of 200 W and a full-load copper loss of 800 W. The load at which efficiency is maximum is:

  1. 25% of full load
  2. 100% of full load
  3. 75% of full load
  4. 50% of full load Correct answer.

Explanation

Maximum efficiency occurs when the variable copper loss equals the constant iron loss. Since copper loss varies with the square of the load fraction x, setting 800x² = 200 gives x = 0.5, so the load is 50% of full load.

Question 31Engineering

A 4-bit successive approximation ADC has a full-scale input of 10 V. The resolution of the converter is approximately:

  1. 0.667 V Correct answer.
  2. 1.000 V
  3. 2.500 V
  4. 0.625 V

Explanation

Resolution equals full-scale voltage divided by (2ⁿ − 1) for n bits, giving 10/(2⁴ − 1) = 10/15 ≈ 0.667 V. This is the smallest voltage step the converter can distinguish.

Question 32Engineering

In a closed traverse, the sum of the interior angles of a five-sided polygon should equal:

  1. 540° Correct answer.
  2. 450°
  3. 720°
  4. 360°

Explanation

The interior angles of an n-sided closed polygon sum to (2n − 4) right angles. For n = 5 this gives (10 − 4) × 90° = 540°, which is the check applied to the observed angles of the traverse.

Question 33Engineering

A soil sample has a void ratio of 0.60 and the specific gravity of its solids is 2.70. Its dry unit weight, taking the unit weight of water as 9.81 kN/m³, is approximately:

  1. 18.9 kN/m³
  2. 12.5 kN/m³
  3. 14.2 kN/m³
  4. 16.6 kN/m³ Correct answer.

Explanation

Dry unit weight equals G·γw/(1 + e). Substituting gives 2.70 × 9.81/(1.60) ≈ 16.6 kN/m³, which is typical for a medium-dense sandy soil.

Question 34Engineering

In a Pelton wheel, the runner is driven mainly by:

  1. the impulse of a high-velocity jet striking the buckets Correct answer.
  2. the reaction of water leaving a rotating runner
  3. the pressure difference across a draft tube
  4. the buoyant force of water in a volute casing

Explanation

A Pelton wheel is an impulse turbine: a high-head jet from a nozzle strikes double-cup buckets, and the change in momentum of the jet produces the driving force. Reaction turbines such as Francis and Kaplan rely on pressure changes across the runner.

Question 35Engineering

A steel rod of length 2 m and cross-sectional area 200 mm² is subjected to an axial tensile load of 40 kN. Taking Young's modulus as 200 GPa, the elongation of the rod is:

  1. 0.5 mm
  2. 2.0 mm Correct answer.
  3. 1.0 mm
  4. 4.0 mm

Explanation

Elongation equals PL/AE. Here P = 40 × 10³ N, L = 2 m, A = 200 × 10⁻⁶ m² and E = 200 × 10⁹ N/m², giving 80 × 10³/(40 × 10⁶) = 2 × 10⁻³ m, i.e. 2.0 mm.

Question 36Engineering

In a heat engine, the ratio of the brake thermal efficiency to the indicated thermal efficiency gives the:

  1. air-standard efficiency
  2. relative efficiency
  3. volumetric efficiency
  4. mechanical efficiency Correct answer.

Explanation

Brake power is the useful shaft output while indicated power is that developed inside the cylinder. Their ratio is the mechanical efficiency, and since brake thermal efficiency equals indicated thermal efficiency times mechanical efficiency, the same ratio follows directly.

Question 37Engineering

A simply supported beam of span 6 m carries a point load of 12 kN at 2 m from the left support. The reaction at the right support is:

  1. 4 kN Correct answer.
  2. 6 kN
  3. 8 kN
  4. 12 kN

Explanation

Taking moments about the left support: R_right × 6 = 12 × 2, so R_right = 4 kN. The remaining 8 kN is carried by the left support, and the two reactions correctly sum to the applied load.

Question 38Engineering

A 3-phase, 50 Hz, 4-pole induction motor runs at a slip of 4%. Its rotor speed is:

  1. 1440 rpm Correct answer.
  2. 1500 rpm
  3. 1380 rpm
  4. 1560 rpm

Explanation

Synchronous speed is 120f/P = 120 × 50/4 = 1500 rpm. Rotor speed equals Ns(1 − s) = 1500 × 0.96 = 1440 rpm, which is below synchronous speed as required for induction-motor action.

Question 39Engineering

A rectangular channel 4 m wide carries water at a depth of 1.5 m with a mean velocity of 2 m/s. Its Froude number is approximately, taking g = 9.81 m/s²:

  1. 1.20
  2. 0.75
  3. 0.52 Correct answer.
  4. 0.30

Explanation

The hydraulic depth is area divided by top width, i.e. (4 × 1.5)/4 = 1.5 m. Froude number is V/√(gD) = 2/√(9.81 × 1.5) ≈ 2/3.84 ≈ 0.52, so the flow is subcritical.

Question 40Engineering

A 3-phase load of 30 kW at a power factor of 0.6 lagging is to be corrected to 0.9 lagging. The reactive power rating of the capacitor bank required is approximately:

  1. 40.0 kVAR
  2. 10.5 kVAR
  3. 25.5 kVAR Correct answer.
  4. 15.0 kVAR

Explanation

Initial reactive power is 30 × tan(cos⁻¹0.6) = 30 × 1.333 = 40 kVAR, and the target is 30 × tan(cos⁻¹0.9) = 30 × 0.484 = 14.5 kVAR. The bank must supply the difference, about 25.5 kVAR.

Question 41Architecture

In architectural drawing practice, what does a scale of 1:100 on a plan mean?

  1. Each room is exactly 100 square metres
  2. The building is 100 times smaller than the drawing sheet
  3. One hundred drawings are required to show the whole building
  4. One unit on the drawing represents 100 of the same units on the building Correct answer.

Explanation

A ratio scale states the relationship between drawing length and real length in the same units, so 1:100 means every drawn unit equals 100 real units. It is a proportional statement, not a count of sheets or an area rule.

Question 42Architecture

Which drawing convention is standard for indicating a door swing on a floor plan?

  1. A quarter-circle arc showing the leaf path with the hinge point marked Correct answer.
  2. A solid filled rectangle across the opening
  3. A double line with an arrow pointing outward
  4. A dashed diagonal cross over the opening

Explanation

Door swings are shown by the leaf line plus an arc traced from the hinge, which communicates both the hinge side and the direction of opening. This convention lets a reader judge clearance and furniture layout directly from the plan.

Question 43Architecture

A load-bearing brick wall is best described by which structural behaviour?

  1. It carries vertical loads to the foundation through its own mass and thickness Correct answer.
  2. It carries loads only through tensile strength of the mortar
  3. It resists loads mainly by bending action like a beam
  4. It transfers all loads to a steel frame beside it

Explanation

Masonry is strong in compression, so load-bearing walls work by accumulating vertical load and passing it down through continuous wall thickness to the footing. Bending and tension are precisely the actions masonry handles poorly.

Question 44Architecture

In a warm-humid climate, which design measure most directly improves indoor comfort?

  1. Sealing the building tightly with small windows
  2. Using dark unshaded roofs to radiate heat
  3. Maximising cross-ventilation with large shaded openings Correct answer.
  4. Increasing thermal mass in external walls

Explanation

In warm-humid conditions the priority is moving air to promote evaporative cooling, so generous shaded openings on opposite sides create cross-ventilation. Shading prevents solar gain while still allowing airflow.

Question 45Architecture

Which element is classified as a building service rather than a building fabric element?

  1. The reinforced concrete slab
  2. The external cavity wall
  3. The drainage stack serving upper-floor sanitary fittings Correct answer.
  4. The roof truss

Explanation

Building services cover the systems that supply or remove water, air, power and waste, and a drainage stack belongs to that group. Walls, slabs and trusses are fabric or structure.

Question 46Architecture

What is the primary purpose of a setback line in urban building regulation?

  1. To define the maximum permitted plot coverage
  2. To reserve land exclusively for public parks
  3. To fix a minimum distance between the building line and the plot boundary Correct answer.
  4. To limit the total number of storeys in a zone

Explanation

A setback controls the distance a building must be kept back from the street or plot boundary, shaping light, air and frontage. It is a dimensional control on position, not on height or coverage alone.

Question 47Architecture

Which material is most commonly used for damp-proof course in masonry walls at plinth level?

  1. Glass wool
  2. Gypsum plaster
  3. Timber board
  4. Polythene sheet Correct answer.

Explanation

A damp-proof course must be impervious and durable, and polythene sheet is the standard choice at plinth level to stop rising damp. Porous or organic materials would either pass moisture or decay.

Question 48Architecture

On a site plan drawn at 1:500, a boundary measures 40 mm on paper. What is the real length?

  1. 8 m
  2. 200 m
  3. 20 m Correct answer.
  4. 2 m

Explanation

At 1:500 each drawn millimetre equals 500 mm, so 40 mm represents 40 × 500 mm = 20 000 mm, which is 20 m. Converting units carefully is the key step.

Question 49Architecture

In a reinforced concrete beam, why is steel placed near the tension face?

  1. Steel prevents shrinkage cracking only
  2. Steel reduces the self-weight of the concrete
  3. Steel resists compression while concrete carries tension
  4. Concrete is weak in tension and steel is provided to resist tensile stresses Correct answer.

Explanation

Concrete performs well in compression but cracks under modest tension, so reinforcement is positioned where tensile stress occurs to carry that force. The two materials thus complement each other in a composite section.

Question 50Architecture

Which staircase provision is required to satisfy basic safety in a public building?

  1. A single continuous flight of unlimited height
  2. Risers taller than treads
  3. Open risers without any nosing
  4. Handrails on both sides of the flight Correct answer.

Explanation

Handrails on both sides give support and guidance on a public stair, where users include the elderly and children. Balanced riser-tread proportions and intermediate landings also matter for safe ascent.