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PIEAS Test practice questions

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Question 1Engineering and Applied Sciences (BS admission test)

A block of mass 4 kg rests on a horizontal surface with coefficient of static friction 0.5. Taking g = 10 m/s², what is the minimum horizontal force needed to just start it moving?

  1. 40 N
  2. 20 N Correct answer.
  3. 10 N
  4. 2 N

Explanation

The limiting static friction equals μs times the normal force, and on a horizontal surface the normal force equals weight mg = 4 × 10 = 40 N. Thus f = 0.5 × 40 = 20 N, which is the minimum applied force to overcome it.

Question 2Engineering and Applied Sciences (BS admission test)

In a series RLC circuit at resonance, which statement about the impedance is correct?

  1. Impedance equals the resistance and is at its minimum Correct answer.
  2. Impedance equals the difference between inductive and capacitive reactance
  3. Impedance is maximum and equals the reactance
  4. Impedance is zero regardless of resistance

Explanation

At resonance the inductive and capacitive reactances are equal in magnitude and cancel, so the net reactance is zero. The impedance then reduces to the pure resistance R, which is the minimum possible value for the series circuit.

Question 3Engineering and Applied Sciences (BS admission test)

Which of the following best describes the function of a moderator in a thermal nuclear reactor?

  1. It absorbs excess neutrons to control the reaction rate
  2. It reflects escaping neutrons back into the core
  3. It slows fast neutrons to thermal energies without absorbing many of them Correct answer.
  4. It shields the reactor from gamma radiation

Explanation

A moderator such as water or graphite reduces neutron kinetic energy through elastic collisions so that fission becomes more probable in U-235. It must have low neutron absorption to avoid removing neutrons needed for the chain reaction.

Question 4Engineering and Applied Sciences (BS admission test)

A car accelerates uniformly from rest to 20 m/s in 5 s. How far does it travel during this time?

  1. 50 m Correct answer.
  2. 40 m
  3. 100 m
  4. 20 m

Explanation

For uniform acceleration starting from rest, distance equals average velocity times time. Average velocity is (0 + 20)/2 = 10 m/s, so distance = 10 × 5 = 50 m.

Question 5Engineering and Applied Sciences (BS admission test)

Which of the following is the primary reason steel is stronger than pure iron?

  1. Steel contains more dislocations that strengthen it directly
  2. Steel has a higher density than iron
  3. Carbon atoms in the lattice impede dislocation motion Correct answer.
  4. Carbon atoms increase the number of grain boundaries to zero

Explanation

Carbon dissolved in iron distorts the crystal lattice and pins dislocations, raising the stress needed for plastic flow. This interstitial solid-solution strengthening is the main reason steel is harder and stronger than pure iron.

Question 6Engineering and Applied Sciences (BS admission test)

For an ideal gas undergoing an isothermal expansion, which quantity remains constant?

  1. Pressure
  2. Entropy
  3. Volume
  4. Temperature Correct answer.

Explanation

Isothermal means the temperature is held constant by definition. During the expansion the pressure falls and volume rises while entropy increases, so only temperature is fixed.

Question 7Engineering and Applied Sciences (BS admission test)

A 2 μF and a 3 μF capacitor are connected in series across a 10 V supply. What is the charge on each capacitor?

  1. 50 μC
  2. 12 μC Correct answer.
  3. 20 μC
  4. 5 μC

Explanation

The equivalent capacitance of the series pair is (2×3)/(2+3) = 1.2 μF. Charge Q = CV = 1.2 μF × 10 V = 12 μC, and series capacitors carry the same charge.

Question 8Engineering and Applied Sciences (BS admission test)

In a binary search on a sorted array of 1024 elements, what is the maximum number of comparisons needed to locate a key?

  1. 512
  2. 10 Correct answer.
  3. 11
  4. 32

Explanation

Binary search halves the search space each step, so the number of steps is about log₂(n). Since 2¹⁰ = 1024, at most 10 comparisons are needed to reduce the range to a single element.

Question 9Engineering and Applied Sciences (BS admission test)

Which of the following statements about the photoelectric effect is correct?

  1. Emission depends mainly on the light intensity regardless of frequency
  2. Emission requires a minimum light intensity at any frequency
  3. Emitted electron energy decreases as frequency increases
  4. Emission occurs only if the incident light frequency exceeds a threshold value Correct answer.

Explanation

The photoelectric effect is governed by photon energy hf, which must exceed the work function for electrons to escape. Below the threshold frequency no emission occurs no matter how intense the light is.

Question 10Engineering and Applied Sciences (BS admission test)

What is the oxidation state of chromium in the dichromate ion, Cr₂O₇²⁻?

  1. +7
  2. +6 Correct answer.
  3. +3
  4. +2

Explanation

Oxygen is normally −2, so seven oxygens contribute −14. The ion carries −2 overall, so 2x − 14 = −2, giving x = +6 for each chromium.

Question 11Engineering and Applied Sciences (BS admission test)

The pH of a 0.01 M solution of a strong monoprotic acid is:

  1. 1
  2. 0.01
  3. 12
  4. 2 Correct answer.

Explanation

A strong acid dissociates completely, so [H⁺] equals the acid concentration, 0.01 M = 10⁻² M. pH = −log(10⁻²) = 2.

Question 12Engineering and Applied Sciences (BS admission test)

In the periodic table, which trend correctly describes atomic radius across a period from left to right?

  1. It increases because more shells are added
  2. It remains constant because protons and electrons increase equally
  3. It decreases because atomic mass decreases
  4. It decreases because effective nuclear charge increases Correct answer.

Explanation

Across a period, protons are added while electrons enter the same shell, so effective nuclear charge rises and pulls electrons closer. This contraction makes the atomic radius decrease from left to right.

Question 13Engineering and Applied Sciences (BS admission test)

Which type of chemical bond results from the electrostatic attraction between oppositely charged ions?

  1. Ionic bond Correct answer.
  2. Metallic bond
  3. Hydrogen bond
  4. Covalent bond

Explanation

An ionic bond forms when one atom transfers electrons to another, creating cations and anions held together by electrostatic attraction. Covalent and metallic bonds involve shared or delocalized electrons instead.

Question 14Engineering and Applied Sciences (BS admission test)

A projectile is launched at 30° to the horizontal with speed 20 m/s. Taking g = 10 m/s², what is its maximum height?

  1. 5 m Correct answer.
  2. 15 m
  3. 20 m
  4. 10 m

Explanation

The vertical component of velocity is 20 sin30° = 10 m/s. Maximum height equals v_y²/(2g) = 100/20 = 5 m.

Question 15Engineering and Applied Sciences (BS admission test)

Which of the following statements about an ideal operational amplifier in a negative-feedback configuration is correct?

  1. Its output saturates whenever feedback is applied
  2. Its input impedance is zero and output impedance is infinite
  3. The voltage difference between its two inputs is driven to nearly zero Correct answer.
  4. Its input current is very large and its gain is infinite at all frequencies

Explanation

With negative feedback and very high open-loop gain, the amplifier adjusts its output so the differential input voltage approaches zero. This is the basis of the virtual-short concept used in op-amp analysis.

Question 16Engineering and Applied Sciences (BS admission test)

A simply supported beam of length L carries a point load at its midspan. Where does the maximum bending moment occur?

  1. At the quarter points
  2. Uniformly along the entire beam
  3. At midspan under the load Correct answer.
  4. At the supports

Explanation

For a central point load on a simply supported beam, the bending moment diagram is triangular, peaking at the load. The maximum value is PL/4 at midspan, while it is zero at the supports.

Question 17Engineering and Applied Sciences (BS admission test)

In a DC shunt motor, what happens to the speed if the field flux is reduced while the armature voltage is held constant?

  1. The speed increases Correct answer.
  2. The speed decreases
  3. The speed stays the same
  4. The motor stops immediately

Explanation

For a DC motor, back-emf E = V − I_a R_a and E is proportional to flux times speed. If flux drops at constant terminal voltage, the speed must rise to maintain the required back-emf.

Question 18Engineering and Applied Sciences (BS admission test)

Which of the following is the correct SI unit of the rate of heat transfer?

  1. Joule
  2. Pascal
  3. Newton
  4. Watt Correct answer.

Explanation

Rate of heat transfer is energy per unit time, and one joule per second is defined as one watt. Joule is energy, while newton and pascal measure force and pressure.

Question 19Engineering and Applied Sciences (BS admission test)

The efficiency of a Carnot engine operating between 600 K and 300 K is:

  1. 50% Correct answer.
  2. 25%
  3. 33%
  4. 100%

Explanation

Carnot efficiency equals 1 − T_cold/T_hot using absolute temperatures. Here 1 − 300/600 = 0.5, so the efficiency is 50%.

Question 20Engineering and Applied Sciences (BS admission test)

A logic circuit implements the function Y = A·B + A·B̄. Which simplified expression is equivalent?

  1. A + B
  2. B
  3. A·B
  4. A Correct answer.

Explanation

Factoring gives A(B + B̄), and since B + B̄ = 1, the expression reduces to A. This is a direct application of the Boolean identity X + X̄ = 1.

Question 21Engineering and Applied Sciences (BS admission test)

Which of the following best explains why a transformer cannot operate on a steady direct current?

  1. DC causes the core to become permanently magnetic and block flux
  2. DC produces a higher frequency than AC and saturates the core
  3. DC creates excessive capacitive coupling between windings
  4. A constant primary current produces no changing magnetic flux to induce a secondary emf Correct answer.

Explanation

Transformer action relies on Faraday's law, requiring a changing magnetic flux to induce voltage. A steady DC primary current creates a constant flux, so no emf is induced in the secondary.

Question 22Engineering and Applied Sciences (BS admission test)

In a heat exchanger, the logarithmic mean temperature difference (LMTD) is used because:

  1. The temperature difference between the fluids varies along the exchanger length Correct answer.
  2. The fluids always flow in parallel
  3. The overall heat transfer coefficient is always constant
  4. It converts heat transfer into a dimensionless quantity

Explanation

In most heat exchangers the hot and cold stream temperatures change along the flow path, so the local temperature difference is not constant. The LMTD provides the correct average driving force for use in Q = U·A·LMTD.

Question 23Engineering and Applied Sciences (BS admission test)

Which of the following is the principal reason for adding a small amount of a solute to depress the freezing point of a solvent?

  1. The solute increases the vapor pressure of the solvent at all temperatures
  2. The solute raises the melting point of the pure solid
  3. The solute lowers the chemical potential of the liquid phase, requiring a lower temperature to freeze Correct answer.
  4. The solute reacts chemically with the solid to dissolve it

Explanation

Dissolved particles lower the chemical potential of the liquid solvent, so the liquid and solid become equal in potential only at a lower temperature. This is the colligative freezing-point depression described by ΔT = K_f·m.

Question 24Engineering and Applied Sciences (BS admission test)

A 3-phase induction motor has a synchronous speed of 1500 rpm and runs at 1440 rpm. What is its slip?

  1. 0.4%
  2. 6%
  3. 4% Correct answer.
  4. 96%

Explanation

Slip equals (synchronous speed − rotor speed) divided by synchronous speed. Here (1500 − 1440)/1500 = 60/1500 = 0.04, which is 4%.

Question 25Engineering and Applied Sciences (BS admission test)

Which of the following statements about the stress–strain curve of a ductile metal is correct?

  1. The ultimate tensile strength is the stress at which elastic deformation begins
  2. Fracture occurs at the proportional limit
  3. The elastic region extends beyond the ultimate tensile strength
  4. The yield point marks the onset of permanent plastic deformation Correct answer.

Explanation

Up to the yield point the material deforms elastically and returns to its original shape. Beyond it, plastic deformation becomes permanent, so the yield point is the practical limit of elastic behavior.

Question 26Engineering and Applied Sciences (BS admission test)

A steel rod of original length 2.0 m is heated through 50 K. Taking the coefficient of linear expansion as 12 × 10⁻⁶ K⁻¹, what is the increase in length?

  1. 1.2 mm Correct answer.
  2. 0.6 mm
  3. 12 mm
  4. 2.4 mm

Explanation

Thermal expansion of a solid is given by ΔL = L₀αΔT, so the increase equals 2.0 × 12 × 10⁻⁶ × 50 = 1.2 × 10⁻³ m, that is 1.2 mm. The coefficient applies to linear dimension only, so the full length must be multiplied once.

Question 27Engineering and Applied Sciences (BS admission test)

In a BJT configured as a common-emitter amplifier, the collector current is 4 mA and the base current is 40 μA. What is the DC current gain β?

  1. 160
  2. 10
  3. 0.01
  4. 100 Correct answer.

Explanation

The common-emitter current gain is the ratio of collector current to base current, β = I_C/I_B. Substituting 4 mA ÷ 40 μA = 100 gives the gain directly.

Question 28Engineering and Applied Sciences (BS admission test)

Which statement correctly describes the function of a moderator in a thermal nuclear reactor?

  1. It slows fast neutrons to thermal energies without capturing many of them. Correct answer.
  2. It cools the fuel rods by transferring heat to the working fluid.
  3. It absorbs excess neutrons to control the chain reaction.
  4. It shields personnel from gamma radiation emitted in fission.

Explanation

A moderator such as light water, heavy water, or graphite reduces neutron kinetic energy through elastic scattering until neutrons reach thermal energies where fission cross-sections are large. It must have low absorption cross-section so that the neutron population is not depleted.

Question 29Engineering and Applied Sciences (BS admission test)

Which of the following quantities is a scalar in classical mechanics?

  1. Electric potential energy Correct answer.
  2. Torque
  3. Linear momentum
  4. Angular velocity

Explanation

Energy is described by magnitude alone and adds algebraically, so it is a scalar. Torque, momentum, and angular velocity all carry direction information and combine by vector addition.

Question 30Engineering and Applied Sciences (BS admission test)

Which class of engineering material is characterised by a large elastic strain range and an approximately constant stress over a long plateau during tensile loading?

  1. Elastomer Correct answer.
  2. Ceramic
  3. Cast iron
  4. Thermosetting polymer

Explanation

Elastomers such as natural rubber extend elastically to very large strains and then show a long rubbery plateau before failure. Ceramics are brittle with almost no ductility, and cast iron shows limited elastic strain followed by brittle fracture.

Question 31Engineering and Applied Sciences (BS admission test)

In a hydroelectric plant, water falls through a net head of 50 m at a flow rate of 10 m³/s. Taking g = 10 m/s² and water density 1000 kg/m³, what is the hydraulic power available?

  1. 50 MW
  2. 0.5 MW
  3. 0.05 MW
  4. 5.0 MW Correct answer.

Explanation

Hydraulic power equals ρgQH, so 1000 × 10 × 10 × 50 = 5 × 10⁶ W, which is 5.0 MW. The density converts volumetric flow to mass flow before multiplying by head and gravity.

Question 32Engineering and Applied Sciences (BS admission test)

Which of the following statements about the second law of thermodynamics is correct?

  1. Entropy is conserved in every irreversible process.
  2. Heat can flow spontaneously from a colder body to a hotter body.
  3. The efficiency of any heat engine can reach 100 percent.
  4. The entropy of an isolated system never decreases. Correct answer.

Explanation

For an isolated system the entropy change is zero for reversible processes and positive for irreversible ones, so it never decreases. This is the Clausius statement of the second law and limits the performance of all real engines.

Question 33Engineering and Applied Sciences (BS admission test)

Which of the following is the correct SI unit of magnetic flux density?

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

Explanation

Magnetic flux density B is measured in tesla, where one tesla equals one weber per square metre. It can also be expressed as a newton per ampere-metre.

Question 34Engineering and Applied Sciences (BS admission test)

A 3-phase, 50 Hz induction motor has 4 poles. What is its synchronous speed?

  1. 750 rpm
  2. 1500 rpm Correct answer.
  3. 1000 rpm
  4. 3000 rpm

Explanation

Synchronous speed is N_s = 120f/P, so 120 × 50 ÷ 4 = 1500 rpm. The factor 120 accounts for the conversion from cycles per second to revolutions per minute and the pole-pair relationship.

Question 35Engineering and Applied Sciences (BS admission test)

In a first-order linear ordinary differential equation of the form dy/dx + Py = Q, what is the integrating factor?

  1. e raised to the integral of Q dx
  2. P multiplied by Q
  3. The integral of P dx
  4. e raised to the integral of P dx Correct answer.

Explanation

Multiplying through by μ = exp(∫P dx) makes the left side an exact derivative of μy, allowing direct integration. The factor depends only on the coefficient P, not on the forcing term Q.

Question 36Engineering and Applied Sciences (BS admission test)

A simply supported beam of length 4 m carries a uniformly distributed load of 10 kN/m over its entire span. What is the maximum bending moment?

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

Explanation

For a uniformly distributed load w over span L on simple supports, the maximum moment at midspan is wL²/8. Substituting gives 10 × 16 ÷ 8 = 20 kN·m.

Question 37Engineering and Applied Sciences (BS admission test)

A 10 kΩ resistor and a 10 kΩ resistor are connected in parallel across a 10 V source. What power is dissipated in each resistor?

  1. 20 mW
  2. 100 mW
  3. 5 mW
  4. 10 mW Correct answer.

Explanation

In parallel each resistor sees the full 10 V, so the power in one resistor is V²/R = 100 ÷ 10 000 = 0.01 W, that is 10 mW. The parallel connection does not divide the voltage between branches.

Question 38Engineering and Applied Sciences (BS admission test)

A gas undergoes an adiabatic throttling process through a porous plug. Which statement about an ideal gas is correct?

  1. Its entropy decreases because the process is adiabatic.
  2. Its temperature rises because the pressure drop adds internal energy.
  3. Its temperature stays unchanged because enthalpy depends only on temperature. Correct answer.
  4. Its temperature falls because work is done against the plug.

Explanation

Throttling is isenthalpic, and for an ideal gas enthalpy is a function of temperature alone, so no temperature change occurs. The Joule–Thomson coefficient of an ideal gas is zero.

Question 39Engineering and Applied Sciences (BS admission test)

A 0.5 kg block sliding on a frictionless horizontal surface at 4 m/s compresses a spring of stiffness 200 N/m. What is the maximum compression?

  1. 0.04 m
  2. 0.20 m Correct answer.
  3. 0.40 m
  4. 0.10 m

Explanation

Equating kinetic energy to elastic potential energy gives ½mv² = ½kx², so x = v√(m/k) = 4 × √(0.5/200) = 0.20 m. Energy is conserved because the surface is frictionless.

Question 40Engineering and Applied Sciences (BS admission test)

Which of the following best explains why a PN junction diode conducts appreciably only in forward bias?

  1. Reverse bias injects minority carriers that recombine in the depletion region.
  2. The junction behaves as an insulator in both directions until breakdown.
  3. Forward bias lowers the potential barrier, allowing majority carriers to diffuse across. Correct answer.
  4. Forward bias increases the depletion width and strengthens the built-in field.

Explanation

In forward bias the applied voltage opposes the built-in potential, narrowing the depletion region and reducing the barrier so that majority carriers can cross. In reverse bias the barrier grows and only a small leakage current flows.

Question 41Engineering and Applied Sciences (BS admission test)

A binary number 1101₂ is to be converted to decimal. What is its value?

  1. 15
  2. 13 Correct answer.
  3. 14
  4. 11

Explanation

Expanding powers of two gives 1×8 + 1×4 + 0×2 + 1×1 = 13. Each bit position carries a weight of two raised to its index from the right, starting at zero.

Question 42Engineering and Applied Sciences (BS admission test)

In a counter-flow heat exchanger, the hot stream enters at 150 °C and leaves at 90 °C, while the cold stream enters at 30 °C and leaves at 70 °C. What is the appropriate temperature difference for sizing?

  1. The larger terminal difference of 80 K
  2. The logarithmic mean of 80 K and 60 K Correct answer.
  3. The smaller terminal difference of 60 K
  4. The arithmetic mean of 80 K and 60 K

Explanation

For counter-flow arrangements the driving force varies along the exchanger, so the logarithmic mean temperature difference of the two terminal differences (80 K and 60 K) is used. The arithmetic mean overestimates the driving force and would undersize the area.

Question 43Engineering and Applied Sciences (BS admission test)

A solution contains 0.10 mol of acetic acid and 0.10 mol of sodium acetate in 1.0 L. Taking pKa of acetic acid as 4.76, what is the pH?

  1. 4.76 Correct answer.
  2. 2.38
  3. 9.24
  4. 7.00

Explanation

The buffer equation pH = pKa + log([A⁻]/[HA]) applies, and equal concentrations of acid and conjugate base make the logarithm zero. The pH therefore equals the pKa, 4.76.

Question 44Engineering and Applied Sciences (BS admission test)

Which statement about a strain gauge bonded to a loaded member is correct?

  1. Its resistance changes in proportion to the strain through the gauge factor. Correct answer.
  2. It measures displacement directly without any bridge circuit.
  3. Its output is independent of temperature when bonded with adhesive.
  4. Its resistance changes in proportion to the applied stress directly.

Explanation

A metallic strain gauge changes resistance according to ΔR/R = G·ε, where G is the gauge factor and ε the strain. Stress is inferred only after applying the material's modulus.

Question 45Engineering and Applied Sciences (BS admission test)

A 16-bit successive-approximation ADC has a full-scale input of 5 V. What is the approximate resolution?

  1. 1.2 mV
  2. 38 μV
  3. 305 μV
  4. 76 μV Correct answer.

Explanation

Resolution equals full-scale voltage divided by 2¹⁶, that is 5 ÷ 65 536 ≈ 76 μV. The number of levels, not the bit count itself, sets the step size.

Question 46Engineering and Applied Sciences (BS admission test)

A closed-loop control system has a forward path gain of 10 and a negative feedback path gain of 0.1. What is the closed-loop gain?

  1. 1.1
  2. 5 Correct answer.
  3. 100
  4. 10

Explanation

For negative feedback the closed-loop gain is G/(1 + GH), giving 10 ÷ (1 + 1) = 5. The feedback reduces the gain from the open-loop value of 10.

Question 47Engineering and Applied Sciences (BS admission test)

A particle moves in a circle of radius 2 m at a constant speed of 6 m/s. What is the magnitude of its centripetal acceleration?

  1. 12 m/s²
  2. 36 m/s²
  3. 18 m/s² Correct answer.
  4. 3 m/s²

Explanation

Centripetal acceleration is v²/r, so 36 ÷ 2 = 18 m/s². It points towards the centre and changes the direction of velocity without altering its magnitude.

Question 48Engineering and Applied Sciences (BS admission test)

A 3-phase star-connected load has a per-phase impedance of 10 Ω and is supplied at 400 V line-to-line. What is the phase current?

  1. 13.3 A
  2. 23.1 A Correct answer.
  3. 69.3 A
  4. 40 A

Explanation

In a star connection the phase voltage is the line voltage divided by √3, giving 231 V, and the phase current is 231 ÷ 10 ≈ 23.1 A. The line current equals the phase current in star.

Question 49Engineering and Applied Sciences (BS admission test)

Which statement about fatigue failure in metals is correct?

  1. Fatigue strength is independent of surface finish and stress concentration.
  2. Failure can occur at stresses below the yield strength after many load cycles. Correct answer.
  3. Fatigue cracks always initiate at the centre of the cross section.
  4. A fatigue limit means the material never fails under cyclic loading of any amplitude.

Explanation

Fatigue is progressive damage from repeated loading, and cracks nucleate at stress raisers, so failure can happen below the monotonic yield stress. Surface condition and notches strongly influence fatigue life.

Question 50Engineering and Applied Sciences (BS admission test)

A 2 kg object moving at 3 m/s collides head-on with a stationary 4 kg object and they stick together. What is the kinetic energy lost in the collision?

  1. 3 J
  2. 9 J
  3. 6 J Correct answer.
  4. 12 J

Explanation

Momentum conservation gives a common velocity of 6 ÷ 6 = 1 m/s, so the final kinetic energy is ½ × 6 × 1² = 3 J against an initial 9 J, a loss of 6 J. A perfectly inelastic collision dissipates energy while conserving momentum.