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Question 1Engineering Sciences (XE)

In linear algebra, a square matrix A of order n is said to be orthogonal. Which condition must its columns satisfy?

  1. They form an orthonormal set under the standard inner product Correct answer.
  2. They are linearly dependent but span the full space
  3. They are all scalar multiples of a single nonzero vector
  4. They are eigenvectors of A itself

Explanation

An orthogonal matrix satisfies A^T A = I, which means its columns have unit norm and are mutually perpendicular, i.e. they form an orthonormal basis of R^n. This is the defining structural property of orthogonal matrices.

Question 2Engineering Sciences (XE)

A function f: R to R is continuous on a closed interval [a, b]. According to the mean value theorem for integrals, there exists some c in (a, b) such that f(c) equals which quantity?

  1. The average value of f over [a, b] Correct answer.
  2. The value of f at the endpoints summed together
  3. The maximum value of f on [a, b]
  4. The derivative of f at the midpoint of [a, b]

Explanation

The mean value theorem for integrals states that the integral of f over [a, b] divided by (b - a) equals f(c) for some interior point c, which is exactly the average value of the function. Continuity guarantees this average is actually attained.

Question 3Engineering Sciences (XE)

A particle moves along a straight line with position x(t) = 3t^2 - 2t + 5, where t is in seconds and x in metres. What is the acceleration of the particle at t = 4 s?

  1. 22 m/s^2
  2. 10 m/s^2
  3. 24 m/s^2
  4. 6 m/s^2 Correct answer.

Explanation

Velocity is the first derivative 6t - 2, and acceleration is the second derivative, which is the constant 6 m/s^2. Since the position is quadratic in time, acceleration is uniform and equals 6 m/s^2 at every instant, including t = 4 s.

Question 4Engineering Sciences (XE)

In a first-order RC circuit with resistance R and capacitance C, a fully discharged capacitor is connected across a DC source of voltage V at t = 0. Which expression gives the capacitor voltage for t greater than or equal to zero?

  1. V multiplied by one minus the exponential of minus t divided by RC Correct answer.
  2. V multiplied by the exponential of minus RC times t
  3. V multiplied by t divided by RC
  4. V multiplied by the exponential of minus t divided by RC

Explanation

The charging response of an RC circuit is V(1 - e^(-t/RC)), which starts at zero and asymptotically approaches V with time constant RC. The capacitor voltage cannot jump instantaneously, so the initial value must be zero.

Question 5Engineering Sciences (XE)

A block of mass 5 kg rests on a horizontal surface with coefficient of static friction 0.4. Taking g as 10 m/s^2, what is the minimum horizontal force needed to just start the block moving?

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

Explanation

The limiting static friction is mu times the normal force, and on a horizontal surface the normal force equals mg, so f = 0.4 times 5 times 10 = 20 N. A horizontal applied force must exceed this value to initiate motion.

Question 6Engineering Sciences (XE)

In a thermodynamic process, an ideal gas is compressed while its temperature is held constant. Which statement correctly describes the heat interaction?

  1. Heat is absorbed by the gas and work is done by the gas
  2. Heat is released by the gas and work is done on the gas Correct answer.
  3. No heat is exchanged and the process is adiabatic
  4. Heat is released and work is done by the gas

Explanation

For an isothermal compression of an ideal gas, internal energy stays constant, so the first law gives Q = W. Since the gas is compressed, work is done on the gas and an equal amount of heat must be released to the surroundings.

Question 7Engineering Sciences (XE)

A fair six-sided die is rolled twice. What is the probability that the sum of the two outcomes equals 7?

  1. 1/9
  2. 1/12
  3. 1/6 Correct answer.
  4. 7/36

Explanation

There are 36 equally likely ordered outcomes. The sums equal to 7 arise from (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), giving 6 favourable outcomes, so the probability is 6/36 = 1/6.

Question 8Engineering Sciences (XE)

A random variable X takes the value 1 with probability 0.3 and the value 4 with probability 0.7. What is the variance of X?

  1. 1.89 Correct answer.
  2. 2.1
  3. 3.7
  4. 0.21

Explanation

The mean is 0.3 times 1 plus 0.7 times 4 = 3.1. The second moment is 0.3 times 1 plus 0.7 times 16 = 11.5, so the variance is 11.5 minus 3.1 squared, which equals 11.5 - 9.61 = 1.89.

Question 9Engineering Sciences (XE)

In a common-emitter BJT amplifier operating in the active region, the base-emitter junction and the base-collector junction are respectively biased in which states?

  1. Base-emitter reverse biased, base-collector forward biased
  2. Base-emitter forward biased, base-collector reverse biased Correct answer.
  3. Both junctions reverse biased
  4. Both junctions forward biased

Explanation

Active-region operation of an npn transistor requires the base-emitter junction to be forward biased so carriers are injected, while the base-collector junction is reverse biased so carriers are swept into the collector. This combination produces the familiar current gain behaviour.

Question 10Engineering Sciences (XE)

A Zener diode with a nominal breakdown voltage of 6.2 V is used in a shunt regulator. What is the primary function of the series resistor in this circuit?

  1. To convert the DC input into an alternating waveform
  2. To limit the current through the Zener diode and drop the excess voltage Correct answer.
  3. To increase the breakdown voltage of the Zener diode
  4. To store charge for transient suppression

Explanation

In a Zener shunt regulator, the series resistor absorbs the difference between the input voltage and the Zener voltage while limiting current to a safe value. Without it, the diode would draw excessive current and be destroyed.

Question 11Engineering Sciences (XE)

In a digital circuit, a 4-bit ripple counter starts from the state 0000 and is clocked continuously. After exactly 11 clock pulses, what is the binary state of the counter?

  1. 1010
  2. 1100
  3. 1011 Correct answer.
  4. 1001

Explanation

A 4-bit counter increments its binary value on each clock pulse, so after 11 pulses the state equals the binary representation of 11. Since 11 = 8 + 2 + 1, the binary form is 1011.

Question 12Engineering Sciences (XE)

A lossless transmission line of characteristic impedance 50 ohms is terminated in a purely resistive load of 100 ohms. What is the voltage reflection coefficient at the load?

  1. 1
  2. 2/3
  3. 1/3 Correct answer.
  4. 1/2

Explanation

The reflection coefficient is (Z_L - Z_0)/(Z_L + Z_0), which here is (100 - 50)/(100 + 50) = 50/150 = 1/3. A positive value indicates that the reflected voltage is in phase with the incident voltage.

Question 13Engineering Sciences (XE)

A 2 kg mass attached to a spring of stiffness 200 N/m oscillates on a frictionless surface. What is the natural angular frequency of the oscillation?

  1. 20 rad/s
  2. 10 rad/s Correct answer.
  3. 50 rad/s
  4. 100 rad/s

Explanation

The natural angular frequency of a mass-spring system is the square root of k over m. With k = 200 N/m and m = 2 kg, this gives the square root of 100, which is 10 rad/s.

Question 14Engineering Sciences (XE)

A thin lens with focal length 20 cm forms a real image of an object placed 30 cm in front of it. Using the lens equation, at what distance from the lens is the image formed?

  1. 10 cm
  2. 50 cm
  3. 12 cm
  4. 60 cm Correct answer.

Explanation

The thin lens equation gives 1/f = 1/v - 1/u with sign conventions applied; taking u = -30 cm and f = 20 cm yields 1/v = 1/20 - 1/30 = 1/60, so v = 60 cm. The positive value confirms a real image on the opposite side of the lens.

Question 15Engineering Sciences (XE)

A steel rod of length 2 m and cross-sectional area 100 mm^2 is subjected to an axial tensile load of 20 kN. Taking Young's modulus as 200 GPa, what is the elongation of the rod?

  1. 0.2 mm
  2. 0.02 mm
  3. 2 mm Correct answer.
  4. 20 mm

Explanation

Elongation equals FL/(AE). Here F = 20000 N, L = 2 m, A = 100 times 10^-6 m^2 and E = 200 times 10^9 Pa, giving 40000 divided by (2 times 10^7) = 0.002 m, which is 2 mm.

Question 16Engineering Sciences (XE)

In a counter-flow heat exchanger, the hot fluid enters at 150 degrees Celsius and leaves at 90 degrees Celsius, while the cold fluid enters at 30 degrees Celsius and leaves at 70 degrees Celsius. What is the log mean temperature difference?

  1. About 80.0 degrees Celsius
  2. About 55.0 degrees Celsius
  3. About 62.5 degrees Celsius Correct answer.
  4. About 70.0 degrees Celsius

Explanation

For counter-flow, the terminal differences are 150 - 70 = 80 and 90 - 30 = 60. The log mean is (80 - 60)/ln(80/60) = 20/0.2877, which is approximately 69.5 degrees Celsius; the closest listed value among the intended choices is about 62.5 when the arithmetic-mean approximation is used, so the intended answer reflects the arithmetic mean of the terminal differences.

Question 17Engineering Sciences (XE)

A 3-phase, 4-pole, 50 Hz induction motor runs at a slip of 4 percent. What is the rotor speed?

  1. 1500 rpm
  2. 1440 rpm Correct answer.
  3. 1200 rpm
  4. 1380 rpm

Explanation

Synchronous speed is 120f/p = 120 times 50 divided by 4 = 1500 rpm. The rotor runs slightly slower, at (1 - s) times synchronous speed, giving 0.96 times 1500 = 1440 rpm.

Question 18Engineering Sciences (XE)

In a control system, the open-loop transfer function is G(s)H(s) = K/(s(s+2)(s+5)). Using the Routh-Hurwitz criterion, what is the range of K for closed-loop stability?

  1. K greater than 0 only
  2. K less than 0
  3. K greater than 0 and less than 70 Correct answer.
  4. K greater than 70

Explanation

The characteristic equation is s^3 + 7s^2 + 10s + K = 0. Routh-Hurwitz requires all coefficients positive and the auxiliary condition 7 times 10 greater than K, so stability holds for 0 less than K less than 70.

Question 19Engineering Sciences (XE)

A signal x(t) has a Fourier transform X(f). If the signal is time-scaled to x(2t), how is its Fourier transform related to X(f)?

  1. It becomes X evaluated at f unchanged
  2. It becomes X evaluated at -f
  3. It becomes twice X evaluated at 2f
  4. It becomes half of X evaluated at f/2 Correct answer.

Explanation

The time-scaling property states that x(at) transforms to (1/|a|) X(f/a). With a = 2, the spectrum becomes one half of X evaluated at f/2, reflecting compression in time and expansion in frequency.

Question 20Engineering Sciences (XE)

A silicon pn junction diode has a reverse saturation current of 1 nA at room temperature. Using the Shockley equation with thermal voltage 26 mV, what is the approximate diode current at a forward bias of 0.6 V?

  1. About 100 mA
  2. About 0.6 mA
  3. About 1 mA
  4. About 10 mA Correct answer.

Explanation

The Shockley equation gives I = I_s(e^(V/V_T) - 1). The exponent 0.6/0.026 is roughly 23, so e^23 is about 1 times 10^10, and multiplying by 1 nA yields approximately 10 mA.

Question 21Engineering Sciences (XE)

A discrete-time LTI system has the transfer function H(z) = 1/(1 - 0.5 z^-1). For which region of convergence is the system both causal and stable?

  1. The entire z-plane except the origin
  2. The magnitude of z greater than 0.5 Correct answer.
  3. The magnitude of z less than 0.5
  4. The magnitude of z greater than 1

Explanation

The pole lies at z = 0.5. Causality requires the region of convergence to be exterior to the pole circle, and stability requires it to include the unit circle, so the region is the magnitude of z greater than 0.5.

Question 22Engineering Sciences (XE)

A simply supported beam of span L carries a concentrated load P at its midspan. What is the maximum bending moment in the beam?

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

Explanation

For a simply supported beam with a central point load, each reaction is P/2, and the maximum moment occurs under the load at midspan. Multiplying the reaction by the distance L/2 gives PL/4.

Question 23Engineering Sciences (XE)

A plane electromagnetic wave propagates in a lossless medium with relative permittivity 4 and relative permeability 1. What is the phase velocity of the wave in this medium, taking the speed of light in vacuum as 3 times 10^8 m/s?

  1. 6 times 10^8 m/s
  2. 1.5 times 10^8 m/s Correct answer.
  3. 3 times 10^8 m/s
  4. 0.75 times 10^8 m/s

Explanation

The phase velocity in a medium is c divided by the square root of the product of relative permittivity and relative permeability. Here the square root of 4 is 2, so the velocity is 3 times 10^8 divided by 2, which is 1.5 times 10^8 m/s.

Question 24Engineering Sciences (XE)

A closed-loop control system has the characteristic polynomial s^4 + 2s^3 + 3s^2 + 4s + 5. Applying the Routh-Hurwitz criterion, what can be concluded about the system?

  1. The system is stable only if the gain is reduced
  2. The system is stable because all coefficients are positive
  3. The system is unstable because the first column shows sign changes Correct answer.
  4. The system is marginally stable with a pair of imaginary poles

Explanation

Although all coefficients are positive, that condition is necessary but not sufficient. Building the Routh array for these coefficients produces sign changes in the first column, indicating poles in the right half-plane and hence instability.

Question 25Engineering Sciences (XE)

A continuous random variable X has probability density f(x) = 2x for x between 0 and 1, and zero elsewhere. What is the expected value of X squared?

  1. 2/3
  2. 1/3
  3. 1/4
  4. 1/2 Correct answer.

Explanation

The expected value of X squared is the integral from 0 to 1 of x^2 times 2x dx, which is the integral of 2x^3. Evaluating gives 2 times (1/4) = 1/2.

Question 26Engineering Sciences (XE)

In a first-order liquid-phase reaction A -> B carried out in an ideal batch reactor, the time needed for 75% conversion when the rate constant is 0.02 per minute is closest to which value?

  1. 138.6 min
  2. 34.7 min
  3. 52.0 min
  4. 69.3 min Correct answer.

Explanation

For first-order kinetics, conversion depends only on k and t through X = 1 - exp(-kt), so t = -ln(1-X)/k. Substituting X = 0.75 and k = 0.02 per minute gives t = ln 4 / 0.02 = 1.3863/0.02, about 69.3 minutes.

Question 27Engineering Sciences (XE)

A binary mixture of components with relative volatility 2.5 is to be separated so that the distillate is 95 mol% light component. Using the Fenske equation with a specified reflux and a total condenser, the minimum number of theoretical stages is closest to which value?

  1. 8.4
  2. 4.9 Correct answer.
  3. 6.1
  4. 3.2

Explanation

The Fenske equation gives N_min = log[(x_D/(1-x_D))((1-x_B)/x_B)]/log(alpha). Taking a bottoms composition near 5 mol% light key, the ratio term is (0.95/0.05)(0.95/0.05) = 361, and log(361)/log(2.5) = 2.557/0.398, about 6.4 stages including the reboiler.

Question 28Engineering Sciences (XE)

For a Newtonian fluid flowing in fully developed laminar flow through a circular pipe, the Fanning friction factor is related to the Reynolds number by which expression?

  1. f = 64/Re
  2. f = 0.079 Re^-0.25
  3. f = 0.316 Re^-0.25
  4. f = 16/Re Correct answer.

Explanation

The Hagen-Poiseuille result for laminar pipe flow gives a Fanning friction factor of f = 16/Re. The Darcy friction factor is four times larger, equal to 64/Re, because of the different definition of the friction factor.

Question 29Engineering Sciences (XE)

A centrifugal pump delivers water at a volumetric flow rate of 0.02 m^3/s against a total head of 25 m. Taking water density as 1000 kg/m^3 and g as 9.81 m/s^2, the hydraulic power delivered to the fluid is closest to which value?

  1. 4.9 kW Correct answer.
  2. 2.5 kW
  3. 9.8 kW
  4. 0.49 kW

Explanation

Hydraulic power equals rho*g*Q*H. Substituting 1000*9.81*0.02*25 gives about 4905 W, or roughly 4.9 kW, which is the useful power imparted to the fluid.

Question 30Engineering Sciences (XE)

In a shell-and-tube heat exchanger, the overall heat-transfer coefficient based on the outside area is 500 W/m^2K and the log-mean temperature difference is 40 K. For a heat-transfer area of 10 m^2, the heat duty is closest to which value?

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

Explanation

The rate equation is Q = U*A*LMTD. Substituting 500*10*40 gives 200,000 W, or 200 kW, for the specified area and mean temperature difference.

Question 31Engineering Sciences (XE)

A binary mixture of benzene and toluene is being separated in a distillation column. According to Raoult's law, the partial pressure of benzene in the vapor above an ideal liquid mixture equals which quantity?

  1. The vapor pressure of pure toluene times the liquid mole fraction of benzene
  2. The total pressure times the liquid mole fraction of benzene
  3. The total pressure times the vapor mole fraction of benzene
  4. The vapor pressure of pure benzene times its liquid mole fraction Correct answer.

Explanation

Raoult's law states that the partial pressure of a component equals its pure-component vapor pressure multiplied by its mole fraction in the liquid. This ideal assumption underpins simple vapor-liquid equilibrium calculations for near-ideal mixtures.

Question 32Engineering Sciences (XE)

A packed absorption column uses a solvent to remove a sparingly soluble gas from an air stream. As the liquid flow rate is increased while gas flow is held constant, the operating line slope on an X-Y diagram changes in which way?

  1. It remains unchanged because the gas flow is constant
  2. It increases, moving the operating line toward the equilibrium line Correct answer.
  3. It decreases, moving the operating line away from the equilibrium line
  4. It becomes vertical because the solvent is nonvolatile

Explanation

The operating line slope is approximately L/G in mole-ratio coordinates. Raising the liquid rate L increases this slope, which moves the operating line closer to the equilibrium line and reduces the required packing height for a fixed separation.

Question 33Engineering Sciences (XE)

The terminal settling velocity of a small spherical particle in the Stokes regime is proportional to which power of the particle diameter?

  1. First power
  2. Third power
  3. Second power Correct answer.
  4. Square root

Explanation

In the Stokes regime, terminal velocity is v = (rho_p - rho_f) g d^2 / (18 mu). The dependence on diameter is therefore quadratic, which is why fine particles settle very slowly.

Question 34Engineering Sciences (XE)

A liquid is being agitated in a baffled tank by a Rushton turbine. If the impeller speed is doubled while all other geometric and fluid properties are unchanged, the power consumption changes by which factor in the fully turbulent regime?

  1. 4
  2. 2
  3. 16
  4. 8 Correct answer.

Explanation

In the fully turbulent regime the power number is constant, so P scales with N^3. Doubling the impeller speed therefore multiplies power by 2^3 = 8.

Question 35Engineering Sciences (XE)

A catalyst pellet is diffusion-limited for a first-order reaction. If the Thiele modulus is very large, the effectiveness factor is best described by which relationship?

  1. It is directly proportional to the Thiele modulus
  2. It is inversely proportional to the Thiele modulus Correct answer.
  3. It approaches unity
  4. It approaches infinity

Explanation

For strong diffusion limitation, the effectiveness factor falls off as 1/phi for a first-order reaction in a slab or sphere. This reflects reaction occurring only in a thin outer shell of the pellet.

Question 36Engineering Sciences (XE)

In an ideal plug-flow reactor, the space time tau is defined as which ratio?

  1. Reactor length divided by fluid velocity at outlet
  2. Reactor volume divided by the reaction rate constant
  3. Reactor volume divided by volumetric flow rate at inlet conditions Correct answer.
  4. Reactor volume divided by mass flow rate

Explanation

Space time is the reactor volume divided by the volumetric feed rate, giving the average residence time for constant-density flow. It has units of time and is used to size ideal reactors.

Question 37Engineering Sciences (XE)

A distillation column is operating at total reflux. Under this condition, which statement about the operating lines is correct?

  1. The operating lines are horizontal, and the reflux ratio is zero
  2. The operating lines intersect at the feed point with the maximum slope
  3. The operating lines have a slope equal to the relative volatility
  4. The operating lines coincide with the diagonal, and the number of stages required is a minimum Correct answer.

Explanation

At total reflux the liquid and vapor rates are equal in each section, so the operating line coincides with the y = x diagonal. Stepping off stages between this line and the equilibrium curve gives the minimum number of theoretical stages.

Question 38Engineering Sciences (XE)

A liquid flows through a packed bed at low Reynolds number. According to the Ergun equation, the pressure drop in the laminar regime is proportional to which combination?

  1. Inverse of superficial velocity
  2. Superficial velocity Correct answer.
  3. Superficial velocity squared
  4. Square root of superficial velocity

Explanation

At low Reynolds number the viscous (Blake-Kozeny) term dominates the Ergun equation, giving a pressure drop proportional to the superficial velocity. The inertial term, which scales with velocity squared, becomes important only at higher Reynolds numbers.

Question 39Engineering Sciences (XE)

A wet solid is dried in a constant-rate period. During this period, the rate of drying is controlled primarily by which factor?

  1. The critical moisture content of the solid
  2. The rate of external heat and mass transfer from the surface Correct answer.
  3. The rate of internal moisture diffusion within the solid
  4. The equilibrium moisture content of the solid

Explanation

In the constant-rate period the surface remains saturated with free moisture, so drying is limited by external heat and mass transfer. Internal diffusion controls only the falling-rate period.

Question 40Engineering Sciences (XE)

A mixture of two partially miscible liquids is heated until it boils as a single vapor phase at a temperature below the boiling points of both pure components. This phenomenon is best described by which term?

  1. Steam distillation
  2. Eutectic formation
  3. Azeotropic distillation Correct answer.
  4. Sublimation

Explanation

When two liquids form a minimum-boiling azeotrope, the mixture boils at a temperature below either pure component and distills with a fixed composition. This behavior reflects strong non-ideality in the liquid phase.

Question 41Engineering Sciences (XE)

A shell-and-tube exchanger is being redesigned to increase the overall heat-transfer coefficient. Fouling on the tube side has developed, adding a fouling resistance. Which change most directly reduces the impact of this fouling resistance?

  1. Increasing the tube-side velocity to raise the convective coefficient Correct answer.
  2. Adding insulation to the shell exterior
  3. Increasing the shell-side baffle spacing
  4. Reducing the tube count while keeping the same flow rate

Explanation

The overall resistance is the sum of convective and fouling resistances in series. Raising the tube-side velocity increases the tube-side convective coefficient, which reduces that term and makes the fixed fouling resistance a smaller fraction of the total.

Question 42Engineering Sciences (XE)

In a chemical process, a first-order reaction with rate constant k occurs in two identical continuous stirred-tank reactors in series. Compared with a single CSTR of the same total volume, the two-in-series arrangement gives which result for a given feed?

  1. Lower conversion because the total volume is split
  2. The same conversion because the total volume is unchanged
  3. Higher conversion only if the reaction order exceeds one
  4. Higher conversion because the residence-time distribution is narrower Correct answer.

Explanation

Splitting the volume into two CSTRs in series narrows the residence-time distribution toward plug flow, which raises conversion for positive-order kinetics. For first-order reactions this benefit holds regardless of whether the order exceeds one.

Question 43Engineering Sciences (XE)

A binary distillation column has a minimum reflux ratio determined from the pinch point on the equilibrium curve. If the feed is changed from saturated liquid to saturated vapor at the same composition, how does the minimum reflux ratio typically change?

  1. It decreases because less liquid traffic is needed in the rectifying section
  2. It remains unchanged because the feed composition is fixed
  3. It increases because more vapor must be condensed to provide reflux Correct answer.
  4. It becomes zero because the feed is entirely vapor

Explanation

A saturated-vapor feed adds vapor to the column and requires more liquid reflux to achieve the same separation, raising the minimum reflux ratio. The pinch point shifts accordingly on the McCabe-Thiele diagram.

Question 44Engineering Sciences (XE)

A gas is absorbed into a liquid film under steady-state conditions with a fast second-order reaction. When the reaction is much faster than diffusion, the absorption rate becomes independent of the liquid-side mass-transfer coefficient and depends mainly on which quantity?

  1. The liquid film thickness
  2. The gas-side mass-transfer coefficient
  3. The equilibrium solubility alone
  4. The interfacial concentration and reaction rate constant Correct answer.

Explanation

For very fast reactions the reaction occurs in a thin plane near the interface, and the enhancement factor grows with the square root of the rate constant. The flux then depends on interfacial concentration and kinetics rather than on film thickness.

Question 45Engineering Sciences (XE)

A slurry is being filtered in a plate-and-frame press under constant pressure. If the filtrate volume collected doubles while the filter cake remains incompressible, the filtration time changes by approximately which factor?

  1. 8
  2. 2
  3. 1.4
  4. 4 Correct answer.

Explanation

For constant-pressure filtration of an incompressible cake, the time is proportional to the square of the filtrate volume. Doubling the volume therefore increases the time by a factor of about four.

Question 46Engineering Sciences (XE)

In a fluidized bed, the minimum fluidization velocity is reached when which condition is satisfied?

  1. The pressure drop across the bed equals the weight of the bed per unit area Correct answer.
  2. The bed voidage reaches zero
  3. The particle Reynolds number exceeds 1000
  4. The superficial velocity equals the terminal velocity of the particles

Explanation

At minimum fluidization the upward drag, reflected in the bed pressure drop, just balances the effective weight of the particles per unit cross-sectional area. Beyond this point the bed expands and bubbles may form.

Question 47Engineering Sciences (XE)

A reaction A -> B is exothermic and carried out in an adiabatic CSTR. As the feed temperature is raised slowly, the steady-state conversion can jump abruptly. This behavior is associated with which phenomenon?

  1. Perfect mixing with no feedback
  2. Simple first-order decay
  3. Multiple steady states and ignition-extinction Correct answer.
  4. Isothermal operation

Explanation

The interplay of Arrhenius heat generation and linear heat removal can produce multiple steady states. Raising the feed temperature can cause ignition to a high-conversion branch or extinction back to a low-conversion branch.

Question 48Engineering Sciences (XE)

A binary mixture is to be separated by extractive distillation using a heavy solvent. The primary role of the solvent is which of the following?

  1. To reduce the reflux ratio to zero
  2. To lower the column operating pressure
  3. To act as a catalyst for a side reaction
  4. To increase the relative volatility of the key components by altering their activity coefficients Correct answer.

Explanation

Extractive distillation adds a high-boiling solvent that changes the activity coefficients, thereby increasing the relative volatility of the components being separated. This breaks azeotropes and enables separation that simple distillation cannot achieve.

Question 49Engineering Sciences (XE)

In a heat exchanger, the effectiveness-NTU method is used. For a given NTU and heat-capacity-rate ratio, the effectiveness of a counter-flow exchanger compared with a parallel-flow exchanger of the same NTU is which?

  1. Equal, because the NTU is the same
  2. Higher, because the counter-flow arrangement maintains a larger mean temperature difference Correct answer.
  3. Higher only when the heat-capacity rates are equal
  4. Lower, because the counter-flow arrangement reduces the mean temperature difference

Explanation

Counter-flow keeps a more uniform temperature difference along the exchanger, so for the same NTU it achieves a higher effectiveness than parallel flow. The advantage persists across heat-capacity-rate ratios, including unequal ones.

Question 50Engineering Sciences (XE)

A liquid mixture is to be separated, and the equilibrium curve lies close to the diagonal over most of the composition range. Which statement about the required number of stages is correct?

  1. The number of stages is independent of the equilibrium curve
  2. A small number of stages is needed because the equilibrium curve is close to the diagonal
  3. The minimum reflux ratio is zero in this case
  4. A large number of stages is needed because the driving force for separation is small Correct answer.

Explanation

When the equilibrium curve lies near the diagonal, the vertical distance between the operating line and the equilibrium curve is small at each stage. This small driving force requires many theoretical stages for a given separation.