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GATE PE practice questions

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Question 1Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a steady-state DC circuit, a capacitor connected between two nodes with a constant potential difference behaves in which manner?

  1. As a voltage source equal to the node difference
  2. As a resistor whose value equals its reactance
  3. As an open circuit, carrying no steady current Correct answer.
  4. As a short circuit, carrying maximum current

Explanation

Under steady DC the capacitor charges until its voltage equals the applied difference, after which dV/dt is zero and the current i = C dV/dt vanishes, so it blocks steady current. Its reactance 1/(ωC) tends to infinity at zero frequency, confirming the open-circuit model.

Question 2Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A simply supported beam of span L carries a central point load W. The maximum bending moment in the beam is:

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

Explanation

Each reaction equals W/2 by symmetry, and the bending moment diagram is triangular with its peak at midspan. The peak value is (W/2)(L/2) = WL/4.

Question 3Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which thermodynamic property is held constant during an isenthalpic throttling process such as flow through an insulated capillary tube?

  1. Gibbs free energy
  2. Specific volume
  3. Enthalpy Correct answer.
  4. Entropy

Explanation

For steady adiabatic flow with negligible kinetic and potential energy changes and no shaft work, the steady-flow energy equation reduces to h1 = h2. Hence the process is isenthalpic, which is the basis of the Joule–Thomson analysis.

Question 4Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In the context of a relational database, which normal form specifically eliminates transitive dependencies of non-prime attributes on the primary key?

  1. Second normal form
  2. Fourth normal form
  3. Third normal form Correct answer.
  4. First normal form

Explanation

Third normal form requires that every non-prime attribute depend only on candidate keys, removing transitive dependencies such as A → B → C where C depends on the key through B. Second normal form removes partial dependencies, and fourth normal form addresses multivalued dependencies.

Question 5Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In C, what does the declaration `int *p[5];` declare?

  1. An array of five ints accessible only through p
  2. A pointer to a function returning int
  3. A pointer to an array of five ints
  4. An array of five pointers to int Correct answer.

Explanation

The postfix subscript operator binds tighter than the unary dereference, so p is first an array of five elements, each of type int *. A pointer to an array would be written as `int (*p)[5];`.

Question 6Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

The Laplace transform of the unit step function u(t) is:

  1. s
  2. 1/s²
  3. 1
  4. 1/s Correct answer.

Explanation

Evaluating the defining integral from zero to infinity gives ∫e^(−st)dt = 1/s for Re(s) > 0. The unit step is the integral of the impulse, whose transform is 1, consistent with division by s.

Question 7Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

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

  1. 1500 rpm
  2. 1560 rpm
  3. 1440 rpm Correct answer.
  4. 720 rpm

Explanation

Synchronous speed is Ns = 120f/P = 120×50/4 = 1500 rpm. Rotor speed is Ns(1 − s) = 1500×0.96 = 1440 rpm.

Question 8Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

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

  1. Watt per metre kelvin
  2. Watt Correct answer.
  3. Joule per kelvin
  4. Joule

Explanation

Rate of heat transfer is energy per unit time, and one joule per second is defined as one watt. The joule measures energy, while the other compound units describe heat capacity and thermal conductivity.

Question 9Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A fair six-sided die is rolled twice. What is the probability that the sum of the two outcomes equals 8?

  1. 1/9
  2. 5/36 Correct answer.
  3. 1/6
  4. 7/36

Explanation

There are 36 equally likely ordered outcomes. The favourable pairs summing to 8 are (2,6), (3,5), (4,4), (5,3), (6,2), giving five outcomes and a probability of 5/36.

Question 10Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A silicon pn junction diode is forward biased. As the forward current increases substantially, the voltage across the junction:

  1. Remains exactly at 0.7 V regardless of current
  2. Increases linearly with current at all levels
  3. Increases only slightly above the cut-in voltage Correct answer.
  4. Decreases as current rises

Explanation

The diode equation I = Is(exp(V/nVT) − 1) is exponential, so the terminal voltage grows only logarithmically with current. Beyond cut-in the voltage changes by a small increment for a large current change.

Question 11Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a turning operation, cutting speed is doubled while feed and depth of cut are unchanged. The tool life, following Taylor's equation VT^n = C with n = 0.25, changes by a factor of approximately:

  1. 0.84 Correct answer.
  2. 0.5
  3. 0.25
  4. 0.0625

Explanation

From Taylor's tool-life equation, T2/T1 = (V1/V2)^(1/n) = (1/2)^4 = 1/16 ≈ 0.0625 for the tool life ratio... careful: with n = 0.25, T2/T1 = (V1/V2)^(1/n) = (0.5)^4 = 0.0625.

Question 12Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which data structure is most appropriate for implementing a function-call stack in a compiler runtime?

  1. Balanced binary search tree
  2. FIFO queue
  3. Priority queue
  4. Last-in-first-out stack Correct answer.

Explanation

Function calls return in reverse order of invocation, so the activation records must be pushed and popped from a LIFO structure. A stack gives O(1) push and pop at the top, matching the call-return discipline.

Question 13Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

The characteristic equation of a closed-loop system is s³ + 2s² + 3s + K = 0. Using the Routh–Hurwitz criterion, the range of K for stability is:

  1. K < 6
  2. 0 < K < 6 Correct answer.
  3. K > 0
  4. K > 6

Explanation

The Routh array gives the first column entries 1, 2, (6 − K)/2, K. For no sign changes, K must be positive and 6 − K must be positive, so 0 < K < 6.

Question 14Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A simply supported rectangular beam of width b and depth d carries a bending moment M. The maximum bending stress is given by:

  1. 12M/(bd³)
  2. 6M/(bd²) Correct answer.
  3. 3M/(2bd)
  4. M/(bd²)

Explanation

Bending stress is σ = My/I, and the maximum occurs at y = d/2. With I = bd³/12, the expression simplifies to σmax = 6M/(bd²).

Question 15Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In an ideal vapour-compression refrigeration cycle, the component that rejects heat to the surroundings is the:

  1. Expansion valve
  2. Evaporator
  3. Compressor
  4. Condenser Correct answer.

Explanation

After compression the refrigerant is at high pressure and temperature and gives up heat to the ambient in the condenser, becoming liquid. The evaporator absorbs heat from the refrigerated space, and the expansion valve throttles the refrigerant isenthalpically.

Question 16Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which type of levelling instrument is designed to maintain a horizontal line of sight automatically by means of a compensator?

  1. Y level
  2. Tilting level
  3. Automatic level Correct answer.
  4. Dumpy level

Explanation

An automatic level contains a prism or mirror compensator suspended so that the line of sight is held horizontal even when the instrument is slightly out of adjustment. Older dumpy and tilting levels require manual bubble centring.

Question 17Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In an electrochemical cell, the standard electrode potential of the hydrogen electrode is assigned a value of zero at which conditions?

  1. Pure water and 1 atm H₂ at 298 K
  2. Unit activity of H⁺ and 0.1 bar H₂ at 273 K
  3. 0.1 M H⁺ and 1 atm H₂ at 273 K
  4. Unit activity of H⁺ and 1 bar H₂ at 298 K Correct answer.

Explanation

The standard hydrogen electrode is defined with unit activity (approximately 1 M) of hydrogen ions, hydrogen gas at 1 bar, and a temperature usually taken as 298 K, and its potential is set to zero by convention.

Question 18Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which of the following best describes the purpose of the `volatile` qualifier in C?

  1. It forces the compiler to re-read the object on each access rather than caching it in a register Correct answer.
  2. It allocates the variable in persistent memory across program runs
  3. It guarantees atomic access to the variable in a multithreaded program
  4. It makes the variable's value constant after initialisation

Explanation

The volatile qualifier tells the compiler that the object may change outside the program's control, such as a memory-mapped register, so it must not optimise away or cache accesses. It says nothing about atomicity or constantness.

Question 19Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A 4-bit successive-approximation ADC has a full-scale input of 5 V. What is the resolution of the converter?

  1. 0.156 V
  2. 0.625 V
  3. 0.3125 V Correct answer.
  4. 1.25 V

Explanation

For an n-bit converter the number of steps is 2^n = 16, so the resolution is 5 V / 16 = 0.3125 V. This is the smallest voltage change the converter can distinguish.

Question 20Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a 2-D stress state, the principal stresses are found by Mohr's circle construction. If σx = 80 MPa, σy = 20 MPa and τxy = 30 MPa, the maximum principal stress is:

  1. 50 MPa
  2. 90 MPa Correct answer.
  3. 110 MPa
  4. 70 MPa

Explanation

The centre of Mohr's circle is (σx + σy)/2 = 50 MPa and its radius is √(((σx − σy)/2)² + τxy²) = √(30² + 30²) = 42.4 MPa. The maximum principal stress is 50 + 42.4 ≈ 92.4 MPa, closest to 90 MPa among the choices.

Question 21Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which of the following describes the role of virtual memory in an operating system?

  1. It permanently stores process data on disk between reboots
  2. It guarantees constant access time for every memory reference
  3. It eliminates the need for any page replacement policy
  4. It gives each process a private logical address space larger than physical RAM Correct answer.

Explanation

Virtual memory maps logical addresses to physical frames through page tables, letting each process see a contiguous space that can exceed physical memory by paging to disk. It does not remove the need for replacement policies or guarantee uniform latency.

Question 22Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A pipeline has five stages with delays of 2, 3, 2, 4 and 2 ns. What is the ideal throughput of the pipeline in millions of instructions per second?

  1. 200
  2. 400
  3. 125
  4. 250 Correct answer.

Explanation

The clock period of a synchronous pipeline is set by the slowest stage, here 4 ns, so the ideal throughput is 1/(4 ns) = 250 million instructions per second. The sum of stage delays determines latency, not throughput.

Question 23Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a binary distillation column, increasing the reflux ratio while keeping the distillate composition fixed will, in general:

  1. Have no effect on the stage requirement
  2. Increase the number of theoretical stages required
  3. Eliminate the need for a reboiler
  4. Decrease the number of theoretical stages required Correct answer.

Explanation

A higher reflux ratio raises the liquid-to-vapour ratio in the rectifying section, moving the operating line closer to the diagonal and reducing the number of equilibrium stages needed for the specified separation. The limiting case is total reflux, which needs the minimum stages.

Question 24Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A linear time-invariant system has the transfer function G(s) = 10/(s² + 2s + 10). Its percentage overshoot for a unit step input is approximately:

  1. 16 percent
  2. 35 percent Correct answer.
  3. 4 percent
  4. 50 percent

Explanation

Comparing with the standard second-order form gives ωn² = 10 and 2ζωn = 2, so ζ = 1/√10 ≈ 0.316. The overshoot is exp(−πζ/√(1−ζ²)) ≈ exp(−1.047) ≈ 0.35, about 35 percent.

Question 25Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a reciprocating compressor, the volumetric efficiency is reduced by which combination of factors?

  1. Large clearance volume and high pressure ratio Correct answer.
  2. Small clearance volume and low pressure ratio
  3. Small clearance volume and high pressure ratio
  4. Large clearance volume and low pressure ratio

Explanation

Volumetric efficiency is approximately 1 + C − C(p2/p1)^(1/n), where C is the clearance ratio. Both a larger clearance volume and a higher pressure ratio increase the re-expansion volume and therefore reduce the fraction of the stroke that delivers fresh gas.

Question 26Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In metal casting, a riser is incorporated into the mould primarily to:

  1. Increase the pouring rate of the molten metal
  2. Reduce the melting point of the alloy being poured
  3. Provide a vent for escaping mould gases
  4. Supply liquid metal to compensate for solidification shrinkage Correct answer.

Explanation

A riser acts as a reservoir of molten metal that feeds the casting as it contracts during solidification, so the shrinkage cavity forms in the riser rather than the casting. It must solidify after the casting to remain effective. Venting and pouring rate are handled by separate features such as vents and sprue design.

Question 27Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which heat-treatment process involves heating steel above its critical temperature, then cooling it in still air?

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

Explanation

Normalising heats steel above the upper critical temperature and allows it to cool in still air, producing a fine pearlitic structure with moderate strength and improved machinability. Quenching uses a rapid medium such as water or oil, while annealing uses controlled slow furnace cooling.

Question 28Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a four-stroke spark-ignition engine, the function of the camshaft is to:

  1. Convert the reciprocating motion of the piston into rotation
  2. Open and close the valves in correct sequence with the crankshaft Correct answer.
  3. Deliver the fuel-air mixture into the cylinder
  4. Ignite the compressed charge at the end of compression

Explanation

The camshaft carries lobes that actuate the inlet and exhaust valves, and it is driven at half crankshaft speed so each valve operates once per two revolutions. Fuel delivery, ignition and conversion of reciprocating motion belong to other components.

Question 29Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

The Reynolds number of flow in a pipe is 1500. The flow is best described as:

  1. Fully rough turbulent
  2. Transitional
  3. Turbulent
  4. Laminar Correct answer.

Explanation

For pipe flow, Reynolds numbers below about 2000 indicate laminar flow, between 2000 and 4000 transitional, and above 4000 turbulent. A value of 1500 therefore lies clearly in the laminar regime, where viscous forces dominate.

Question 30Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a DC shunt generator, the field winding is connected:

  1. In series with the load and the armature
  2. In parallel with the armature Correct answer.
  3. Across the commutator through a separate exciter only
  4. In series with the armature

Explanation

A shunt (parallel) generator has its field winding connected in parallel with the armature so that the field current is a small fraction of the armature current. Series generators instead connect the field in series with the armature and load.

Question 31Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

The decimal number 13 is represented in 4-bit binary as:

  1. 1101 Correct answer.
  2. 1011
  3. 1110
  4. 1001

Explanation

Thirteen equals 8 + 4 + 1, so the bits in the 8, 4, 2, 1 positions are 1, 1, 0, 1, giving 1101. Checking the place values confirms that no other listed pattern sums to 13.

Question 32Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which SQL clause is used to filter groups produced by a GROUP BY clause?

  1. WHERE
  2. DISTINCT
  3. ORDER BY
  4. HAVING Correct answer.

Explanation

HAVING applies a condition to aggregated groups after GROUP BY has formed them, so it can reference aggregate functions such as COUNT or SUM. WHERE filters individual rows before grouping and cannot be used on aggregate results in the same way.

Question 33Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a first-angle orthographic projection, the view placed below the front view is the:

  1. Right side view
  2. Bottom view
  3. Top view Correct answer.
  4. Left side view

Explanation

First-angle projection places the object between the observer and the plane, so the top view appears below the front view and the left side view appears on the right. This convention is standard in Indian drawing practice under IS 696.

Question 34Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A simply supported beam of span 4 m carries a central point load of 20 kN. The maximum bending moment is:

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

Explanation

For a simply supported beam with a central point load W over span L, the maximum bending moment is WL/4 at midspan. Substituting W = 20 kN and L = 4 m gives 20 × 4 / 4 = 20 kN·m.

Question 35Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a vapour-compression refrigeration cycle, the function of the expansion device is to:

  1. Raise the refrigerant pressure before it enters the condenser
  2. Reduce the refrigerant pressure from condenser level to evaporator level Correct answer.
  3. Increase the enthalpy of the refrigerant before compression
  4. Remove moisture from the refrigerant liquid

Explanation

The expansion valve or capillary throttles the liquid refrigerant from condensing pressure down to evaporating pressure, which also drops its temperature and produces a liquid-vapour mixture. Compression, not expansion, raises pressure to condenser level.

Question 36Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A stream of water flows through a horizontal pipe that narrows from 100 mm to 50 mm diameter. If the velocity in the wider section is 1 m/s, the velocity in the narrower section is:

  1. 0.5 m/s
  2. 2 m/s
  3. 8 m/s
  4. 4 m/s Correct answer.

Explanation

Continuity for an incompressible fluid gives A1V1 = A2V2, and area scales with the square of diameter. The diameter halves, so the area falls to one quarter and the velocity rises fourfold, from 1 m/s to 4 m/s.

Question 37Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A 10 kΩ resistor and a 10 kΩ resistor are connected in parallel. The equivalent resistance is:

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

Explanation

For two equal resistors in parallel, the equivalent resistance is half the individual value, since 1/R = 1/10 + 1/10 = 2/10 kΩ⁻¹, giving R = 5 kΩ. Parallel combination always yields a value smaller than the smallest branch resistance.

Question 38Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a bipolar junction transistor operating in the active region, the base-emitter junction is:

  1. Forward biased and the base-collector junction is forward biased
  2. Forward biased and the base-collector junction is reverse biased Correct answer.
  3. Reverse biased and the base-collector junction is forward biased
  4. Reverse biased and the base-collector junction is reverse biased

Explanation

Active-region operation requires the emitter-base junction to be forward biased so carriers are injected, while the collector-base junction is reverse biased to sweep them into the collector. This combination provides transistor action with current gain.

Question 39Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A 50 Hz sinusoidal voltage is applied to a pure inductor. If the inductance is doubled while the supply frequency is halved, the inductive reactance:

  1. Halves
  2. Becomes four times larger
  3. Remains unchanged Correct answer.
  4. Doubles

Explanation

Inductive reactance is XL = 2πfL, so it is proportional to both frequency and inductance. Halving the frequency halves XL while doubling L doubles it, and the two effects cancel exactly, leaving the reactance unchanged.

Question 40Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

Which of the following is an intensive thermodynamic property?

  1. Total enthalpy
  2. Mass
  3. Temperature Correct answer.
  4. Volume

Explanation

Intensive properties are independent of the amount of substance present, and temperature is one of them. Volume, mass and total enthalpy all scale with system size and are therefore extensive properties.

Question 41Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a CNC machining centre, the function of the machine control unit is to:

  1. Interpret the part program and generate command signals for the drives Correct answer.
  2. Measure the tool wear and replace worn tools automatically
  3. Supply coolant at the correct pressure to the cutting zone
  4. Physically clamp the workpiece during machining

Explanation

The machine control unit processes the part program, performs interpolation and issues position and velocity commands to the axis drives. Clamping, coolant delivery and automatic tool changing are functions of separate machine subsystems.

Question 42Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A shaft transmits 15 kW at 1500 rpm. The torque transmitted by the shaft is approximately:

  1. 10 N·m
  2. 95.5 N·m Correct answer.
  3. 150 N·m
  4. 1432 N·m

Explanation

Power equals torque times angular velocity, with ω = 2πN/60 = 157.1 rad/s at 1500 rpm. Torque is therefore 15000 / 157.1 ≈ 95.5 N·m.

Question 43Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In the simplex method of linear programming, the basic feasible solution at which the objective function is optimised occurs at:

  1. The point farthest from the origin
  2. A vertex of the feasible region Correct answer.
  3. The centroid of the feasible region
  4. Any interior point of the feasible region

Explanation

The fundamental theorem of linear programming states that if an optimum exists, it occurs at an extreme point, that is, a vertex of the feasible polytope. The simplex method moves between such vertices while improving the objective.

Question 44Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A fair coin is tossed four times. The probability of getting exactly two heads is:

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

Explanation

The number of heads follows a binomial distribution with n = 4 and p = 1/2, so P(X = 2) = C(4,2)(1/2)^4 = 6/16 = 3/8. The six favourable sequences each have probability 1/16.

Question 45Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

The Laplace transform of the function f(t) = e^(−3t) for t ≥ 0 is:

  1. 3/s
  2. 1/(s + 3) Correct answer.
  3. 1/(s² + 9)
  4. 1/(s − 3)

Explanation

The standard result is that the Laplace transform of e^(−at) is 1/(s + a) for s > −a. With a = 3 this gives 1/(s + 3), with the region of convergence s > −3.

Question 46Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

In a PID controller, the integral action is included mainly to:

  1. Increase the speed of the transient response
  2. Reduce the sensitivity of the loop to high-frequency noise
  3. Eliminate the steady-state error to a step input Correct answer.
  4. Limit the rate of change of the controller output

Explanation

Integral action accumulates the error over time, so a nonzero steady-state error would keep driving the output until the error vanishes, thereby removing offset. Derivative action, by contrast, responds to the rate of change of error and can speed the transient.

Question 47Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A closed-loop system has the characteristic equation s² + 4s + K = 0. For the system to be marginally stable, the value of K must be:

  1. Any positive value
  2. Zero Correct answer.
  3. Four
  4. Negative four

Explanation

Marginal stability requires a pair of purely imaginary roots, which occurs here when the constant term vanishes, that is K = 0, leaving roots at s = 0 and s = −4. For K > 0 both roots have negative real parts and the system is stable, while K < 0 gives one positive real root and instability.

Question 48Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A cantilever beam of length L carries a point load W at its free end. The deflection at the free end is:

  1. WL²/(2EI)
  2. WL³/(3EI) Correct answer.
  3. WL³/(48EI)
  4. WL³/(8EI)

Explanation

For an end-loaded cantilever the free-end deflection is WL³/(3EI), obtained by integrating the bending moment diagram with the appropriate boundary conditions. The other expressions correspond to different beams or to slope rather than deflection.

Question 49Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A 3-phase, 400 V, 50 Hz, 4-pole star-connected induction motor has a per-phase rotor resistance of 0.2 Ω and standstill rotor reactance of 1.0 Ω. The slip at which the developed torque is maximum is:

  1. 0.10
  2. 0.20 Correct answer.
  3. 0.80
  4. 0.50

Explanation

Maximum torque occurs when the rotor resistance equals the slip-scaled rotor reactance, so s = R2/X2 at standstill values. Here s_m = 0.2/1.0 = 0.20. This is independent of supply voltage, which affects the magnitude but not the slip at which peak torque occurs.

Question 50Engineering / Technology / Architecture / Science / Commerce / Arts / Humanities undergraduate subjects (test-paper specific; no weight breakdown published in source)

A binary distillation column separates an ideal binary mixture with constant relative volatility of 2.0. If the liquid mole fraction on a tray is 0.5, the equilibrium vapour mole fraction leaving that tray is:

  1. 0.750
  2. 0.333
  3. 0.500
  4. 0.667 Correct answer.

Explanation

Using y = αx/[1 + (α − 1)x] with α = 2 and x = 0.5 gives y = 1.0/(1 + 0.5) = 0.667. The vapour is always richer in the more volatile component than the liquid in equilibrium with it.