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GATE EY practice questions

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Question 1Engineering/Technology/Architecture (undergraduate-level subjects)

In a steady-state DC analysis of a circuit containing a capacitor and an ideal inductor, which statement describes the behaviour of each element?

  1. The capacitor acts as an open circuit and the inductor acts as a short circuit Correct answer.
  2. Both elements act as open circuits
  3. Both elements act as short circuits
  4. The capacitor acts as a short circuit and the inductor acts as an open circuit

Explanation

After a long time in a DC circuit, the current through a capacitor is zero because dv/dt is zero, so it behaves as an open circuit. The voltage across an ideal inductor is zero because di/dt is zero, so it behaves as a short circuit.

Question 2Engineering/Technology/Architecture (undergraduate-level subjects)

A simply supported beam of span L carries a central point load W. What is the magnitude of the maximum bending moment?

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

Explanation

For a simply supported beam with a central point load, each reaction is W/2 and the maximum moment occurs at midspan. The moment there equals (W/2)(L/2) = WL/4.

Question 3Engineering/Technology/Architecture (undergraduate-level subjects)

Which data structure provides average O(1) insertion and lookup by key while storing elements in no guaranteed order?

  1. Sorted array
  2. Hash table Correct answer.
  3. Balanced binary search tree
  4. Min-heap

Explanation

A hash table maps keys to buckets through a hash function, giving average constant-time insert and lookup. It does not preserve key order, unlike a balanced search tree or sorted array.

Question 4Engineering/Technology/Architecture (undergraduate-level subjects)

In an ideal transformer with N1 primary turns and N2 secondary turns, what is the ratio of secondary voltage to primary voltage?

  1. N1/N2
  2. N2/N1 Correct answer.
  3. (N1/N2)^2
  4. (N2/N1)^2

Explanation

Faraday's law applied to an ideal core gives the voltage ratio equal to the turns ratio V2/V1 = N2/N1. The squared ratios apply to impedance transformation, not voltage.

Question 5Engineering/Technology/Architecture (undergraduate-level subjects)

Which thermodynamic cycle is the ideal model used to analyse spark-ignition internal combustion engines?

  1. Brayton cycle
  2. Otto cycle Correct answer.
  3. Rankine cycle
  4. Diesel cycle

Explanation

The Otto cycle models heat addition at constant volume, which approximates combustion in a spark-ignition engine. The Diesel cycle adds heat at constant pressure for compression-ignition engines.

Question 6Engineering/Technology/Architecture (undergraduate-level subjects)

What is the output of the C expression 7 / 2 when both operands are of type int?

  1. 3.0
  2. 3 Correct answer.
  3. 3.5
  4. 4

Explanation

In C, integer division truncates toward zero, so 7/2 evaluates to 3. No floating-point conversion occurs unless at least one operand is a floating type.

Question 7Engineering/Technology/Architecture (undergraduate-level subjects)

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

  1. Torque
  2. Linear momentum
  3. Kinetic energy Correct answer.
  4. Angular momentum

Explanation

Kinetic energy is described by a single magnitude with no direction, so it is a scalar. Angular momentum, torque and linear momentum all have direction and are vectors.

Question 8Engineering/Technology/Architecture (undergraduate-level subjects)

In relational algebra, which operation returns only the rows of a relation that satisfy a given Boolean condition?

  1. Cartesian product
  2. Union
  3. Projection
  4. Selection Correct answer.

Explanation

Selection filters rows using a predicate and is often denoted by sigma. Projection instead chooses columns and discards the rest.

Question 9Engineering/Technology/Architecture (undergraduate-level subjects)

A silicon pn-junction diode is forward biased with a current of 1 mA. Using the ideal diode equation with thermal voltage 26 mV and ideality factor 1, what is the approximate voltage drop?

  1. 0.18 V
  2. 1.20 V
  3. 0.60 V Correct answer.
  4. 0.026 V

Explanation

The diode equation gives V = n·VT·ln(I/IS). With IS near 1e-14 A and I = 1 mA, the logarithm is about 23, so V ≈ 0.026 × 23 ≈ 0.60 V, matching typical silicon behaviour.

Question 10Engineering/Technology/Architecture (undergraduate-level subjects)

An amplifier has a voltage gain of 100 and is connected between a 1 kΩ source and a 1 kΩ load. If the input and output resistances are matched to the source and load respectively, what is the power gain in dB?

  1. 20 dB
  2. 60 dB
  3. 40 dB Correct answer.
  4. 100 dB

Explanation

With equal input and output resistances, power gain equals voltage gain squared, so Ap = 100² = 10⁴. In decibels this is 10·log10(10⁴) = 40 dB.

Question 11Engineering/Technology/Architecture (undergraduate-level subjects)

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

  1. 1200 rpm
  2. 1560 rpm
  3. 1440 rpm Correct answer.
  4. 1500 rpm

Explanation

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

Question 12Engineering/Technology/Architecture (undergraduate-level subjects)

A cantilever beam of length 2 m carries a point load of 5 kN at its free end. What is the magnitude of the maximum bending moment at the fixed support?

  1. 5 kN·m
  2. 2.5 kN·m
  3. 20 kN·m
  4. 10 kN·m Correct answer.

Explanation

For a cantilever with an end point load, the maximum moment occurs at the fixed end and equals P·L. Here 5 kN × 2 m = 10 kN·m.

Question 13Engineering/Technology/Architecture (undergraduate-level subjects)

A sample of 100 measurements has mean 50 and standard deviation 8. Using the empirical rule for an approximately normal distribution, about what percentage of observations lie between 42 and 58?

  1. 99.7%
  2. 50%
  3. 95%
  4. 68% Correct answer.

Explanation

The interval 42 to 58 is one standard deviation on either side of the mean. For a normal distribution, approximately 68% of observations fall within one standard deviation.

Question 14Engineering/Technology/Architecture (undergraduate-level subjects)

A binary search tree is built by inserting keys 50, 30, 70, 20, 40, 60, 80 in that order. Which key is the parent of 20?

  1. 70
  2. 40
  3. 30 Correct answer.
  4. 50

Explanation

Inserting 20 compares it with 50 (go left) then 30 (go left), so 30 becomes its parent. The resulting tree is balanced with 30 as the root of the left subtree of 50.

Question 15Engineering/Technology/Architecture (undergraduate-level subjects)

What is the minimum number of NAND gates needed to implement a two-input XOR function, assuming only two-input NAND gates and constants are available?

  1. 3
  2. 5
  3. 4 Correct answer.
  4. 6

Explanation

A standard XOR realisation using only two-input NAND gates requires four gates. It computes NAND(a,b) and uses it with a and b to generate the final output.

Question 16Engineering/Technology/Architecture (undergraduate-level subjects)

In the context of operating systems, what does thrashing describe?

  1. Fragmentation of the file system allocation table
  2. High CPU utilisation caused by too many ready processes
  3. A deadlock involving three or more processes
  4. Excessive paging activity that leaves little time for useful work Correct answer.

Explanation

Thrashing occurs when the sum of working sets exceeds available memory, so the system spends most of its time servicing page faults. CPU utilisation then collapses because little useful computation occurs.

Question 17Engineering/Technology/Architecture (undergraduate-level subjects)

A control system has open-loop transfer function G(s)H(s) = K / (s(s+2)). Using the Routh-Hurwitz criterion, for which range of K is the closed-loop system stable?

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

Explanation

The closed-loop characteristic equation is s² + 2s + K = 0. Routh-Hurwitz requires all coefficients positive, giving K > 0 for stability of this second-order system.

Question 18Engineering/Technology/Architecture (undergraduate-level subjects)

A heat engine operates between reservoirs at 600 K and 300 K. What is its maximum possible thermal efficiency?

  1. 100%
  2. 50% Correct answer.
  3. 67%
  4. 25%

Explanation

Carnot efficiency is 1 − Tc/Th = 1 − 300/600 = 0.5, or 50%. No real engine operating between these reservoirs can exceed this value.

Question 19Engineering/Technology/Architecture (undergraduate-level subjects)

A uniform rod of length L and mass M rotates about an axis through one end perpendicular to its length. What is its moment of inertia?

  1. ML²/2
  2. ML²
  3. ML²/3 Correct answer.
  4. ML²/12

Explanation

The moment of inertia about the centre is ML²/12. Applying the parallel-axis theorem with d = L/2 gives ML²/12 + ML²/4 = ML²/3.

Question 20Engineering/Technology/Architecture (undergraduate-level subjects)

A 4-bit ripple-carry adder adds 0111 and 0001. What are the 4-bit sum and the carry-out?

  1. Sum 0000, carry-out 1
  2. Sum 1000, carry-out 1
  3. Sum 0111, carry-out 1
  4. Sum 1000, carry-out 0 Correct answer.

Explanation

0111 is 7 and 0001 is 1, giving 8, which is 1000 in 4 bits. Since 8 fits within four bits, the carry-out of the most significant stage is 0.

Question 21Engineering/Technology/Architecture (undergraduate-level subjects)

Which normal form eliminates partial dependencies of non-prime attributes on a candidate key?

  1. Boyce-Codd normal form
  2. Third normal form
  3. Second normal form Correct answer.
  4. First normal form

Explanation

Second normal form requires that the relation be in 1NF and that no non-prime attribute depend on part of a candidate key. Third normal form additionally removes transitive dependencies.

Question 22Engineering/Technology/Architecture (undergraduate-level subjects)

A 2 kg block slides down a frictionless incline of 30° from rest over a distance of 4 m along the incline. Taking g = 9.8 m/s², what is its speed at the bottom?

  1. 8.9 m/s
  2. 6.3 m/s Correct answer.
  3. 12.5 m/s
  4. 4.4 m/s

Explanation

Conservation of energy gives v = √(2g·h), where h = 4·sin30° = 2 m. Thus v = √(2×9.8×2) ≈ 6.3 m/s, independent of mass.

Question 23Engineering/Technology/Architecture (undergraduate-level subjects)

A CMOS inverter has a load capacitance of 10 pF, a supply of 1.8 V, and switches at 100 MHz. Neglecting short-circuit and leakage power, what is the approximate dynamic power?

  1. 3.24 mW Correct answer.
  2. 0.32 mW
  3. 1.62 mW
  4. 32.4 mW

Explanation

Dynamic power is P = α·C·V²·f. With α = 1 for a full switching cycle, P = 10 pF × (1.8 V)² × 100 MHz = 3.24 mW.

Question 24Engineering/Technology/Architecture (undergraduate-level subjects)

In a 3-phase star-connected system with balanced line voltage 400 V rms, what is the phase voltage?

  1. 400 V
  2. 693 V
  3. 231 V Correct answer.
  4. 200 V

Explanation

For a star connection, phase voltage equals line voltage divided by √3. Thus 400/1.732 ≈ 231 V rms.

Question 25Engineering/Technology/Architecture (undergraduate-level subjects)

A feedback amplifier has open-loop gain A = 10⁴ and feedback factor β = 0.01. What is the closed-loop gain and the loop gain?

  1. Closed-loop gain ≈ 100, loop gain 100
  2. Closed-loop gain ≈ 99.01, loop gain 100 Correct answer.
  3. Closed-loop gain ≈ 10⁴, loop gain 10⁴
  4. Closed-loop gain ≈ 1, loop gain 0.01

Explanation

Loop gain is Aβ = 10⁴ × 0.01 = 100. Closed-loop gain is A/(1+Aβ) = 10⁴/101 ≈ 99.01, close to 1/β.

Question 26Engineering/Technology/Architecture (undergraduate-level subjects)

In the engineering drawing convention for first-angle projection, where is the top view placed relative to the front view?

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

Explanation

In first-angle projection the object is imagined between the observer and the plane of projection, so the view obtained from above is projected onto a plane placed below the object and appears below the front view. Third-angle projection places the top view above the front view.

Question 27Engineering/Technology/Architecture (undergraduate-level subjects)

A simply supported beam of span 6 m carries a uniformly distributed load of 4 kN/m over its entire length. What is the maximum shear force in the beam?

  1. 24 kN
  2. 12 kN Correct answer.
  3. 6 kN
  4. 48 kN

Explanation

For a simply supported beam with a full-span UDL, the total load is wL = 4 × 6 = 24 kN, shared equally by the two reactions, giving 12 kN at each support. The maximum shear force equals the reaction, 12 kN, and it occurs at the supports.

Question 28Engineering/Technology/Architecture (undergraduate-level subjects)

Which of the following statements about the entropy change of an isolated system undergoing an irreversible process is correct?

  1. It equals the entropy change of the surroundings
  2. It is positive because entropy is generated within the system Correct answer.
  3. It is always zero because no heat crosses the boundary
  4. It is negative because irreversibilities destroy order

Explanation

The second law states that the entropy of an isolated system increases for any irreversible process and remains constant only for a reversible one. Irreversibilities such as friction or unrestrained expansion generate entropy internally even with no heat transfer.

Question 29Engineering/Technology/Architecture (undergraduate-level subjects)

In the C programming language, what does the declaration `int *p[10];` mean?

  1. p is a pointer to a pointer to int
  2. p is a pointer to an array of 10 integers
  3. p is a function returning a pointer to int
  4. p is an array of 10 pointers to int Correct answer.

Explanation

The postfix subscript operator binds more tightly than the unary dereference, so `p[10]` is formed first, giving an array of 10 elements; the `int *` then makes each element a pointer to int. A pointer to an array would be written `int (*p)[10];`.

Question 30Engineering/Technology/Architecture (undergraduate-level subjects)

Which of the following is a defining characteristic of a real-time operating system compared with a general-purpose operating system?

  1. It always provides a graphical user interface
  2. It maximizes average throughput of batch jobs
  3. It guarantees bounded worst-case response time to events Correct answer.
  4. It uses demand paging for all processes

Explanation

A real-time operating system must satisfy timing constraints, so its scheduler is designed to give a predictable upper bound on response latency for critical tasks. Throughput-oriented or interactive general-purpose systems optimise average performance rather than worst-case determinism.

Question 31Engineering/Technology/Architecture (undergraduate-level subjects)

In a DC machine, what is the function of the commutator together with the brushes?

  1. To convert the alternating emf in the armature coils into unidirectional terminal voltage Correct answer.
  2. To reduce eddy-current losses in the armature core
  3. To provide the main magnetic field flux in the air gap
  4. To mechanically balance the rotor at high speed

Explanation

The armature coils of a DC machine inherently carry alternating quantities as they rotate through the field; the commutator and brushes act as a mechanical rectifier, delivering unidirectional voltage at the terminals in a generator. In a motor the same arrangement performs the inverse function of current reversal.

Question 32Engineering/Technology/Architecture (undergraduate-level subjects)

In a binary tree, the number of nodes of degree two (nodes with exactly two children) is related to the number of leaf nodes. For a non-empty binary tree with L leaves and T nodes of degree two, which relation holds?

  1. T = L - 1 Correct answer.
  2. T = L + 1
  3. T = 2L
  4. T = L / 2

Explanation

Counting edges gives n - 1 = n1 + 2T for n nodes, while n = L + n1 + T; eliminating n1 yields T = L - 1. This holds for every non-empty binary tree regardless of shape.

Question 33Engineering/Technology/Architecture (undergraduate-level subjects)

In surveying, which instrument is used primarily to measure horizontal and vertical angles to a high precision by reading two opposite positions of the graduated circle?

  1. Theodolite Correct answer.
  2. Clinometer
  3. Tacheometer
  4. Planimeter

Explanation

A theodolite measures horizontal and vertical angles, and its design allows readings on opposite sides of the graduated circle to eliminate instrumental errors such as eccentricity. A planimeter measures area, a clinometer measures slope angle only, and a tacheometer is a theodolite adapted for distance measurement.

Question 34Engineering/Technology/Architecture (undergraduate-level subjects)

A silicon sample is doped with donor concentration N_D = 10^16 cm^-3 and acceptor concentration N_A = 4 × 10^15 cm^-3 at room temperature, where complete ionisation may be assumed. What is the approximate electron concentration?

  1. 1.4 × 10^16 cm^-3
  2. 6 × 10^15 cm^-3 Correct answer.
  3. 4 × 10^15 cm^-3
  4. 10^16 cm^-3

Explanation

With both dopants present, charge neutrality gives n ≈ N_D - N_A when the net doping greatly exceeds the intrinsic concentration. The net donor excess is 10^16 - 4 × 10^15 = 6 × 10^15 cm^-3.

Question 35Engineering/Technology/Architecture (undergraduate-level subjects)

A discrete-time LTI system has impulse response h[n] = (0.5)^n u[n]. Which statement about the system is correct?

  1. It is stable because the poles lie inside the unit circle Correct answer.
  2. It is unstable because the impulse response decays too slowly
  3. Stability cannot be judged from the impulse response
  4. It is marginally stable because the pole lies on the unit circle

Explanation

An LTI system is bounded-input bounded-output stable exactly when the impulse response is absolutely summable. Here the sum of (0.5)^n over n ≥ 0 equals 2, a finite value, which corresponds to a pole at z = 0.5 inside the unit circle.

Question 36Engineering/Technology/Architecture (undergraduate-level subjects)

A 3-phase, 400 V, 50 Hz, 4-pole star-connected induction motor has a per-phase stator resistance of 0.5 Ω and draws a line current of 10 A at a power factor of 0.8 lagging. Neglecting stator iron and rotational losses, what is the approximate air-gap power transferred to the rotor?

  1. Approximately 5.4 kW Correct answer.
  2. Approximately 4.8 kW
  3. Approximately 2.8 kW
  4. Approximately 8.0 kW

Explanation

Input power is √3 × V_L × I_L × cos φ = 1.732 × 400 × 10 × 0.8 ≈ 5.54 kW. Stator copper loss is 3 I² R = 3 × 100 × 0.5 = 150 W, so the air-gap power is about 5.54 - 0.15 ≈ 5.4 kW.

Question 37Engineering/Technology/Architecture (undergraduate-level subjects)

A 10 kΩ resistor with a tolerance of ±5% is used in a circuit. If the actual resistance is at its lower limit and the voltage across it is exactly 10 V, what is the power dissipated?

  1. Approximately 11.1 mW
  2. Approximately 10.5 mW Correct answer.
  3. Approximately 10.0 mW
  4. Approximately 9.5 mW

Explanation

The lower limit of resistance is 10 kΩ × 0.95 = 9.5 kΩ. Power is V²/R = 100 / 9500 ≈ 10.5 mW, which is slightly above the nominal 10 mW because the resistance is smaller.

Question 38Engineering/Technology/Architecture (undergraduate-level subjects)

A 2 kg block moving at 3 m/s collides head-on with a stationary 4 kg block on a frictionless surface. If the collision is perfectly inelastic, what is the loss of kinetic energy?

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

Explanation

Momentum conservation gives the common velocity v = (2 × 3)/(2 + 4) = 1 m/s. Initial kinetic energy is ½ × 2 × 9 = 9 J and final is ½ × 6 × 1 = 3 J, so the loss is 6 J.

Question 39Engineering/Technology/Architecture (undergraduate-level subjects)

The characteristic equation of a feedback system is s³ + 2s² + 3s + K = 0. Using the Routh array, for what range of K is the system stable?

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

Explanation

The Routh array for a cubic gives the first-column terms 1, 2, (6 - K)/2 and K. Stability requires all to be positive, so K > 0 and 6 - K > 0, giving 0 < K < 6.

Question 40Engineering/Technology/Architecture (undergraduate-level subjects)

In a relational database, a relation R(A, B, C) has the functional dependencies A → B and B → C. Which statement about the normal form of R is correct?

  1. R is in 3NF but not in BCNF
  2. R is in 2NF but not in 3NF because of the transitive dependency A → B → C Correct answer.
  3. R is in BCNF because A is a candidate key
  4. R is not in 2NF because C is partially dependent on A

Explanation

The only candidate key is A, since A determines B, and B determines C, so A determines all attributes. Because B is a non-prime attribute determining C, the transitive dependency A → B → C violates 3NF, though R is in 2NF since there are no partial dependencies on the single-attribute key.

Question 41Engineering/Technology/Architecture (undergraduate-level subjects)

A TCP sender uses slow start with an initial congestion window of 1 MSS and a threshold initially set very high. If no loss occurs, after how many round-trip times does the congestion window first reach 16 MSS?

  1. 8 round-trip times
  2. 4 round-trip times Correct answer.
  3. 5 round-trip times
  4. 16 round-trip times

Explanation

During slow start the congestion window doubles each RTT: 1, 2, 4, 8, 16 MSS. The window reaches 16 MSS after four round-trip times.

Question 42Engineering/Technology/Architecture (undergraduate-level subjects)

A 50 Hz sinusoidal voltage v(t) = 100 sin(314t) V is applied to a series RL circuit with R = 30 Ω and inductive reactance X_L = 40 Ω. What is the magnitude of the current?

  1. 1.6 A
  2. 2.5 A
  3. 3.3 A
  4. 2 A Correct answer.

Explanation

The impedance magnitude is √(30² + 40²) = 50 Ω. The peak current is 100 / 50 = 2 A, and the rms value would be 2/√2 ≈ 1.41 A; the question asks for the magnitude corresponding to the given peak amplitude.

Question 43Engineering/Technology/Architecture (undergraduate-level subjects)

A boost converter operates from a 12 V input with a duty ratio of 0.5 in continuous conduction mode. Neglecting losses, what is the output voltage?

  1. 24 V Correct answer.
  2. 12 V
  3. 18 V
  4. 6 V

Explanation

For an ideal boost converter the conversion ratio is V_o/V_in = 1/(1 - D). With D = 0.5 the ratio is 2, so the output is 24 V.

Question 44Engineering/Technology/Architecture (undergraduate-level subjects)

In the simplex method for linear programming, a basic feasible solution is optimal when which condition is satisfied?

  1. All slack variables are zero
  2. The objective coefficients are all positive
  3. All reduced costs of the non-basic variables are non-negative in a minimisation problem Correct answer.
  4. The number of constraints equals the number of variables

Explanation

Optimality in the simplex method is certified by the sign of the reduced costs: for minimisation, no non-basic variable has a negative reduced cost, so no entering variable can improve the objective. The optimal solution may well have positive slack variables.

Question 45Engineering/Technology/Architecture (undergraduate-level subjects)

A steel shaft of diameter 50 mm transmits 60 kW at 300 rpm. What is the maximum shear stress in the shaft, taking π ≈ 3.14?

  1. Approximately 16 MPa
  2. Approximately 32.5 MPa Correct answer.
  3. Approximately 65 MPa
  4. Approximately 8 MPa

Explanation

Torque is T = P/ω with ω = 2π × 300/60 ≈ 31.4 rad/s, giving T ≈ 1910 N·m. For a solid shaft τ = 16T/(πd³) = 16 × 1910 / (3.14 × 0.05³) ≈ 32.5 MPa.

Question 46Engineering/Technology/Architecture (undergraduate-level subjects)

A 4-bit successive-approximation ADC has a full-scale reference of 5 V. What is the approximate resolution (smallest distinguishable voltage step)?

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

Explanation

A 4-bit converter has 2^4 = 16 levels, so the step size is 5 V / 16 = 0.3125 V. This equals one least significant bit of the converter.

Question 47Engineering/Technology/Architecture (undergraduate-level subjects)

A single-plate clutch has an outer radius of 150 mm and an inner radius of 100 mm. Using the uniform-wear theory with a friction coefficient of 0.3 and an axial force of 5 kN, what is the friction torque?

  1. Approximately 187.5 N·m Correct answer.
  2. Approximately 225 N·m
  3. Approximately 150 N·m
  4. Approximately 375 N·m

Explanation

Under uniform wear the torque is T = μ W (r_o + r_i)/2 = 0.3 × 5000 × (0.15 + 0.10)/2 ≈ 187.5 N·m. The mean radius appears because pressure is assumed inversely proportional to radius.

Question 48Engineering/Technology/Architecture (undergraduate-level subjects)

A vapour-compression refrigeration cycle using R-134a operates between an evaporator saturation temperature of -10 °C and a condenser saturation temperature of 40 °C. If the compressor work per unit mass is 40 kJ/kg and the refrigerating effect is 140 kJ/kg, what is the coefficient of performance?

  1. 2.5
  2. 3.5 Correct answer.
  3. 0.286
  4. 4.5

Explanation

The COP of a refrigerator is the refrigerating effect divided by the compressor work, so COP = 140/40 = 3.5. The Carnot COP between the same absolute temperatures, about 5.26, is an upper bound that this real cycle does not reach.

Question 49Engineering/Technology/Architecture (undergraduate-level subjects)

In the context of compiler design, which statement about an LL(1) grammar is correct?

  1. It permits a predictive parser that needs at most one lookahead token and requires the FIRST/FOLLOW sets of alternatives to be disjoint Correct answer.
  2. It requires backtracking because left recursion is preserved
  3. It can parse all context-free grammars that are not ambiguous
  4. It requires the grammar to be right-recursive but places no restriction on FIRST sets

Explanation

LL(1) parsing builds a predictive table using FIRST and FOLLOW sets, and the table has at most one entry per cell only when the alternatives have disjoint FIRST sets and any nullable alternative does not overlap with the FOLLOW set. This permits deterministic parsing with one token of lookahead and no backtracking.

Question 50Engineering/Technology/Architecture (undergraduate-level subjects)

A discrete memoryless source emits four symbols with probabilities 1/2, 1/4, 1/8 and 1/8. What is the source entropy, and how does it compare with the average length of a Huffman code for this source?

  1. Entropy is 1.75 bits/symbol and the Huffman code has the same average length Correct answer.
  2. Entropy is 2 bits/symbol and the Huffman code averages 1.75 bits/symbol
  3. Entropy is 1.75 bits/symbol and the Huffman code averages 2 bits/symbol
  4. Entropy is 1.5 bits/symbol and the Huffman code averages 1.5 bits/symbol

Explanation

Entropy is Σ p log2(1/p) = 0.5 + 0.5 + 0.375 + 0.375 = 1.75 bits/symbol. Because the probabilities are negative powers of two, the Huffman code assigns lengths 1, 2, 3 and 3, giving average length 1.75 bits, exactly equal to the entropy.