← MES Jr. Grade
Past Questions — 2024
Sketch the root locus for a system with open-loop transfer function G(s)H(s)= K/s(s+4).
What is the relation between output response and input signal in closed loop system?
A)
Nonlinear
B)
Linear
C)
Exponential
D)
Parabolic
In the study of Control Systems, specifically for the purpose of analysis using Transfer Functions (Laplace Transforms), we assume the system is a Linear Time-Invariant (LTI) system. For a closed-loop system, the relationship between the output response Y(s) and the input signal R(s) is defined by the Closed-Loop Transfer Function: T(s) = Y(s)/R(s) = G(s) / [1 + G(s)H(s)]. Because the transfer function is a ratio of polynomials in the complex frequency domain, it represents a linear relationship between the input and output. While real-world physical systems may exhibit nonlinearities (like saturation), the fundamental theoretical framework used in competitive engineering exams for 'Control Systems' assumes linearity to allow for superposition and frequency response analysis. Therefore, the standard expected answer is 'Linear'.
The condition which will satisfy the dimensions of the waveguide is:
A)
a = b
B)
a > b
C)
a < b
D)
ab = 0
In the context of rectangular waveguides, 'a' typically denotes the width (the wider dimension) and 'b' denotes the height (the narrower dimension). For a rectangular waveguide to operate in the dominant mode (the TE10 mode), the dimensions must satisfy the condition a > b. The cutoff frequency for a TE mode is given by fc = (c/2) * sqrt((m/a)^2 + (n/b)^2). For the dominant mode (TE10), m=1 and n=0, making the cutoff frequency fc = c/(2a). To ensure that the TE10 mode is the first mode to propagate and to maintain the stability of the mode propagation, the width 'a' is designed to be larger than the height 'b'. Typically, a ratio of a = 2b is commonly used in standard waveguides. If a = b, the waveguide becomes a square waveguide, which has different degenerate mode properties. If a < b, the labels are simply swapped, and 'b' becomes the dominant dimension. Therefore, the standard convention for a rectangular waveguide is a > b.
What will be the oscillator frequency of Hartley oscillator if inductances L1, L2 are equal to 1 mH and 2 mH respectively and capacitor C is 10 nF, (Neglect mutual inductance)?
A)
50 KHz
B)
29 KHz
C)
40 KHz
D)
57 KHz
Step-by-step calculation for the frequency of a Hartley Oscillator:
1. **Identify the given values:**
- Inductance L1 = 1 mH = 1 × 10⁻³ H
- Inductance L2 = 2 mH = 2 × 10⁻³ H
- Capacitance C = 10 nF = 10 × 10⁻⁹ F
2. **Formula for Hartley Oscillator Frequency:**
The frequency of oscillation (f) for a Hartley oscillator is given by:
f = 1 / (2π√(L_eq * C))
where L_eq is the equivalent inductance. Since mutual inductance is neglected, the inductors are in series:
L_eq = L1 + L2
3. **Calculate L_eq:**
L_eq = 1 mH + 2 mH = 3 mH = 3 × 10⁻³ H
4. **Substitute values into the frequency formula:**
f = 1 / (2 * π * √(3 × 10⁻³ * 10 × 10⁻⁹))
f = 1 / (2 * π * √(30 × 10⁻¹²})
f = 1 / (2 * π * 5.477 × 10⁻⁶)
f = 1 / (3.441 × 10⁻⁵)
f ≈ 29,057 Hz
5. **Convert to KHz:**
f ≈ 29.06 KHz
Comparing this result to the given options, the closest value is 29 KHz.
The unwanted characteristics of amplifier output apart from the desired output is collectively termed as:
A)
Inefficiency
B)
Damage
C)
Fault
D)
Distortion
In electronics and amplifier theory, 'Distortion' is defined as the unwanted alteration of the output waveform compared to the input waveform. It represents any change in the shape, frequency, or phase of the signal that is not part of the intended amplification process. Common types include Harmonic Distortion (due to non-linearity), Intermodulation Distortion, and Phase Distortion.
Why other options are incorrect:
- a. Inefficiency: Refers to the ratio of AC output power to DC input power; it relates to power loss (usually as heat), not the quality/characteristics of the output signal waveform.
- b. Damage: Refers to physical or electrical failure of the components (e.g., a blown capacitor), which is a state of failure rather than a characteristic of the output signal.
- c. Fault: A general term for a malfunction or defect in a circuit that prevents it from operating as intended, whereas distortion can occur even in a 'functioning' amplifier due to design limits or saturation.
The number of select lines for a 16-to-1 multiplexer is:
A)
2
B)
4
C)
8
D)
16
A multiplexer (MUX) is a combinational circuit that selects one of many input signals and forwards the selected input into a single output line. The relationship between the number of input lines (n) and the number of select lines (m) is given by the formula: 2^m = n. In this question, the multiplexer is a 16-to-1 MUX, meaning there are n = 16 input lines. Substituting this into the formula: 2^m = 16. Since 16 = 2^4, it follows that m = 4. Therefore, 4 select lines are required to uniquely address each of the 16 input lines.
Analysis of options:
- Option (a) 2: 2^2 = 4 inputs (Incorrect).
- Option (b) 4: 2^4 = 16 inputs (Correct).
- Option (c) 8: 2^8 = 256 inputs (Incorrect).
- Option (d) 16: 2^16 = 65,536 inputs (Incorrect).
Divergence theorem is based on:
A)
Gauss law
B)
Stoke’s law
C)
Ampere law
D)
Lenz law
The Divergence Theorem (also known as Gauss's Theorem) relates the flux of a vector field through a closed surface to the divergence of the field within the volume enclosed by that surface. Mathematically, it is expressed as: ∬S (V · n) dS = ∭V (∇ · V) dV. In electromagnetics, this theorem is the fundamental mathematical basis for Gauss's Law, which states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space.
Why other options are incorrect:
- b. Stoke's law: This is based on the Curl theorem, relating a surface integral of the curl of a vector field to a line integral around the boundary curve.
- c. Ampere law: While Ampere's law can be converted using the Divergence theorem in certain contexts, it is fundamentally a manifestation of the Curl theorem (relating current to the circulation of the magnetic field).
- d. Lenz law: This is a physical law regarding the direction of induced electromotive force (EMF) and is not a mathematical theorem of vector calculus.
Which of the following amplifier class have the highest linearity and lowest distortion?
A)
Class A
B)
Class B
C)
Class C
D)
Class B push-pull
To determine which amplifier class has the highest linearity and lowest distortion, we analyze the conduction angle and biasing of the active device (transistor) for each class:
1. **Class A**: In a Class A amplifier, the transistor is biased such that it conducts for the full cycle (360°) of the input signal. Because the operating point (Q-point) is placed in the center of the load line, the signal remains within the linear region of the transistor's characteristic curve. This results in the highest linearity and the lowest harmonic distortion among all classes.
2. **Class B**: The transistor conducts for only half of the input cycle (180°). This leads to 'crossover distortion' at the point where the signal switches from the positive half-cycle to the negative half-cycle, significantly increasing distortion compared to Class A.
3. **Class C**: The transistor conducts for less than half of the cycle (less than 180°). This class is highly non-linear and produces massive distortion, making it unsuitable for audio amplification; it is primarily used in tuned RF amplifiers where a LC tank circuit filters out the harmonics.
4. **Class B push-pull**: While this configuration improves efficiency and reduces some distortion compared to a single Class B stage, it still suffers from crossover distortion unless modified into Class AB. It cannot match the inherent linearity of a pure Class A amplifier.
Conclusion: Class A provides the most faithful reproduction of the input waveform, ensuring the highest linearity and lowest distortion.
How is a J-K flip-flop made to toggle?
A)
J = 0, K = 0
B)
J = 1, K = 0
C)
J = 0, K = 1
D)
J = 1, K = 1
A J-K flip-flop is a universal flip-flop that overcomes the 'invalid state' problem of the S-R flip-flop. Its behavior is determined by the inputs J and K as follows:
1. **Hold State (J=0, K=0):** The output remains unchanged (Q_next = Q_present). This corresponds to option (a).
2. **Reset State (J=0, K=1):** The output is forced to 0 (Q_next = 0). This corresponds to option (c).
3. **Set State (J=1, K=0):** The output is forced to 1 (Q_next = 1). This corresponds to option (b).
4. **Toggle State (J=1, K=1):** The output switches to the complement of its current state (Q_next = NOT Q_present). If the output was 0, it becomes 1; if it was 1, it becomes 0. This is known as the 'toggle' condition.
Therefore, to make a J-K flip-flop toggle, both inputs J and K must be set to high (1).
A lossless coaxial cable has L = 250 nH/m and C = 100 pF/m. Calculate its characteristic impedance and velocity of propagation.
In a zener regulator, the input D.C is 10 V±20%. The output requirement are 5 V and 20 mA. Assuming Izmin and Izmax as 5 mA and 80 mA. Design the zener regulator.
Distinguish between direct and indirect band gap semiconductors.
Fourier transform of a signum function is:
A)
2/Ω
B)
2/jΩ
C)
2/(jΩ)2
D)
-2/jΩ
The signum function is defined as sgn(t) = 1 for t > 0 and sgn(t) = -1 for t < 0. To find its Fourier Transform, we can express it as the limit of a decaying exponential: sgn(t) = lim(a→0) [e^{-at}u(t) - e^{at}u(-t)].
1. The Fourier Transform of e^{-at}u(t) is 1/(jΩ + a).
2. The Fourier Transform of -e^{at}u(-t) is -1/(jΩ - a).
3. Adding these together: F(Ω) = 1/(jΩ + a) - 1/(jΩ - a) = [(jΩ - a) - (jΩ + a)] / [(jΩ + a)(jΩ - a)] = -2a / ((jΩ)^2 - a^2).
4. However, a more direct approach for the signum function uses the duality property or the fact that sgn(t) is the derivative of |t|/2.
5. Alternatively, using the standard transform pair: The Fourier Transform of u(t) (unit step) is 1/jΩ + πδ(Ω). Since sgn(t) = 2u(t) - 1, its transform is 2[1/jΩ + πδ(Ω)] - 2πδ(Ω) = 2/jΩ.
Comparing this result to the options:
- Option (a) 2/Ω is missing the imaginary unit j.
- Option (b) 2/jΩ matches the derived result.
- Option (c) 2/(jΩ)^2 is the transform of a different function (related to t).
- Option (d) -2/jΩ is the negative of the correct transform.
What is the primary factor affecting the resistivity of a material?
A)
Voltage
B)
Temperature
C)
Current
D)
Magnetism
Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current.
1. Why Temperature is correct: For most materials, resistivity is highly dependent on temperature. In conductors (like metals), as temperature increases, the lattice ions vibrate more vigorously, increasing the frequency of collisions between charge carriers (electrons) and the lattice, thereby increasing resistivity. In semiconductors, resistivity typically decreases as temperature increases because more charge carriers are thermally excited into the conduction band.
2. Why Voltage is incorrect: According to Ohm's Law (V = IR), voltage is the driving force that causes current to flow, but it does not change the inherent resistivity of the material itself.
3. Why Current is incorrect: Current is the result of the applied voltage and the resistance of the material; it is an effect, not a cause that alters the material's intrinsic resistivity.
4. Why Magnetism is incorrect: While strong magnetic fields can influence the path of electrons (e.g., Hall Effect or magnetoresistance), magnetism is not the primary or general factor that defines the resistivity of a material in standard material science contexts compared to temperature.
Which of the following is a periodic signal?
A)
x(t) = A u(t)
B)
x(t) = A e –jbt
C)
x(t) = A e bt
D)
x(t) = A t
A signal x(t) is periodic if there exists a positive constant T such that x(t + T) = x(t) for all t.
1. Analysis of Option (b): x(t) = A e^{–jbt}. Using Euler's formula, e^{–jbt} = cos(bt) – j sin(bt). Both sine and cosine functions are periodic with a fundamental period T = 2π/b. Therefore, x(t + 2π/b) = A e^{–jb(t + 2π/b)} = A e^{–jbt} e^{–j2π} = A e^{–jbt} (1) = x(t). This signal is periodic.
2. Analysis of Option (a): x(t) = A u(t), where u(t) is the unit step function. This signal is 0 for t < 0 and A for t ≥ 0. It never repeats its values in a cyclic manner; thus, it is non-periodic.
3. Analysis of Option (c): x(t) = A e^{bt}. This is an exponential growth or decay function (depending on the sign of b). It monotonically increases or decreases and never returns to a previous value; thus, it is non-periodic.
4. Analysis of Option (d): x(t) = A t. This is a linear ramp function. As t increases, x(t) increases linearly to infinity; it does not repeat; thus, it is non-periodic.
Which type of dielectric material is commonly used in capacitors for its high dielectric constant?
A)
Air
B)
Mica
C)
Ceramic
D)
Polyester
The dielectric constant (relative permittivity, εr) determines how much electrical charge a capacitor can store for a given volume.
1. **Ceramic (Option c):** Ceramic materials are known for having very high dielectric constants, ranging from 10 to several thousands (depending on the composition, such as Barium Titanate). This allows for the production of very small capacitors with high capacitance values, making them the standard choice for high-dielectric constant applications.
2. **Air (Option a):** Air has a dielectric constant of approximately 1.0, which is the lowest possible value. It is used for precision tuning but not for high capacitance.
3. **Mica (Option b):** Mica has a dielectric constant typically between 3 and 6. While it is highly stable and used in high-voltage/high-frequency applications, its dielectric constant is significantly lower than that of ceramics.
4. **Polyester (Option d):** Polyester is a polymer with a dielectric constant typically between 3 and 3.3. It is used for general-purpose capacitors but cannot compete with the high permittivity of ceramics.
Therefore, among the given options, Ceramic is the material used specifically for its high dielectric constant.
Thevenin’s theorem with AC circuits contains ______.
A)
Resistive impedances
B)
Reactive impedances
C)
Capacitive reactance
D)
Both (a) and (b)
Thevenin's Theorem is applicable to both DC and AC circuits. In DC circuits, the theorem deals with resistance. However, in AC circuits, the components are represented by 'Impedance' (Z), which is a complex quantity. Impedance consists of two parts: the real part, which is the Resistance (R), and the imaginary part, which is the Reactance (X). Reactance can be either Inductive (XL) or Capacitive (XC). Therefore, an AC circuit analyzed via Thevenin's theorem contains both resistive impedances (resistances) and reactive impedances (inductors and capacitors). Option (a) only covers the real part, and option (b) only covers the imaginary part; thus, option (d) is the most comprehensive and correct answer as it encompasses the total impedance of the AC network.
A _____________ shift register can convert serial to parallel data:
A)
SISO
B)
SIPO
C)
PISO
D)
PIPO
A shift register is a sequential logic circuit used for the storage and transfer of data. The classification of shift registers is based on how data enters (input) and exits (output) the register:
1. **SIPO (Serial-In, Parallel-Out):** Data is fed into the register one bit at a time (serially) through a single input line. Once the register is filled, all stored bits are available simultaneously at the output pins (parallelly). Therefore, it converts serial data to parallel data.
2. **SISO (Serial-In, Serial-Out):** Data enters serially and exits serially. It acts as a delay line and does not perform data conversion.
3. **PISO (Parallel-In, Serial-Out):** Data is loaded into the register all at once (parallelly) and then shifted out one bit at a time (serially). This converts parallel data to serial data.
4. **PIPO (Parallel-In, Parallel-Out):** Data is loaded parallelly and retrieved parallelly. It is used primarily for temporary data storage (buffer) and does not perform conversion.
Which of the following is also known as the dual of Norton’s theorem?
A)
Thevenin’s theorem
B)
Superposition theorem
C)
Maximum power transfer theorem
D)
Millman’s theorem
In network theory, duality refers to the relationship between two circuits where the mesh equations of one are identical to the nodal equations of the other. Thevenin's Theorem and Norton's Theorem are duals of each other because they describe the same linear network from two different perspectives:
1. Thevenin's Theorem represents a complex network as an equivalent circuit consisting of a single voltage source (Vth) in series with a resistance (Rth). This is a voltage-source representation.
2. Norton's Theorem represents the same complex network as an equivalent circuit consisting of a single current source (In) in parallel with a resistance (Rn). This is a current-source representation.
Mathematically, they are linked by Ohm's Law: Vth = In * Rth, and the equivalent resistances are identical (Rth = Rn).
Why other options are incorrect:
- Superposition theorem: Deals with the linear addition of responses from multiple independent sources; it is not a dual of Norton's theorem.
- Maximum power transfer theorem: Describes the condition under which a load extracts maximum power from a source; it is an application of Thevenin/Norton theorems, not a dual.
- Millman's theorem: A method to simplify multiple parallel voltage sources into a single voltage source; while related to simplification, it is not the formal dual of Norton's theorem.
In an AC circuit, resistance 50 Ω, inductance 0.3 H and capacitance 15 μF is connected to an AC voltage source 25 V, 50 Hz. Determine the current in the circuit.
A)
A
B)
0.2 A
C)
0.02 A
D)
0.002 A
Option B is correct: 0.2 A.
What is the resistivity of a pure semiconductor at absolute zero?
A)
Zero
B)
Infinity
C)
Same as that of conductors at room temperature
D)
Same as that of insulators at room temperature
1. Understanding Pure Semiconductors: A pure semiconductor (intrinsic semiconductor) like Silicon or Germanium has a completely filled valence band and an empty conduction band at absolute zero (0 Kelvin).
2. Energy Gap: There is a forbidden energy gap (band gap) between the valence band and the conduction band. For an electron to contribute to electrical conduction, it must be excited from the valence band to the conduction band.
3. Effect of Absolute Zero: At 0 K, there is no thermal energy available to excite electrons across the band gap. Consequently, the conduction band remains entirely empty, and the valence band remains entirely full. Since there are no free charge carriers (electrons or holes) available to move through the crystal lattice, the material cannot conduct electricity.
4. Resistivity Calculation: Electrical conductivity (σ) is proportional to the concentration of charge carriers. At 0 K, conductivity σ = 0. Resistivity (ρ) is the reciprocal of conductivity (ρ = 1/σ). As conductivity approaches zero, resistivity approaches infinity.
Why other options are incorrect:
- Option (a) Zero: This describes a perfect conductor or a superconductor, not a semiconductor.
- Option (c) and (d): These are incorrect because the resistivity of a pure semiconductor at 0 K is far higher than that of typical conductors or standard insulators at room temperature; it behaves as a perfect insulator.
Derive the expression for ripple factor and efficiency of a half wave rectifier.
In which of the following the magnetic moments align themselves parallel to each other?
A)
Paramagnetic material
B)
Ferromagnetic material
C)
Ferrimagnetic material
D)
Diamagnetic material
The classification of materials based on their magnetic properties depends on how their atomic magnetic moments (dipoles) behave:
1. **Ferromagnetic materials (Option b):** In these materials, there is a strong positive exchange interaction that causes the magnetic moments of neighboring atoms to align themselves **parallel** to each other, even in the absence of an external magnetic field. This creates regions called 'domains' with high net magnetization. Examples include Iron (Fe), Cobalt (Co), and Nickel (Ni).
2. **Paramagnetic materials (Option a):** These materials have randomly oriented magnetic moments due to thermal agitation. They only align partially and parallel to an external field, but they do not maintain this alignment once the field is removed.
3. **Ferrimagnetic materials (Option c):** In these materials, the magnetic moments are aligned **anti-parallel** (opposite directions), but because the moments are of unequal magnitude, they do not cancel out completely, resulting in a net spontaneous magnetization. Examples include Ferrites.
4. **Diamagnetic materials (Option d):** These materials have no permanent magnetic moments. When placed in a magnetic field, they develop an induced magnetic moment in the direction **opposite** to the applied field.
In Superposition theorem, while considering a source, all other voltage sources are:
A)
open circuited
B)
short circuited
C)
change its position
D)
removed from the circuit
The Superposition Theorem states that in a linear bilateral network containing multiple independent sources, the current through (or voltage across) any element is the algebraic sum of the currents (or voltages) produced by each source acting alone, while all other independent sources are replaced by their internal resistances.
1. To 'turn off' an independent voltage source, its output voltage must be set to zero. A circuit element with zero voltage across it is a short circuit. Therefore, ideal voltage sources are replaced by a short circuit.
2. Conversely, to 'turn off' an independent current source, its output current must be set to zero. A circuit element with zero current flowing through it is an open circuit. Therefore, ideal current sources are replaced by an open circuit.
Since the question specifically asks about voltage sources, they must be short circuited.
- Option (a) is incorrect because open circuiting is for current sources.
- Option (c) is irrelevant to the theorem.
- Option (d) is imprecise; 'removed' could imply an open circuit, whereas the theorem specifically requires a short circuit for voltage sources to maintain the network's connectivity.
Determine the impulse response sequence of the dicrete time LTI system defined by y(n) - 2y(n-1) + y(n-2) = x(n) + 3x(n-3).