1. Fourier Series (Continuous-time Signals)
What is the primary purpose of representing a periodic signal using a Fourier series?

1. To convert the signal to the time domain
2. To express the signal as a sum of sinusoidal components
3. To determine the signal’s transient response
4. To compute the signal’s z-transform

Answer: b

Explanation: The Fourier series represents a periodic continuous-time signal as a sum of harmonically related sinusoids (or complex exponentials), allowing analysis of its frequency components.

2. Fourier Transform (Continuous-time Signals)
Which property of the Fourier transform ensures that the transform of a real-valued signal has conjugate symmetry?

1. Time-shifting property
2. Linearity property
3. Conjugate symmetry property
4. Scaling property

Answer: c

Explanation: For a real-valued signal x(t), its Fourier transform X(jω) satisfies X(−jω) = X∗(jω), meaning the transform has conjugate symmetry (magnitude is even, phase is odd).

3. Sampling Theorem (Continuous-time Signals)
According to the Nyquist sampling theorem, what is the minimum sampling frequency required to reconstruct a band-limited signal with a maximum frequency of 5 kHz without aliasing?

1. 5 kHz
2. 10 kHz
3. 2.5 kHz
4. 20 kHz

Answer: b

Explanation: The Nyquist sampling theorem states that the sampling frequency fs must be at least twice the maximum frequency of the band-limited signal to avoid aliasing. For a maximum frequency of 5 kHz, fs ≥ 2⋅5 = 10 kHz.

4. Sampling Theorem Applications
What is the consequence of undersampling a continuous-time signal below the Nyquist rate?

1. The signal is perfectly reconstructed
2. Aliasing occurs, causing frequency components to overlap
3. The signal becomes unstable
4. The signal’s amplitude is reduced

Answer: b

Explanation: Undersampling (sampling below the Nyquist rate) causes aliasing, where higher frequency components of the signal fold back into lower frequencies, making it impossible to reconstruct the original signal accurately.

5. Discrete-time Fourier Transform (DTFT)
What is the periodicity of the DTFT of a discrete-time signal x[n]?

1. Non-periodic
2. Periodic with period π
3. Periodic with period 2π
4. Periodic with period N

Answer: c

Explanation:

6. Discrete Fourier Transform (DFT)
Which of the following is a key characteristic of the DFT compared to the DTFT?

1. DFT is continuous in frequency
2. DFT is computed over a finite number of samples
3. DFT is non-periodic in frequency
4. DFT does not require digital processing

Answer: b

Explanation: The DFT is a finite-length version of the DTFT, computed over N samples of a discrete-time signal, resulting in N frequency points. It is discrete and periodic in both time and frequency domains.

7. Z-Transform (Discrete-time Signals)
What is the significance of the region of convergence (ROC) in the z-transform of a discrete-time signal?

1. It determines the signal’s frequency response
2. It specifies the values of z for which the z-transform converges
3. It indicates the signal’s time-domain amplitude
4. It defines the signal’s causality

Answer: b

Explanation:

8. Discrete-time Processing of Continuous-time Signals
In the process of discrete-time processing of a continuous-time signal, what role does the anti-aliasing filter play?

1. It amplifies the signal before sampling
2. It removes frequency components above half the sampling frequency
3. It converts the signal to the z-domain
4. It reconstructs the continuous-time signal from samples

Answer: b

Explanation: An anti-aliasing filter is a low-pass filter applied before sampling to remove frequency components above the Nyquist frequency (fs/2), preventing aliasing during sampling.

9. LTI Systems: Definition
What defines a Linear Time-Invariant (LTI) system?

1. Its output depends nonlinearly on the input
2. Its properties change with time
3. It satisfies linearity and time-invariance properties
4. It is only applicable to continuous-time signals

Answer: c

Explanation: An LTI system is characterized by linearity (superposition holds) and time-invariance (response does not change with time shift).

10. LTI Systems: Causality
For an LTI system to be causal, what condition must its impulse response h[n] satisfy?

1. h[n]=0 for all n
2. h[n]=0 for n<0
3. h[n]=0 for n>0
4. h[n] must be periodic

Answer: b

Explanation: A system is causal if its output at any time depends only on present and past inputs, meaning h[n]=0 for n<0.

11. LTI Systems: Stability
What is the condition for a discrete-time LTI system to be BIBO (Bounded-Input Bounded-Output) stable?

1. The impulse response must be periodic
2. The sum of the absolute values of the impulse response must be finite
3. The system must have no poles
4. The frequency response must be constant

Answer: b

Explanation:

12. Convolution (LTI Systems)
What is the significance of the convolution operation in an LTI system?

1. It computes the system’s frequency response
2. It determines the output for any input given the impulse response
3. It converts the system to a nonlinear system
4. It calculates the system’s poles and zeros

Answer: b

Explanation: Convolution is the operation used to compute the output of an LTI system from its input and impulse response.

13. Poles and Zeros (LTI Systems)
In a discrete-time LTI system, what do the poles of the transfer function H(z) indicate?

1. The frequencies where the system’s response is zero
2. The values of z where the system’s response becomes infinite
3. The time-domain amplitude of the impulse response
4. The phase delay of the system

Answer: b

Explanation: The poles are values of z where H(z) → ∞, determining system dynamics and stability.

14. Frequency Response (LTI Systems)
How is the frequency response of a discrete-time LTI system related to its impulse response?

1. It is the z-transform of the impulse response
2. It is the DTFT of the impulse response
3. It is the Laplace transform of the impulse response
4. It is the inverse of the impulse response

Answer: b

Explanation:

15. Group Delay and Phase Delay (LTI Systems)
What does the group delay of an LTI system represent?

1. The time delay experienced by the entire signal
2. The average time delay of the signal’s frequency components
3. The phase shift of the signal in radians
4. The amplitude distortion caused by the system

Answer: b

Explanation:

Q1. Energy Bands in Intrinsic Semiconductors
What is the primary characteristic of the energy band structure in an intrinsic semiconductor?

• a) The conduction band is completely filled, and the valence band is empty.
• b) The Fermi level lies approximately in the middle of the band gap.
• c) The band gap is zero, allowing free electron movement.
• d) The valence band is partially filled with electrons.

Answer: b

Explanation: In an intrinsic semiconductor (e.g., pure silicon), there are no impurities, and the electron and hole concentrations are equal. The Fermi level is located near the center of the band gap, ensuring thermal equilibrium where electrons are excited from the valence band to the conduction band at room temperature.

Q2. Extrinsic Semiconductors
What effect does doping a semiconductor with a pentavalent impurity have?

• a) It creates a p-type semiconductor with holes as majority carriers.
• b) It creates an n-type semiconductor with electrons as majority carriers.
• c) It increases the band gap of the semiconductor.
• d) It reduces the mobility of charge carriers.

Answer: b

Explanation: Pentavalent impurities (e.g., phosphorus) have five valence electrons. When doped into a semiconductor like silicon, they donate an extra electron, forming an n-type semiconductor where electrons are the majority carriers and holes are the minority carriers.

Q3. Equilibrium Carrier Concentration
In an intrinsic semiconductor, how is the equilibrium carrier concentration related to temperature?

• a) It decreases exponentially with increasing temperature.
• b) It increases exponentially with increasing temperature.
• c) It remains constant regardless of temperature.
• d) It increases linearly with temperature.

Answer: b

Explanation: The intrinsic carrier concentration ni increases exponentially with temperature due to the exponential term involving the band gap energy Eg in the equation ni ∝ exp(-Eg/2kT).

Q4. Direct and Indirect Band-gap Semiconductors
Which of the following is a key difference between direct and indirect band-gap semiconductors?

• a) Direct band-gap semiconductors have a larger band gap than indirect ones.
• b) In direct band-gap semiconductors, electron-hole recombination emits photons efficiently.
• c) Indirect band-gap semiconductors are always extrinsic.
• d) Direct band-gap semiconductors have lower carrier mobility.

Answer: b

Explanation: In direct band-gap semiconductors (e.g., GaAs), the conduction band minimum and valence band maximum align, enabling efficient photon emission during electron-hole recombination, which is ideal for LEDs and lasers.

Q5. Carrier Transport: Drift Current
What is the primary cause of drift current in a semiconductor?

• a) Random thermal motion of carriers
• b) Concentration gradient of carriers
• c) Application of an electric field
• d) Generation of electron-hole pairs

Answer: c

Explanation: Drift current arises when an electric field is applied to a semiconductor, causing charge carriers (electrons and holes) to move in response, generating current.

Q6. Carrier Transport: Diffusion Current
What drives the diffusion current in a semiconductor?

• a) An applied electric field
• b) A gradient in carrier concentration
• c) Thermal generation of carriers
• d) Recombination of electron-hole pairs

Answer: b

Explanation: Diffusion current occurs due to carrier movement from regions of high to low concentration, driven by the carrier concentration gradient.

Q7. Mobility and Resistivity
How is the resistivity of a semiconductor related to carrier mobility?

• a) Resistivity is directly proportional to mobility.
• b) Resistivity is inversely proportional to mobility.
• c) Resistivity is independent of mobility.
• d) Resistivity is equal to mobility.

Answer: b

Explanation: Resistivity ρ is the inverse of conductivity σ, and conductivity depends on carrier mobility. Thus, higher mobility leads to lower resistivity.

Q8. Generation and Recombination
What is the primary mechanism for carrier recombination in an indirect band-gap semiconductor?

• a) Direct radiative recombination
• b) Recombination via phonons or traps
• c) Auger recombination only
• d) No recombination occurs

Answer: b

Explanation: In indirect band-gap semiconductors (e.g., Si), recombination typically involves phonons or traps to conserve momentum during the process, unlike direct recombination.

Q9. Poisson Equation
What does the Poisson equation describe in the context of a semiconductor?

• a) The relationship between electric field and carrier velocity
• b) The distribution of electric potential due to charge density
• c) The rate of carrier generation and recombination
• d) The continuity of current flow

Answer: b

Explanation: The Poisson equation relates the second derivative of electric potential to the charge density in a material, critical for analyzing junctions and electric fields.

Q10. Continuity Equation
What is the primary purpose of the continuity equation in semiconductor physics?

• a) To describe the conservation of charge carriers
• b) To calculate the band gap energy
• c) To determine the mobility of carriers
• d) To model the electric field distribution

Answer: a

Explanation:

11. P-N Junction
What is the primary function of the depletion region in a P-N junction under equilibrium?
a) To allow free flow of carriers across the junction
b) To create a potential barrier that prevents carrier diffusion
c) To increase the band gap of the semiconductor
d) To generate electron-hole pairs
Answer: b
Explanation:
In a P-N junction at equilibrium, the depletion region forms due to recombination of diffused carriers, creating a space charge region with a built-in potential barrier. This barrier opposes further diffusion of majority carriers, maintaining equilibrium.

12. Zener Diode
What distinguishes a Zener diode from a regular P-N junction diode?
a) It operates primarily in the forward bias region.
b) It is designed to conduct in reverse bias under breakdown conditions.
c) It has a larger band gap than a regular diode.
d) It cannot handle high currents.
Answer: b
Explanation:
A Zener diode is heavily doped to have a sharp reverse breakdown voltage (Zener or avalanche breakdown). It is designed to operate safely in reverse bias at this breakdown voltage, used for voltage regulation.

13. Bipolar Junction Transistor (BJT)
What is the role of the base region in an NPN BJT operating in the active mode?
a) To block current flow between emitter and collector
b) To control the collector current through a small base current
c) To act as the primary source of charge carriers
d) To increase the device’s breakdown voltage
Answer: b
Explanation:
In an NPN BJT in active mode, the base-emitter junction is forward-biased, and a small base current controls a much larger collector current. The base region is thin and lightly doped to allow efficient injection of electrons from the emitter to the collector.

14. MOSFET
What is the primary advantage of a MOSFET over a BJT in integrated circuits?
a) Higher current gain
b) Lower input impedance
c) Voltage-controlled operation with negligible gate current
d) Faster switching speed in all applications
Answer: c
Explanation:
A MOSFET is a voltage-controlled device where the gate voltage controls the channel conductivity, requiring negligible gate current due to the insulated gate (oxide layer). This makes it ideal for low-power integrated circuits compared to BJTs, which require base current.

15. LED (Light Emitting Diode)
Why are direct band-gap semiconductors preferred for LEDs?
a) They have higher resistivity than indirect band-gap materials.
b) They allow efficient radiative recombination of electron-hole pairs.
c) They have a larger band gap, reducing thermal losses.
d) They support higher doping levels.
Answer: b
Explanation:
In direct band-gap semiconductors (e.g., GaAs), electron-hole recombination directly emits photons with high efficiency, as the conduction and valence band extrema align in momentum. This makes them ideal for LEDs, unlike indirect band-gap materials (e.g., Si) where recombination involves phonons and is less efficient for light emission.

1. Diode Circuits: Clipping
What is the primary function of a clipping circuit using diodes?

• a) To amplify the input signal
• b) To limit the output voltage to a specific range
• c) To shift the DC level of the signal
• d) To convert AC to DC

Answer: b

Explanation:
Clipping circuits use diodes to restrict the output voltage by clipping portions of the input signal exceeding specific thresholds.

2. Diode Circuits: Clamping
What defines the operation of a clamping circuit?

• a) It removes high-frequency components from the signal.
• b) It shifts the entire signal to a different DC level.
• c) It converts an AC signal to a DC signal.
• d) It amplifies the input signal’s amplitude.

Answer: b

Explanation:
Clamping circuits shift the DC level of an AC signal to align its peaks to a reference voltage, preserving the signal’s shape.

3. Diode Circuits: Rectifiers
What is the primary advantage of a full-wave rectifier over a half-wave rectifier?

• a) It requires fewer diodes.
• b) It produces a smoother DC output with higher frequency.
• c) It operates without a transformer.
• d) It has lower power losses.

Answer: b

Explanation:
Full-wave rectifiers convert both AC halves to DC, doubling the output frequency and reducing ripple compared to half-wave rectifiers.

4. BJT Amplifiers: Biasing
What is the primary purpose of biasing in a BJT amplifier?

• a) To increase the input signal’s amplitude
• b) To set the operating point in the active region
• c) To eliminate high-frequency noise
• d) To reduce the transistor’s power dissipation

Answer: b

Explanation:
Biasing establishes a stable DC operating point for linear amplification without distortion.

5. MOSFET Amplifiers: Biasing
Why is a MOSFET amplifier often preferred over a BJT amplifier in certain applications?

• a) It requires a higher input current for operation.
• b) It has a voltage-controlled gate with negligible DC current.
• c) It has a lower gain compared to BJT amplifiers.
• d) It operates only in the saturation region.

Answer: b

Explanation:
MOSFETs require negligible gate current, ideal for low-power and high-impedance applications.

6. BJT Amplifiers: AC Coupling
What is the role of AC coupling capacitors in a BJT amplifier?

• a) To stabilize the DC bias point
• b) To block DC signals while passing AC signals
• c) To increase the amplifier’s gain
• d) To reduce the output impedance

Answer: b

Explanation:
AC coupling capacitors isolate DC bias voltages, allowing only AC signals to pass.

7. Small Signal Analysis (BJT)
What is the key assumption in small signal analysis of a BJT amplifier?

• a) The input signal is large enough to drive the transistor into saturation.
• b) The AC signal variations are small compared to the DC bias.
• c) The transistor operates in the cutoff region.
• d) The output signal is purely DC.

Answer: b

Explanation:
Small signal analysis assumes small AC perturbations for linear modeling.

8. Frequency Response (Amplifiers)
What factor primarily limits the high-frequency response of a BJT amplifier?

• a) The DC bias voltage
• b) The parasitic capacitances of the transistor
• c) The load resistance
• d) The input signal amplitude

Answer: b

Explanation:
Parasitic capacitances cause low-pass filtering, reducing gain at high frequencies.

9. Current Mirrors
What is the primary function of a current mirror in analog circuits?

• a) To amplify the input current
• b) To replicate a reference current in another branch
• c) To stabilize the voltage across a load
• d) To filter high-frequency signals

Answer: b

Explanation:
Current mirrors copy a reference current for biasing and amplification.

10. Differential Amplifiers
What is a key advantage of a differential amplifier over a single-ended amplifier?

• a) It requires fewer transistors.
• b) It rejects common-mode signals while amplifying differential signals.
• c) It operates without a bias circuit.
• d) It has a lower input impedance.

Answer: b

Explanation:
Differential amplifiers provide high common-mode rejection for noise reduction.

11. Op-amp Circuits: Amplifiers
What characterizes an ideal operational amplifier (op-amp) in a linear amplifier configuration?

1. Finite open-loop gain and limited bandwidth
2. Infinite input impedance and zero output impedance
3. Zero input offset voltage and infinite slew rate
4. Non-inverting input always grounded

Answer: b
Explanation: Ideal op-amps have infinite input impedance and zero output impedance for precise amplification.

12. Op-amp Circuits: Integrators
What is the primary function of an op-amp integrator circuit?

1. To amplify the input signal’s amplitude
2. To produce an output proportional to the time integral of the input
3. To differentiate the input signal
4. To filter low-frequency signals

Answer: b
Explanation: Integrators output a voltage proportional to the integral of the input voltage.

13. Op-amp Circuits: Active Filters
What is the advantage of using an op-amp in an active filter compared to a passive filter?

1. Active filters require no external power supply.
2. Active filters provide gain and better frequency selectivity.
3. Active filters are simpler to design.
4. Active filters have infinite bandwidth.

Answer: b
Explanation: Active filters offer gain and sharper responses without bulky inductors.

14. Op-amp Circuits: Schmitt Triggers
What is the primary characteristic of a Schmitt trigger circuit using an op-amp?

1. It produces a linear output proportional to the input.
2. It exhibits hysteresis in its voltage transfer characteristic.
3. It integrates the input signal over time.
4. It generates a sinusoidal output.

Answer: b
Explanation: Schmitt triggers use positive feedback for hysteresis, enhancing noise immunity.

15. Op-amp Circuits: Oscillators
What is the key requirement for an op-amp oscillator to sustain oscillations?

1. The loop gain must be less than unity.
2. The phase shift around the feedback loop must be zero or 360 degrees.
3. The input signal must be DC.
4. The op-amp must operate in the linear region.

Answer: b
Explanation: The Barkhausen criterion requires unity loop gain and a 0°/360° phase shift.

Q1. Number Representations: Binary
What is the primary advantage of using two’s complement representation for signed integers in digital systems?

• a) It simplifies addition and subtraction operations.
• b) It eliminates the need for a sign bit.
• c) It allows representation of only positive numbers.
• d) It increases the precision of floating-point numbers.

Answer: a
Explanation:
Two’s complement representation simplifies arithmetic operations, particularly addition and subtraction, as it allows both positive and negative integers to be handled uniformly without requiring special operations for the sign bit.

Q2. Number Representations: Floating-Point Numbers
What is the role of the exponent in a floating-point number representation?

• a) To determine the precision of the number
• b) To scale the mantissa to the appropriate magnitude
• c) To indicate the sign of the number
• d) To represent the integer part of the number

Answer: b
Explanation:
The exponent in floating-point representation scales the mantissa by shifting its decimal point, enabling the representation of a wide range of magnitudes, both very large and very small.

Q3. Combinatorial Circuits: Boolean Algebra
Which Boolean identity is used to simplify the expression ( A + A.B )?

• a) Idempotent law: ( A + A = A )
• b) Absorption law: ( A + A.B = A )
• c) Distributive law: ( A.(B + C) = A.B + A.C )
• d) De Morgan’s law

Answer: b
Explanation:
The absorption law simplifies Boolean expressions by eliminating redundant terms. In this case, A+A⋅B simplifies directly to A.

Q4. Combinatorial Circuits: Karnaugh Map
What is the primary purpose of a Karnaugh map in digital circuit design?

• a) To design sequential circuits
• b) To minimize Boolean functions by grouping minterms
• c) To convert binary numbers to decimal
• d) To analyze the timing of flip-flops

Answer: b
Explanation:
Karnaugh maps (K-maps) help simplify Boolean expressions by visually grouping adjacent minterms, which leads to minimized logic circuits.

Q5. Combinatorial Circuits: Logic Gates (CMOS)
What is a key advantage of static CMOS logic gate implementations?

• a) They consume power only during switching transitions.
• b) They require fewer transistors than NMOS logic.
• c) They are inherently resistant to noise.
• d) They operate without a power supply.

Answer: a
Explanation:
Static CMOS gates consume very low static power, and significant power is only consumed during switching transitions (when the gate changes states).

Q6. Combinatorial Circuits: Arithmetic Circuits
What is the primary function of a full adder circuit?

• a) To add two binary digits without considering carry-in
• b) To add three binary inputs, producing a sum and carry-out
• c) To subtract two binary numbers
• d) To multiply two binary digits

Answer: b
Explanation:
A full adder handles three inputs for multi-bit binary addition.

Q7. Combinatorial Circuits: Multiplexers
What is the role of a multiplexer in a digital circuit?

• a) To decode a binary input into multiple outputs
• b) To select one of multiple input signals based on a control signal
• c) To store data in a memory element
• d) To generate a clock signal

Answer: b
Explanation:
A multiplexer routes one of several inputs to the output based on select lines.

Q8. Sequential Circuits: Latches vs. Flip-Flops
What distinguishes a flip-flop from a latch in sequential circuits?

• a) A latch is edge-triggered, while a flip-flop is level-sensitive.
• b) A flip-flop is edge-triggered, while a latch is level-sensitive.
• c) A latch requires a clock signal, while a flip-flop does not.
• d) A flip-flop stores multiple bits, while a latch stores one bit.

Answer: b
Explanation:
Flip-flops update on clock edges, while latches respond to enable signal levels.

Q9. Sequential Circuits: Counters
What defines a ripple counter?

• a) All flip-flops are triggered simultaneously by the same clock.
• b) Each flip-flop is triggered by the output of the previous flip-flop.
• c) It counts only in the downward direction.
• d) It requires no clock signal.

Answer: b
Explanation:
Ripple counters are asynchronous, with flip-flops triggered sequentially.

Q10. Sequential Circuits: Timing Parameters
What does the setup time in a flip-flop represent?

• a) The duration required for the output to settle after a clock transition
• b) The minimum interval for which the input must remain stable prior to the active clock edge
• c) The delay experienced between the clock signal and the resulting output
• d) The highest frequency at which the flip-flop can function correctly

Answer: b
Explanation:
Setup time is critical for ensuring that the input data is correctly captured by the flip-flop; the input must remain stable for this minimum duration before the clock edge for proper latching.

Q11. Data Converters: Sample and Hold Circuits
What is the primary function of a sample and hold circuit in an ADC?

• a) To amplify the analog input signal
• b) To maintain a constant analog voltage during conversion
• c) To convert digital signals to analog
• d) To filter high-frequency noise

Answer: b
Explanation:
A sample and hold circuit captures the analog input at a specific moment and holds it steady, ensuring that the ADC receives a constant voltage for accurate digital conversion.

Q12. Data Converters: ADCs
What is a key characteristic of a flash ADC compared to other ADC types?

• a) It is the slowest but most accurate.
• b) It uses a single comparator for conversion.
• c) It is the fastest but requires many resistors or comparators.
• d) It operates without a clock signal.

Answer: c
Explanation:
Flash ADCs use parallel comparators for high speed but are complex.

Q13. Semiconductor Memories: SRAM vs. DRAM
What distinguishes SRAM from DRAM in semiconductor memories?

• a) SRAM requires periodic refreshing, while DRAM does not.
• b) SRAM uses flip-flops, while DRAM uses capacitors to store data.
• c) SRAM is slower but cheaper than DRAM.
• d) SRAM is volatile, while DRAM is non-volatile.

Answer: b
Explanation:
SRAM is faster but costlier; DRAM requires refreshing.

Q14. Computer Organization: Addressing Modes
What is the primary advantage of the register addressing mode in a CPU?

• a) It allows direct access to memory locations.
• b) It is the fastest as it uses registers within the CPU.
• c) It supports complex memory calculations.
• d) It requires no instruction decoding.

Answer: b
Explanation:
Register addressing is fast due to direct register access.

Q15. Computer Organization: Instruction Pipelining
What is a pipeline hazard in instruction pipelining?

• a) An increase in the clock frequency of the CPU
• b) A situation that prevents the next instruction from executing in its designated clock cycle
• c) A failure in the ALU to perform arithmetic operations
• d) An overflow in the memory address space

Answer: b
Explanation:
Pipeline hazards (data, control, structural) cause delays in instruction execution.

Q16. Combinatorial Circuits: Logic Gates and Minimization
Which of the following statements are true about combinatorial circuits?

• a) Boolean algebra can be used to simplify logic expressions.
• b) A Karnaugh map guarantees the most simplified form of a Boolean function.
• c) Static CMOS logic gates consume power only during switching transitions.
• d) A multiplexer can only be used to select between two input signals.

Answer: a, c
Explanation:
a) True: Boolean algebra simplifies logic expressions.
b) False: Karnaugh maps help simplify expressions but may not always provide the simplest form.
c) True: Static CMOS gates consume power primarily during switching transitions, making them efficient.
d) False: A multiplexer can select between multiple input signals, not just two.

Q17. Sequential Circuits: Timing and State Machines
Which of the following are true regarding sequential circuits?

• a) The setup time is the minimum time the input must be stable before the clock edge.
• b) A finite state machine can have multiple states but only one output.
• c) Propagation delay is the time taken for the output to change after a clock edge.
• d) A shift-register can only shift data in one direction.

Answer: a, c
Explanation:
a) True: The setup time ensures that the input is stable before the clock edge, allowing proper data capture.
b) False: A finite state machine (FSM) can have multiple outputs based on its states.
c) True: Propagation delay refers to the time it takes for the output to change after a clock edge is applied.
d) False: Shift registers can shift data in both directions (serial-in serial-out or serial-in parallel-out).

Q1. The divergence of the magnetic flux density 𝐵⃗ is always:

• a) Zero
• b) Infinite
• c) Equal to charge density
• d) Time dependent

Answer: a)
Explanation:
According to Maxwell's equations, ∇·𝐵 = 0 because magnetic monopoles do not exist.

Q2. The time-varying electric field in free space will always produce:

• a) A constant magnetic field
• b) A current
• c) A time-varying magnetic field
• d) An electric dipole

Answer: c)
Explanation:
Faraday’s Law states that a changing electric field induces a changing magnetic field.

Q3. The boundary condition for the tangential component of the electric field across the interface of two dielectric media is:

• a) It is discontinuous
• b) It must be zero
• c) It is continuous
• d) It is equal to the permittivity ratio

Answer: c)
Explanation:
The tangential electric field remains continuous across dielectric boundaries.

Q4. In a lossless transmission line, the characteristic impedance is defined as:

• a) L/C
• b) C/L
• c) √(LC)
• d) 1/(LC)

Answer: a)
Explanation:
For a lossless transmission line, Z₀ = √(L/C).

Q5. The electric field in a plane wave propagating in free space is oriented along the x-axis. The magnetic field will be oriented along which axis?

• a) x-axis
• b) y-axis
• c) z-axis
• d) Parallel to the electric field

Answer: b)
Explanation:
For a plane wave in free space, the electric field, magnetic field, and direction of propagation are mutually perpendicular. If the electric field is along the x-axis, the magnetic field will be along the y-axis, and the direction of propagation will be along the z-axis.

Q6. The Poynting vector represents:

• a) Magnetic energy density
• b) Electric field potential
• c) Power flow per unit area
• d) Losses in dielectric medium

Answer: c)
Explanation:
S⃗ = E⃗ × H⃗ gives power flow per unit area.

Q7. The skin depth of a wave in a conductor:

• a) Decreases with frequency
• b) Increases with frequency
• c) Is independent of frequency
• d) Depends only on permittivity

Answer: a)
Explanation:
Skin depth δ ∝ 1/√f; higher frequency leads to lower skin depth.

Q8. Which of the following boundary conditions is correct for the normal component of D⃗?

• a) Discontinuous by a factor of conductivity
• b) Always zero
• c) Discontinuous due to surface charge
• d) Continuous across any boundary

Answer: c)
Explanation:
D₁n - D₂n = ρs, where ρs is surface charge density.

Q9. In microwave engineering, the primary function of a waveguide is to:

• a) Amplify microwave signals
• b) Convert microwave signals from one frequency to another
• c) Propagate microwave signals with minimal loss
• d) Convert DC signals into AC microwave signals

Answer: c)
Explanation:
Waveguides are used to propagate microwave signals with minimal loss by confining the electromagnetic waves to a particular path.

Q10. The Smith chart is used to:

• a) Calculate wave speed
• b) Match impedance
• c) Plot magnetic field lines
• d) Analyze polarization

Answer: b)
Explanation:
The Smith chart is used for impedance matching in RF circuits.

Q11. A linear array of antennas is used to achieve:

• a) Uniform radiation in all directions
• b) A directional radiation pattern
• c) A circular polarization pattern
• d) A perfect isotropic radiation pattern

Answer: b)
Explanation:
A linear array of antennas can be designed to produce a directional radiation pattern by arranging the antennas in a straight line.

Q12. Which of the following is the primary principle behind the operation of optical fibers?

• a) Diffraction
• b) Total internal reflection
• c) Refraction
• d) Dispersion

Answer: b)
Explanation:
Optical fibers operate on the principle of total internal reflection, where light is confined within the fiber core due to the difference in refractive indices.

Q13. The group velocity of an electromagnetic wave is defined as:

• a) The speed at which the energy or information is transmitted
• b) The speed at which the phase of the wave propagates
• c) The rate at which the electric field oscillates
• d) The velocity of the magnetic field component of the wave

Answer: a)
Explanation:
The group velocity represents the speed at which the energy or information associated with the wave propagates through a medium.

Q14. In rectangular waveguides, TE10 mode is dominant because:

• a) It has the lowest frequency cutoff
• b) It has uniform field lines
• c) It propagates in all directions
• d) It is the only mode possible

Answer: a)
Explanation:
TE10 mode has the lowest cutoff frequency and dominates propagation.

Q15. The reflection coefficient at a short-circuited load is:

• a) +1
• b) –1
• c) 0
• d) ∞

Answer: b)
Explanation:
At a short circuit, all incident energy is reflected with a 180° phase shift, resulting in a reflection coefficient of -1.

Q16. Which of the following are true for a lossless transmission line?

• a) Voltage and current vary sinusoidally
• b) No attenuation of wave
• c) Complex propagation constant
• d) Real characteristic impedance

Answer: a), b), d)
Explanation:
Lossless lines have real impedance, sinusoidal waveforms, and zero attenuation.

Q17. The conditions for total internal reflection in optical fiber are:

• a) Light must travel from high to low refractive index
• b) Angle of incidence must be greater than the critical angle
• c) Medium must be lossy
• d) Refractive indices must be equal

Answer: a), b)
Explanation:
Total internal reflection occurs when light moves from a denser to rarer medium with a high incidence angle.

Q18. Consider a uniform plane wave traveling through a perfect dielectric. Which of the following hold true?

• a) Wave propagates with constant velocity
• b) No energy is dissipated
• c) Electric and magnetic fields are perpendicular
• d) Skin effect dominates

Answer: a), b), c)
Explanation:
In a perfect dielectric, EM waves propagate with no loss and orthogonal E and H fields.

Q1. In a unity feedback system, if the open-loop transfer function is G(s)=10/(s(s+2)), the type and steady-state error for a unit ramp input are:

• a) Type 1, zero error
• b) Type 1, finite error
• c) Type 0, infinite error
• d) Type 2, zero error

Answer: b
Explanation:
Type 1 system has finite error for ramp input. Error constant 〖K_v=〗⁡〖lim〖_(s→0)〗〗 sG(s)

Q2. The phase crossover frequency in Bode plot corresponds to:

• a) Gain = 1
• b) Phase = 0°
• c) Phase = –180°
• d) Phase = –90°

Answer: c
Explanation:
Phase crossover frequency is where phase reaches –180°, important for Nyquist criterion.

Q3. Which of the following leads to reduced bandwidth in frequency response?

• a) Adding a lead compensator
• b) Adding a lag compensator
• c) Increasing system gain
• d) Decreasing system pole

Answer: b
Explanation:
Lag compensators slow down the system response, thus reduce bandwidth.

Q4. Which of the following is true for lead compensation?

• a) Increases rise time
• b) Decreases bandwidth
• c) Improves phase margin
• d) Decreases gain margin

Answer: c
Explanation:
Lead compensators improve phase margin and speed of response.

Q5. The system defined by x˙=Ax is marginally stable if:

• a) All eigenvalues of A have positive real parts
• b) Some eigenvalues have positive real parts
• c) All eigenvalues have non-positive real parts and at least one purely imaginary
• d) All eigenvalues are zero

Answer: c
Explanation:
Marginal stability requires no poles in RHP, and at least one on jω-axis without multiplicity.

Q6. Which is correct about the signal flow graph and Mason’s gain formula?

• a) Applies only to first-order systems
• b) Works only for feedback systems
• c) Gives closed-loop transfer function
• d) Ignores forward paths

Answer: c
Explanation:
Mason’s formula is used to compute overall transfer function from SFG.

Q7. The root locus of a system shifts to the left when:

• a) A zero is added in LHP
• b) A pole is added in LHP
• c) A zero is added in RHP
• d) Gain is decreased

Answer: a
Explanation:
LHP zeros improve transient response by shifting root locus leftward.

Q8. In state-space form, controllability implies:

• a) State variables can be observed
• b) All states can be made zero
• c) States can be reached with appropriate input
• d) Eigenvalues are stable

Answer: c
Explanation:
Controllability means you can drive the system to any state using input.

Q9. Bode plot of a minimum-phase system has:

• a) Constant phase margin
• b) Monotonic phase response
• c) Phase lead only
• d) Negative phase shift always

Answer: b
Explanation:
Minimum-phase systems have monotonically decreasing phase.

Q10. In frequency response analysis, a phase margin of 45° indicates:

• a) The system is marginally stable
• b) The system has poor transient response
• c) The system has good relative stability
• d) The system is unstable

Answer: c
Explanation:
A phase margin of 45° suggests that the system has good relative stability and acceptable transient response.

Q11. The Routh-Hurwitz criterion is used to determine:

• a) The exact location of system poles
• b) The time response of a system
• c) The stability of a system without computing poles
• d) The frequency response of a system

Answer: c
Explanation:
The Routh-Hurwitz criterion allows for the assessment of system stability by examining the sign changes in the first column of the Routh array, without explicitly calculating the poles.

Q12. A system has an open-loop transfer function with unity feedback. To improve the steady-state error without significantly affecting the transient response, a lag compensator is added. Which statement best describes the effect of the lag compensator on the Bode plot and system performance?

• a) It increases the gain crossover frequency, improving phase margin.
• b) It adds gain at low frequencies, reducing steady-state error.
• c) It shifts the phase plot upward, reducing stability margins.
• d) It reduces the bandwidth, increasing the settling time.

Answer: b
Explanation:

Q13. Which of the following conditions ensure a stable LTI system?

• a) All poles in left-half s-plane
• b) Closed-loop poles with negative real parts
• c) Transfer function has no zeros
• d) All roots of characteristic equation have positive imaginary parts

Answer: a), b)
Explanation:
Stability requires poles in LHP or CL poles with negative real parts.

Q14. Lead compensator offers which advantages?

• a) Improves phase margin
• b) Reduces steady-state error
• c) Increases bandwidth
• d) Reduces gain crossover frequency

Answer: a), c)
Explanation:
Lead increases system speed, phase margin, bandwidth.

Q15. Which of the following statements are true for Nyquist stability criterion?

• a) Based on frequency response
• b) Can be used for discrete systems
• c) Requires number of encirclements of –1 point
• d) Needs open-loop poles in LHP only

Answer: a), c)
Explanation:
Nyquist criterion checks encirclements of –1 using open-loop FRF and number of RHP poles.

Q1. Which of the following statements accurately defines the autocorrelation function of a random signal?

• a) It is the Fourier transform of the power spectral density
• b) It measures the similarity between a signal and its time-shifted version
• c) It is the convolution of the signal with itself
• d) It is the derivative of the power spectral density

Answer: b
Explanation:
The autocorrelation function quantifies how similar a signal is to itself at different time shifts.

Q2. In amplitude modulation (AM), the carrier frequency is generally:

• a) Much higher than the message signal frequency
• b) Zero
• c) Equal to the signal frequency
• d) Much lower than the message signal frequency

Answer: a
Explanation:
The carrier frequency in AM is significantly higher than the message signal frequency to enable effective transmission.

Q3. Which of the following describes the noise figure (NF) of a system?

• a) It quantifies how much noise is introduced by the system
• b) It measures the power dissipated in the system
• c) It indicates the ability of the system to reduce noise
• d) It shows how much distortion the system introduces

Answer: a
Explanation:
Noise figure is a measure of the noise added by the system, which degrades the signal-to-noise ratio (SNR).

Q4. What does the power spectral density of a signal represent?

• a) The rate at which information is transmitted by the signal
• b) How the signal’s power is distributed across various frequencies
• c) The distortion in the signal due to noise
• d) The amplitude of the signal at each frequency

Answer: b
Explanation:
Power spectral density describes the distribution of signal power across different frequency components.

Q5. The bandwidth of an FM signal is primarily determined by:

• a) The carrier frequency
• b) The message signal's amplitude
• c) The frequency deviation and the bandwidth of the modulating signal
• d) The noise level in the system

Answer: c
Explanation:
FM bandwidth depends on both the frequency deviation and the bandwidth of the modulating signal.

Q6. In a superheterodyne receiver, the intermediate frequency (IF) serves to:

• a) Simplify the process of frequency conversion and filtering
• b) Increase the system's signal-to-noise ratio
• c) Directly demodulate the signal
• d) Decrease the overall bandwidth of the received signal

Answer: a
Explanation:
The IF helps in simplifying the process of signal amplification and filtering, which is key for effective demodulation.

Q7. In Shannon's channel capacity theorem, the channel capacity represents:

• a) The bandwidth of the communication channel
• b) The maximum rate at which information can be transmitted error-free
• c) The amount of noise present in the channel
• d) The total power transmitted through the channel

Answer: b
Explanation:
Channel capacity is the maximum achievable data rate for error-free communication, as described by Shannon's theorem.

Q8. Which modulation scheme is the most bandwidth-efficient?

• a) Amplitude Shift Keying (ASK)
• b) Quadrature Amplitude Modulation (QAM)
• c) Frequency Shift Keying (FSK)
• d) Phase Shift Keying (PSK)

Answer: b
Explanation:
QAM offers a higher bandwidth efficiency by combining both amplitude and phase modulation.

Q9. The advantage of differential PCM (DPCM) over regular PCM is that it:

• a) Reduces the bandwidth required for transmission
• b) Has a higher signal-to-noise ratio
• c) Simplifies the receiver design
• d) Increases the error correction capability

Answer: a
Explanation:
DPCM encodes the difference between successive samples, thereby reducing the bandwidth requirement compared to standard PCM.

Q10. The purpose of a matched filter receiver in communication systems is to:

• a) Maximize the signal-to-noise ratio (SNR)
• b) Increase the bandwidth of the received signal
• c) Minimize the error rate in the channel
• d) Filter out higher-frequency noise

Answer: a
Explanation:
The matched filter is designed to maximize the SNR for detecting a known signal in noise.

Q11. The probability of error in binary phase-shift keying (BPSK) is minimized by:

• a) Increasing the signal power
• b) Reducing the modulation index
• c) Increasing the signal bandwidth
• d) Changing the carrier frequency

Answer: a
Explanation:
Increasing the signal power helps in reducing the probability of error in BPSK by making the signal more distinguishable from noise.

Q12. In information theory, entropy measures:

• a) The efficiency of the modulation scheme
• b) The uncertainty or randomness of a message source
• c) The rate of information transmission
• d) The channel capacity

Answer: b
Explanation:
Entropy quantifies the amount of uncertainty or randomness associated with a source of information.

Q13. The modulation index in frequency modulation (FM) is determined by:

• a) The ratio of frequency deviation to the signal’s bandwidth
• b) The ratio of the frequency deviation to the modulating signal frequency
• c) The ratio of the message signal frequency to the carrier frequency
• d) The ratio of the carrier frequency to the signal frequency

Answer: b
Explanation:
The modulation index in FM is the ratio of the frequency deviation to the frequency of the modulating signal.

Q14. In a Pulse Code Modulation (PCM) system, the signal is quantized into:

• a) Discrete time intervals
• b) Continuous levels
• c) Discrete amplitude levels
• d) Continuous time intervals

Answer: c
Explanation:
PCM involves quantizing the amplitude of the signal into discrete levels for digitization.

Q15. Mutual information in a communication system measures:

• a) The error probability in the system
• b) The amount of information one variable provides about another
• c) The system’s signal-to-noise ratio
• d) The bandwidth efficiency of a modulation scheme

Answer: b
Explanation:
Mutual information quantifies the reduction in uncertainty of one variable due to knowledge of the other.

Q16. Which of the following statements are true regarding white noise?

• a) White noise has constant power spectral density across all frequencies
• b) White noise is always periodic in nature
• c) The autocorrelation of white noise is a delta function
• d) White noise contains only low-frequency components

Answers: a), c)
Explanation:
White noise has a flat (constant) power spectral density and a delta autocorrelation. It is not periodic and contains all frequencies.

Q17. Which statements are correct regarding Amplitude Modulation (AM)?

• a) In DSB-SC AM, the carrier is transmitted along with the sidebands
• b) The total bandwidth required for AM is twice the message bandwidth
• c) In AM, the carrier contains all the information
• d) The envelope of AM signal carries the message

Answers: b), d)
Explanation:
In AM, total bandwidth is 2 × message bandwidth. The envelope carries the message, not the carrier itself. DSB-SC does not transmit the carrier.

Q18. Which of the following are true for Hamming codes used in digital communications?

• a) They can correct single-bit errors and detect two-bit errors
• b) They require fewer parity bits as the message length increases
• c) They are based on linear block codes
• d) They are primarily used for analog signals

Answers: a), c)
Explanation:
Hamming codes are linear block codes capable of single-error correction and two-bit error detection. They're used in digital systems, and longer messages typically require more parity bits.

Why prioritize basic questions?

• • They reinforce conceptual clarity.
• • They serve as stepping stones to higher-level problem-solving.
• • Most tricky questions are just layered applications of basic ideas.
• • A clear understanding of these basics not only helps in solving difficult questions with ease but also improves accuracy and confidence.