AP PGECET 2024 Electronics and Communication Engineering Question Paper with Answer Key PDF

Identify the Y equivalent of a network of the circuit shown in Figure below.

The mesh current method

• (I) Works with both planar and non-planar circuits
• (1) I and II
• (2) II only
• (3) I only
• (4) Neither I nor II

If there are 5 branches and 4 nodes in the graph, then the number of mesh equations that can be formed are?

• (1) 2
• (2) 4
• (3) 6
• (4) 8

The current waveform \(i(t)\) in a pure resistor of 20 \( \Omega \) is as shown in the figure below, then the power dissipated in the resistor is

• (1) 135W
• (2) 540W
• (3) 270W
• (4) 14.58W

In the following figure, \(C_1\) and \(C_2\) are ideal capacitors. \(C_1\) has been charged to 12V before the ideal switch \(S\) is closed at \(t = 0\). The current \(i(t)\) for all \(t\) is

• (1) Zero
• (2) An impulse function
• (3) An exponentially decaying function
• (4) A step function

Among the four networks, N1, N2, N3, and N4, given in the following figure, the networks having identical driving point function are

• (1) N1 and N2
• (2) N2 and N4
• (3) N1 and N3
• (4) N1 and N4

The 2-port admittance matrix of the circuit shown is given by

• (1) \(\begin{bmatrix} 15 & 5
  5 & 15 \end{bmatrix}\)
• (2) \(\begin{bmatrix} 1 & 0
  0 & 1 \end{bmatrix}\)
• (3) \(\begin{bmatrix} 0.3 & 0.2
  0.2 & 0.3 \end{bmatrix}\)
• (4) \(\begin{bmatrix} 3.33 & 5
  5 & 3.33 \end{bmatrix}\)

In superposition theorem, when we consider the effect of one voltage source, all the other current sources are

• (1) Shorted
• (2) Opened
• (3) Removed
• (4) Undisturbed

The circuit shown in Figure is equivalent to a load of

• (1) \(\frac{4}{3}\) Ohms
• (2) 4 Ohms
• (3) \(\frac{8}{3}\) Ohms
• (4) 2 Ohms

The current through a series RL circuit is \( \frac{1}{4} e^{-\frac{3}{4} t} \) when excited by a unit impulse voltage. The values of R and L are respectively

• (1) 8, 4
• (2) 4, 2
• (3) 2, 4
• (4) 1, 4

If \( E_p \) (Fermi energy level) \( > E_f \) (intrinsic Fermi energy level), then the type of semiconductor is

• (1) n-type
• (2) Elementary
• (3) p-type
• (4) Compound

In the circuit shown below, the Zener diode is ideal and Zener voltage is 6V. The output voltage \( V_o \) (in volts) is

• (1) 2.5V
• (2) 5V
• (3) 6V
• (4) 3V

Which process of the Electron-hole pair is responsible for emitting of light?

• (1) Gradient
• (2) Drift
• (3) Recombination
• (4) Diffusion

In MOSFET fabrication, the channel length is defined during the process of

• (1) Isolation oxide growth
• (2) Channel stop implantation
• (3) Poly-silicon gate patterning
• (4) Lithography step leading to the contact pads

How does a FET behave when the V-I characteristics are to the left of pinch off for an n-channel FET?

• (1) Voltage controlled resistor
• (2) Amplifier
• (3) Switch
• (4) Diode

The direction of the diffusion current depends on

• (1) Applied field
• (2) Mobility of charge carrier
• (3) Charge carrier concentration
• (4) Permittivity

Match items in Group-I with items in Group-II, most suitably.

• (1) P - 1, Q - 2, R - 4, S - 3
• (2) P - 2, Q - 3, R - 1, S - 4
• (3) P - 3, Q - 4, R - 1, S - 2
• (4) P - 2, Q - 1, R - 4, S - 3

A silicon PN junction diode is forward biased with a constant current at room temperature carrying a constant current of 1 mA. When the temperature is increased by 10°C, the forward bias voltage across the PN junction is approximately equal to

• (1) Increases by 60 mV
• (2) Increases by 25 mV
• (3) Decreases by 60 mV
• (4) Decreases by 25 mV

The early effect in a bipolar junction transistor is caused by

• (1) Fast turn-on
• (2) Large collector-base reverse bias
• (3) Fast turn-off
• (4) Large emitter-base forward bias

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces

• (1) Superior quality oxide with a higher growth rate
• (2) Inferior quality oxide with a higher growth rate
• (3) Inferior quality oxide with a lower growth rate
• (4) Superior quality oxide with a lower growth rate

If P is Passivation, Q is n-well implant, R is metallization and S is source/drain diffusion, then the order in which they are carried out in a standard n-well CMOS fabrication process, is

• (1) P - Q - R - S
• (2) Q - S - R - P
• (3) R - P - S - Q
• (4) S - R - Q - P

Let R denote the responsivity of a PIN photodetector and \(\lambda\) is the wavelength. Figure of merit for the photo detector is quantum efficiency. The expression for quantum efficiency \(\mu\) is given by

• (1) \(\mu = \frac{12.4R}{\lambda}\)
• (2) \(\mu = \frac{12400R}{\lambda}\)
• (3) \(\mu = \frac{1.24R}{\lambda}\)
• (4) \(\mu = \frac{0.124R}{\lambda}\)

For an N-channel enhancement-type MOSFET, if the source is connected at a higher potential than that of the bulk (i.e., VSB > 0), the threshold voltage \( V_{th} \) of the MOSFET will

• (1) Remains unchanged
• (2) Decreases
• (3) Change in polarity
• (4) Increases

The phenomenon known as "early effect" in a bipolar transistor refers to a reduction of the effective base width caused by

• (1) Electron-hole recombination at the base
• (2) The reverse biasing of the base-collector junction
• (3) The forward biasing of emitter-base junction
• (4) The early removal of stored base charge during saturation to cut-off switching

The DC current gain (\( \beta \)) of a BJT is 50. Assuming that the emitter injection efficiency is 0.995, the base transport factor is

• (1) 0.985
• (2) 0.990
• (3) 0.980
• (4) 0.995

A circuit that uses an amplifier with passive filter elements is called as a(n)

• (1) Relaxation oscillator
• (2) Signal generator
• (3) Differential amplifier
• (4) Active filter

If the input to a comparator is a sine wave, the output is

• (1) Ramp voltage
• (2) Sine wave
• (3) Rectangular wave
• (4) Sawtooth wave

In the silicon BJT circuit shown below, assume that emitter area of transistor Q1 is half that of transistor Q2, then what is the value of the current \( I_o \) is approximately

• (1) 0.5 mA
• (2) 9.3 mA
• (3) 2.0 mA
• (4) 15 mA

Three identical amplifiers with each one having a voltage gain of 50, input resistance of 1 kΩ and output resistance of 250 Ω are cascaded. The open circuit voltage gain of the combined amplifier is

• (1) 49 dB
• (2) 102 dB
• (3) 98 dB
• (4) 51 dB

Which of the following statements are true?

P: JFET is biased to operate it in active region

Q: MOSFET is biased to operate it in saturation region

• (1) Both P and Q are correct
• (2) P is correct and Q is incorrect
• (3) P is incorrect and Q is correct
• (4) Both P and Q are incorrect

In the circuit shown in the following Figure, what is the output voltage (\( V_{out} \)) if a silicon transistor Q and an ideal op-amp are used?

• (1) -15 V
• (2) -0.7 V
• (3) +0.7 V
• (4) +15 V

In Wien's bridge oscillator, if \( R_1 = R_2 \) and \( C_1 = C_2 \), then the typical values of open loop gain and feedback factor to obtain the sustained oscillations are

• (1) 1, 1
• (2) \( \infty, 0 \)
• (3) 1, \( \frac{1}{2} \)
• (4) \( \frac{3}{2}, \frac{1}{3} \)

A negative going trigger pulse is applied to pin 2 of the IC 555 timer, passes through the threshold level of

• (1) \( \frac{V_{CC}}{3} \) and sets the Flip-flop
• (2) \( \frac{V_{CC}}{3} \) and resets the Flip-flop
• (3) \( \frac{2V_{CC}}{3} \) and sets the Flip-flop
• (4) \( \frac{2V_{CC}}{3} \) and resets the Flip-flop

An amplifier has \( A_v = 1000 \pm 100 \). Determine the feedback needed to keep the gain within \( \pm 10% \).

• (1) 0.099
• (2) 1.000
• (3) 1.100
• (4) 10.00

How to achieve 50% duty cycle in adjustable rectangular wave generator? (Assume \( R_1 \) is Resistor connected between supply and discharge and \( R_2 \) is Resistor connected between discharge and trigger input.)

• (1) \( R_1 < R_2 \)
• (2) \( R_1 > R_2 \)
• (3) \( R_1 = R_2 \)
• (4) \( R_1 \geq R_2 \)

Simplify the following expression with A, B, C three variables, \( F(A, B, C) = \Sigma(1, 3, 5, 7) \)

• (1) \( \overline{A}C + AB \)
• (2) A
• (3) B
• (4) C

The decimal equivalent of \( (101111.1101)_2 \) is

• (1) 52.6789
• (2) 38.6254
• (3) 47.8125
• (4) 51.6328

Which of the following circuit is used as a special signal to demultiplex the address bus and data bus?

• (1) Priority Encoder
• (2) Decoder
• (3) Address Latch Enable
• (4) Demultiplexer

The number of memory cycles required to execute the 8085 instruction LDA 3000 H is

• (1) 4
• (2) 2
• (3) 3
• (4) 5

The POS form is suitable for circuits using

• (1) NOR
• (2) AND
• (3) XOR
• (4) NAND

\( A + A.B + A.B.C + A.B.C.D \) simplifies to

• (1) \( A + D \)
• (2) \( A + C' \)
• (3) \( A + B \)
• (4) \( A \)

The minimum number of comparators required to build an eight-bit flash ADC is

• (1) 8
• (2) 255
• (3) 256
• (4) 64

The logic function implemented by the circuit shown in the Figure below is (ground implies a logic '0')

• (1) \( F = XOR(P, Q) \)
• (2) \( F = OR(P, Q) \)
• (3) \( F = XNOR(P, Q) \)
• (4) \( F = AND(P, Q) \)

The number of memory cycles required to execute the following 8085 instructions

I. STA 3000 H

II. LXI D, 3000 H

• (1) 4 for (I) and 4 for (II)
• (2) 4 for (I) and 3 for (II)
• (3) 3 for (I) and 3 for (II)
• (4) 3 for (I) and 4 for (II)

The logic circuit shown in Figure below is a

• (1) Half adder
• (2) XOR
• (3) Equality detector
• (4) Full adder

For a square wave signal with a frequency of 10 KHz, calculate the output frequencies for Mod 2, Mod 4, and Mod 10 counters.

• (1) 20 KHz, 40 KHz, 100 KHz
• (2) 50 Hz, 25 Hz, 0.1 Hz
• (3) 50 KHz, 25 KHz, 10 KHz
• (4) 5 KHz, 2.5 KHz, 1 KHz

A 10-bit successive approximation type A/D converter has quantization error of 10 mV. The digital output corresponding to an analog input of 4.365 V would be

• (1) 0110110110
• (2) 0100100100
• (3) 0110110100
• (4) 1101011100

One example of the use of an S-R flip-flop is

• (1) Transition pulse generator
• (2) Racer
• (3) Switch debouncer
• (4) Astable oscillator

The primary function of a clamper circuit is

• (1) Suppress variations in signal voltage
• (2) Raise the positive cycle of the signal
• (3) Lower the negative cycle of the signal
• (4) Introduce a DC level to an AC signal

What is the period of the following signal, \( x(t) = \sin(18\pi t + 78^\circ) \)?

• (1) \( \frac{1}{9} \)
• (2) \( \frac{1}{3} \)
• (3) \( \frac{2}{9} \)
• (4) \( \frac{4}{9} \)

A PAM signal can be detected by using

• (1) An ADC
• (2) A bandpass filter
• (3) An integrator
• (4) A high pass filter

A function \( x(t) \) is said to have half-wave odd symmetry if

• (1) \( x(t) = -x\left[t \pm \frac{T}{2}\right] \)
• (2) \( x(t) = x\left[t - \frac{T}{4}\right] \)
• (3) \( x(t) = x\left[t - \frac{T}{2}\right] \)
• (4) \( x(t) = -x\left[t + \frac{T}{4}\right] \)

What are the conditions called which are required for a signal to fulfill to be represented as Fourier series?

• (1) Dirichlet's conditions
• (2) Gibbs phenomenon
• (3) Fourier conditions
• (4) Fourier phenomenon

The impulse response of a continuous time system is given by \( h(t) = \delta(t - 1) + \delta(t - 3) \). The value of the step response at \( t = 2 \) is

• (1) 2
• (2) 3
• (3) 0
• (4) 1

Find the initial value, if it exists of the signal with Laplace transform given below:
\[ X(s) = \frac{s + 4}{s^2 + 3s + 5} \]

• (1) 1
• (2) 4/5
• (3) 5/4
• (4) \infty

Fourier transform of \( x(t) = e^{-at}u(t - 2) \) is

• (1) \( \frac{e^{jw}}{a^2 + w^2} \)
• (2) \( \frac{e^{jw}}{a^2 - w^2} \)
• (3) \( \frac{e^{-jw}}{a^2 + w^2} \)
• (4) \( \frac{e^{-jw}}{2a + w^2} \)

As \( x \) is increased from \( -\infty \) to \( \infty \), the function \( f(x) = \frac{e^x}{1+e^x} \) behaves as

• (1) Monotonically increases
• (2) Increases to a maximum value and then decreases
• (3) Monotonically decreases
• (4) Decreases to a minimum value and then increases

What is the fundamental angular frequency in rad/sec for the given waveform?

• (1) 5
• (2) \( 5\pi \)
• (3) 10
• (4) \( 10\pi \)

A discrete-time signal \( x[n] = \sin(\pi n^2) \), where \( n \) is an integer, is

• (1) Periodic with period \( \pi \)
• (2) Periodic with period \( \pi/2 \)
• (3) Periodic with period \( \pi^2 \)
• (4) Not periodic

Which of the following system is not stable with input \( x(n) \) and output \( y(n) \)?

• (1) \( y(n) = 20 \sin(x(n)) + 10 \)
• (2) \( y(n) = e^{x(n)} \)
• (3) \( y(n) = \sum_{k=-\infty}^{n} x(k) \)
• (4) \( y(n) = \sum_{k=-2}^{2} x(n - k) \)

If \( x[n] = \{1, 0, -2, 3\} \) and \( y[n] = x[n] \ast x[n] \), the maximum value of \( y[n] \) is

• (1) 4
• (2) 9
• (3) 2
• (4) 6

A signal is processed by a causal filter with transfer function \( G(s) \). For a distortion-free output signal waveform, \( G(s) \) must

• (1) Provide zero phase shift for all frequencies
• (2) Provide constant phase shift for all frequencies
• (3) Provide linear phase shift that is proportional to frequency
• (4) Provide a phase shift that is inversely proportional to frequency

Which type of control system uses both feedforward and feedback control strategies?

• (1) Open-loop control system
• (2) Closed-loop control system
• (3) Proportional control system
• (4) On-off control system

According to Nyquist stability criterion, where should be the position of all zeros of \(G(s)\) corresponding to \(s-plane\)?

• (1) On left half
• (2) At the centre
• (3) On right half
• (4) Random

According to Nyquist stability criterion, where should be the position of all zeros of \( G(s) \) corresponding to \( s \)-plane?

• (1) On left half
• (2) At the centre
• (3) On right half
• (4) Random

The open-loop DC gain of a unity negative feedback system with closed-loop transfer function is given by \( \frac{5}{4 + 5s + 13s^2} \), what is the open-loop DC gain?

• (1) \( \frac{4}{13} \)
• (2) 4
• (3) \( \frac{4}{9} \)
• (4) 13

The polar plot of a transfer function passes through the critical point (+1,0). Gain margin is

• (1) Zero
• (2) \(-1dB\)
• (3) \( 1dB \)
• (4) Infinity

In the signal flow graph of figure \( \frac{y}{x} \) equals

• (1) 3
• (2) \( \frac{5}{3} \)
• (3) 2
• (4) \( \frac{5}{2} \)

%Question text
Routh Hurwitz criterion is used to determine

• (1) Relative stability of the system.
• (2) Time response of the system.
• (3) Absolute stability of the system.
• (4) Roots of characteristic equation graphically.

%Question text
If the characteristic equation of a closed-loop system is \( s^2 + 2s + 2 = 0 \), then the system is

• (1) Overdamped.
• (2) Critically damped.
• (3) Undamped.
• (4) Underdamped.

In a Proportional-Integral-Derivative (PID) controller

• (1) The proportional term introduces damping to the system.
• (2) The derivative term eliminates steady-state error.
• (3) The integral term improves transient response.
• (4) The proportional term contributes to steady-state accuracy.

Consider a stable linear time-invariant (LTI) system with a transfer function G(s). Which of the following statements regarding Bode and Nyquist plots is true?

• (1) Bode plots provide information about the system's stability, while Nyquist plots provide information about its frequency response.
• (2) Bode plots are used to analyze the system's transient response, while Nyquist plots are used for steady-state analysis.
• (3) Nyquist plots are applicable only for stable systems, while Bode plots can be used for both stable and unstable systems.
• (4) Bode plots display the magnitude and phase response of the system, while Nyquist plots show the system's gain and phase margin.

The roots of the characteristic equation \(2S^3 + 3S^2 + 4S + 6 = 0\) are

• (1) \(S = -1.5, S = \pm \sqrt{2}\)
• (2) \(S = -1, S = \pm \sqrt{2}\)
• (3) \(S = -1, S = -4, S = -6\)
• (4) \(S = -1, S = -2, S = -3\)

Which one of the following is not the property of root loci?

• (1) The root locus is symmetrical about imaginary axis.
• (2) They start from the open loop poles and terminate at the open loop zeroes.
• (3) The breakaway points are determined from dK/ds = 0.
• (4) Segments of the real axis are the part of the root locus if and only if the total number of real poles and zeroes to their right is odd.

A transfer function of control system does not have pole-zero cancellation. Which one of the following statements is true?

• (1) System is neither controllable nor observable.
• (2) System is completely controllable and observable.
• (3) System is observable but uncontrollable.
• (4) System is controllable but unobservable.

If the highest modulation frequency is 5 kHz, find out bandwidth.

• (1) 5 kHz
• (2) 10 kHz
• (3) 2.5 kHz
• (4) 705 kHz

Identify the true statement with reference to immediate addressing mode

• (1) In this mode, data is accessed by specifying the register name in which it is stored.
• (2) In this mode, value of operand is held within the instruction itself.
• (3) In this mode, memory location of data is stored in a register.
• (4) This mode is useful for accessing fixed memory locations such as memory mapped I/O devices.

In PCM, if the number of quantization levels is increased from 4 to 64, then the bandwidth requirement will approximately equal to

• (1) 3 times
• (2) 4 times
• (3) 2 times
• (4) 6 times

At a given probability of error, binary coherent FSK is inferior to binary coherent PSK by

• (1) 6 dB
• (2) 3 dB
• (3) 2 dB
• (4) 0 dB

In QAM, both ____ of a carrier frequency are varied.

• (1) Frequency and amplitude
• (2) Phase and frequency
• (3) Amplitude and phase
• (4) Differential amplitude

Which of the following analog modulation schemes requires the minimum transmitted power and minimum channel bandwidth?

• (1) VSB
• (2) DSBCS
• (3) SSB
• (4) AM

For a modulation index much less than 1, the FM signal is considered as

• (1) Narrow band VSB
• (2) Narrow band FM
• (3) Wideband AM
• (4) Wideband FM

A TDMA system uses 25 MHz for the forward link, which is broken into radio channels of 200 kHz. If 8 speech channels are supported on a single radio channel, how many simultaneous users can be accommodated?

• (1) 25
• (2) 200
• (3) 1600
• (4) 1000

Coherent demodulation of FSK signal can be detected using

• (1) Bandpass filters
• (2) Bandpass filters and envelope detectors
• (3) Matched filter
• (4) Discriminator

The use of non-uniform quantization leads to

• (1) Reduction in transmission bandwidth
• (2) Increase in maximum SNR
• (3) Increase in SNR for low-level signals
• (4) Simplification of quantization process

How many users or voice channels are supported for each 200 KHz channel in GSM?

• (1) 8
• (2) 3
• (3) 64
• (4) 12

The midband gain of an amplifier is 100 and the lower cutoff frequency is 1kHz. The gain of the amplifier at a frequency of 20Hz is approximately

• (1) 2
• (2) 20
• (3) 50
• (4) 100

Match the following:

• (1) (i) - (a), (ii) - (d), (iii) - (c), (iv) - (b)
• (2) (i) - (b), (ii) - (a), (iii) - (c), (iv) - (d)
• (3) (i) - (c), (ii) - (e), (iii) - (b), (iv) - (d)
• (4) (i) - (a), (ii) - (c), (iii) - (b), (iv) - (d)
• (i) A filter is used to convert alternating current into pulsating current.

The following multiplexer gives the logic gate of a/an ___\

• (1) Ex-OR gate
• (2) Ex-NOR gate
• (3) NOR gate
• (4) NAND gate

How many minimum number of flip-flops are required to make a mod-479 counter? ___\

• (1) 6
• (2) 7
• (3) 8
• (4) 9

___ is used for the removal of SiO2 from desired regions such that the desired impurities can be diffused.

• (1) Photo etching
• (2) Epitaxial growth
• (3) Oxidation
• (4) Chemical Vapour Deposition

The characteristic equation of JK flip-flop is ___\

• (1) \( Q(t + 1) = JQ(t) + k \)
• (2) \( Q(t + 1) = J + KQ(t) \)
• (3) \( Q(t + 1) = JQ(t) + KQ(t) \)
• (4) \( Q(t + 1) = JQ(t) + \overline{K} Q(t) \)

Which of the following statement is correct with respect to Latch?

• (1) It normally samples its inputs and changes its outputs only at times determined by the clocking signal
• (2) It checks all of its inputs continuously and changes its outputs accordingly at any time independent of a clocking signal
• (3) It is an electronic circuit with three stable states
• (4) It is a tristate device and used in memories

The output of each stage of flip-flop is connected to input of next stage flip-flop and the complement output of the last stage flip-flop is again connected to the input of first stage flip-flop then this is called

• (1) Ring counter
• (2) Twisted ring counter
• (3) Ripple counter
• (4) Decade counter

The number of flip-flops used in a decade counter is ___\

• (1) 8
• (2) 5
• (3) 4
• (4) 10

Add the two numbers 87H and 79H in the 8085 microprocessors, then

• (1) Carry flag = 0 and zero flag = 0
• (2) Carry flag = 0 and zero flag = 1
• (3) Carry flag = 1 and zero flag = 0
• (4) Carry flag = 1 and zero flag = 1

Which theorem relates the line integral of a vector field over a closed curve to the surface integral of the curl of the field over the surface bounded by the curve?

• (1) Stokes's theorem
• (2) Gauss's theorem
• (3) Green's theorem
• (4) Divergence theorem

The curl of a vector field \( F \) is zero throughout a region of space. What does this imply about the behavior of \( F \)?

• (1) The field \( F \) is solenoidal.
• (2) The field \( F \) is irrotational.
• (3) The field \( F \) is conservative.
• (4) The field \( F \) is neither solenoidal nor irrotational.

Which of the following assertions accurately describes Gauss's theorem?

• (1) It connects a line integral of a vector field with a surface integral of the field's curl.
• (2) It links a surface integral of a vector field with a line integral of the field's curl.
• (3) It correlates a line integral of a vector field with a volume integral of the field's curl.
• (4) It associates a surface integral of a vector field with a volume integral of the field's divergence.

Which of the following is not a source of magnetostatic fields?

• (1) A dc current in a wire
• (2) A permanent magnet
• (3) An electric field linearly changing with time
• (4) A charged disk rotating at uniform speed

Which one of the following field patterns represents a TEM wave traveling in the positive \( z \)-direction?

• (1) \( E = +3\hat{y}, H = -4\hat{z} \)
• (2) \( E = -2\hat{y}, H = -3\hat{z} \)
• (3) \( E = +2\hat{z}, H = +2\hat{y} \)
• (4) \( E = -3\hat{y}, H = +4\hat{z} \)

If an electromagnetic wave travels in the positive \( x \)-direction, and its electric field oscillates in the \( y \)-direction, what is the polarization of the wave?

• (1) Linear polarization along the \( x \)-axis
• (2) Elliptical polarization
• (3) Circular polarization
• (4) Linear polarization along the \( y \)-axis

In which scenario would you expect the highest amount of refraction to occur when an electromagnetic wave passes from one medium to another?

• (1) When the incident angle is close to 0 degrees.
• (2) When the incident angle is close to 90 degrees.
• (3) When the incident angle is close to 45 degrees.
• (4) Refraction is independent of the incident angle.

In a transmission line with a characteristic impedance \( Z_0 \), what happens if the load impedance \( Z_L \) matches \( Z_0 \)?

• (1) Maximum power is transferred to the load
• (2) No power is transferred to the load
• (3) Half of the power is transferred to the load
• (4) The voltage across the load is maximum

The primary advantage of using a rectangular waveguide over other transmission line types is

• (1) Lower attenuation
• (2) Higher power handling capability
• (3) Easier fabrication
• (4) Greater flexibility in design

Fundamental principle behind the propagation of light in dielectric waveguides and optical fibers is

• (1) Total internal reflection
• (2) Diffraction
• (3) Absorption
• (4) Refraction

What is the radiation pattern of a point source antenna in free space?

• (1) Isotropic
• (2) Omnidirectional
• (3) Bidirectional
• (4) Directional

The purpose of using a transmission line segment with a length of \( \lambda/4 \) in impedance matching is

• (1) To introduce a phase shift of 90 degrees
• (2) To provide a direct connection between the source and the load
• (3) To transform the impedance seen by the load
• (4) To minimize signal reflections at the load

Determine the value of \( p \) such that the rank of matrix \( A \) is 2:

\[ A = \begin{bmatrix} 1 & 2 & 3 & 4
0 & 0 & 2 & p
1 & 0 & p & 7 \end{bmatrix} \]

• (1) \( \frac{8}{5} \)
• (2) \( \frac{21}{5} \)
• (3) \( \frac{20}{7} \)
• (4) \( \frac{3}{4} \)

The matrix \( A = \begin{bmatrix} 3 & -1 & 1
1 & -5 & 1
1 & -1 & 3 \end{bmatrix} \) has eigenvalues 2, 3, 6 then the eigenvalues of \( A^4 \) are

• (1) \( 2, \frac{4}{3}, \frac{2}{3} \)
• (2) \( 2, 3, 6 \)
• (3) \( 8, 12, 24 \)
• (4) \( \frac{1}{2}, \frac{1}{3}, \frac{1}{6} \)

The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1
0 & -2
1 & 1 \end{bmatrix} \) are

• (1) \( 0, 0, 0 \)
• (2) \( 1, 1, 1 \)
• (3) \( -1, -1, 1 \)
• (4) \( 0, 1, 1 \)

The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is

• (1) 12
• (2) 13
• (3) 11
• (4) 14

A solution of the ODE \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \) is such that \( y(0) = 2 \) and \( y'(0) = 3 \). The value of \( y''(0) \) is

• (1) 4
• (2) 2
• (3) -3
• (4) 0

Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is

• (1) \( z = \frac{1}{12}(6x + a)^2 + \frac{1}{54}(2y - a)^3 + b \)
• (2) \( z = \frac{1}{72}(6x - a)^3 + \frac{1}{54}(2y - a)^3 + b \)
• (3) \( z = \frac{1}{12}(6x - a)^2 + \frac{1}{72}(2y - a)^3 + b \)
• (4) \( z = \frac{1}{54}(6x - a)^3 + \frac{1}{12}(2y - a)^3 + b \)

The radius of convergence of Taylor's series expansion of \( f(z) = \frac{1}{(z - 1)^2} \) in powers of \( (z - 1) \) is ...

• (1) 1
• (2) 0
• (3) \( \infty \)
• (4) -1

Evaluate \( \int_C \frac{dz}{z^2 + 9} \), where \( C \) is \( |z - 3| = 4 \)

• (1) \( \frac{\pi}{6} \)
• (2) \( \frac{\pi}{4} \)
• (3) \( \frac{\pi}{3} \)
• (4) \( \frac{\pi}{2} \)

A die is thrown at random, find the probability of getting 5 or a number greater than 2 and is even

• (1) \( \frac{1}{6} \)
• (2) \( \frac{2}{6} \)
• (3) \( \frac{4}{6} \)
• (4) \( \frac{3}{6} \)

For any two arbitrary events \( A \) and \( B \), which of the following is true?

• (1) \( P(A \cap B) = P(A) P(B) \)
• (2) \( P(A \cup B) = P(A) + P(B) \)
• (3) \( P(A \cup B) \leq P(A) + P(B) \)
• (4) \( P(A \cap B) = P(A) + P(B) \)

Starting from \( x_0 = 1 \), one step Newton-Raphson method in solving the equation \( x^3 + 3x - 7 = 0 \) gives the next value as

• (1) 0.5
• (2) 1.5
• (3) 1.415
• (4) 1.9