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General Aptitude(10)Engineering Mathematics(6)Networks, Signals and Systems(13)Electronic Devices(6)Analog Circuits(6)Digital Circuits(4)Control Systems(7)Communications(6)Electromagnetics(7)

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

"I cannot support this proposal. My _______ will not permit it."

(A)

conscious

(B)

consensus

(C)

conscience

(D)

consent

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Courts : Judiciary :: Parliament : Legislature (By word meaning)

(A)

Judiciary

(B)

Executive

(C)

Governmental

(D)

Legal

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

What is the smallest number with distinct digits whose digits add up to 45?

(A)

123555789

(B)

123457869

(C)

123456789

(D)

99999

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

In a class of 100 students, (i) there are 30 students who neither like romantic movies nor comedy movies, (ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and (iii) the number of students who like both romantic movies and comedy movies is 20. How many students in the class like romantic movies?

(A)

40

(B)

20

(C)

60

(D)

30

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

How many rectangles are present in the given figure?

(A)

8

(B)

9

(C)

10

(D)

12

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q6

MCQ[2 Marks]

Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious. Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A)

All creatures with claws are animals.

(B)

Some creatures with claws are non-ferocious.

(C)

Some non-ferocious creatures have claws.

(D)

Some ferocious creatures are creatures with claws.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Which one of the following options represents the given graph?

(A)

$f(x) = x^2 2^{-|x|}$

(B)

$f(x) = x 2^{-|x|}$

(C)

$f(x) = |x| 2^{-x}$

(D)

$f(x) = x 2^{-x}$

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q8

MCQ[2 Marks]

Which one of the following options can be inferred from the given passage alone?

(A)

It is a child's description of what he or she likes.

(B)

It is an adult's memory of what he or she liked as a child.

(C)

The child in the passage read stories about interplanetary travel only in parts.

(D)

It teaches us that stories are good for children.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A)

700

(B)

600

(C)

800

(D)

1000

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

A $100 \text{ cm} \times 32 \text{ cm}$ rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions $100 \text{ cm} \times 1 \text{ cm}$. The total number of creases visible when the sheet is unfolded is

(A)

32

(B)

5

(C)

31

(D)

63

Explanation

Engineering Mathematics

6 Questions

GATE→2023→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Let $v_1 = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}$ and $v_2 = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix}$ be two vectors. The value of the coefficient $\alpha$ in the expression $v_1 = \alpha v_2 + e$ which minimizes the length of the error vector $e$, is

(A)

$\frac{7}{2}$

(B)

$\frac{-2}{7}$

(C)

$\frac{2}{7}$

(D)

$\frac{-7}{2}$

Explanation

GATE→2023→Engineering Mathematics→Vector Analysis

Q12

MCQ[1 Mark]

The rate of increase of a scalar field $f(x, y, z) = xyz$ in the direction $v = (2, 1, 2)$ at a point $(0, 2, 1)$ is

(A)

$\frac{2}{3}$

(B)

$\frac{4}{3}$

(C)

2

(D)

4

Explanation

GATE→2023→Engineering Mathematics→Complex Analysis

Q13

MCQ[1 Mark]

Let $w^4 = 16j$. Which of the following cannot be a value of w?

(A)

$2e^{\frac{j2\pi}{8}}$

(B)

$2e^{\frac{j\pi}{8}}$

(C)

$2e^{\frac{j5\pi}{8}}$

(D)

$2e^{\frac{j9\pi}{8}}$

Explanation

GATE→2023→Engineering Mathematics→Complex Analysis

Q14

MCQ[1 Mark]

The value of the contour integral, $\oint_C \left(\frac{z+2}{z^2+2z+2}\right)dz$, where the contour C is $\{z : |z + 1 - \frac{3}{2}j| = 1\}$ taken in the counter clockwise direction, is

(A)

$-\pi(1+j)$

(B)

$\pi(1+j)$

(C)

$\pi(1-j)$

(D)

$-\pi(1-j)$

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q15

MCQ[1 Mark]

Let the sets of eigenvalues and eigenvectors of a matrix B be $\{\lambda_k | 1 \le k \le n\}$ and $\{v_k | 1 \le k \le n\}$, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where $B = P^{-1}AP$, respectively, are

(A)

$\{\lambda_k \det(A) | 1 \le k \le n\}$ and $\{Pv_k | 1 \le k \le n\}$

(B)

$\{\lambda_k | 1 \le k \le n\}$ and $\{v_k | 1 \le k \le n\}$

(C)

$\{\lambda_k | 1 \le k \le n\}$ and $\{Pv_k | 1 \le k \le n\}$

(D)

$\{\lambda_k | 1 \le k \le n\}$ and $\{P^{-1}v_k | 1 \le k \le n\}$

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q16

NAT[2 Marks]

The value of the integral $\iint_R xy \, dx \, dy$ over the region R, given in the figure, is _______ (rounded off to the nearest integer).

Explanation

Networks, Signals and Systems

13 Questions

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q17

MCQ[1 Mark]

A series RLC circuit has a quality factor Q of 1000 at a center frequency of $10^6$ rad/s. The possible values of R, L and C are

(A)

$R = 1~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(B)

$R = 0.1~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(C)

$R = 0.01~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(D)

$R = 0.001~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

Explanation

GATE→2023→Networks, Signals and Systems→LTI Systems

Q18

MCQ[1 Mark]

Consider a system with input $x(t)$ and output $y(t) = x(e^t)$. The system is

(A)

Causal and time invariant.

(B)

Non-causal and time varying.

(C)

Causal and time varying.

(D)

Non-causal and time invariant.

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q19

MCQ[1 Mark]

The Fourier transform $X(\omega)$ of $x(t) = e^{-t^2}$ is Note: $\int_{-\infty}^{\infty} e^{-y^2} dy = \sqrt{\pi}$

(A)

$\sqrt{\pi} e^{\frac{\omega^2}{2}}$

(B)

$\frac{e^{-\frac{\omega^2}{4}}}{2\sqrt{\pi}}$

(C)

$\sqrt{\pi} e^{-\frac{\omega^2}{4}}$

(D)

$\sqrt{\pi} e^{-\frac{\omega^2}{2}}$

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q20

MCQ[1 Mark]

In the table shown below, match the signal type with its spectral characteristics.

(A)

(A) (i)->(a), (ii)->(b), (iii)->(c), (iv)->(d)

(B)

(B) (i)->(a), (ii)->(c), (iii)->(b), (iv)->(d)

(C)

(C) (i)->(d), (ii)->(b), (iii)->(c), (iv)->(a)

(D)

(D) (i)->(a), (ii)->(c), (iii)->(d), (iv)->(b)

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q21

NAT[1 Mark]

In the circuit shown below, the current i flowing through $200~\Omega$ resistor is _______ mA (rounded off to two decimal places).

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q22

NAT[1 Mark]

For the two port network shown below, the [Y]-parameters is given as $[Y] = \frac{1}{100} \begin{bmatrix} 2 & -1 \\ -1 & 4/3 \end{bmatrix}$ S. The value of load impedance $Z_L$ in $\Omega$, for maximum power transfer will be

Explanation

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q23

NAT[1 Mark]

In the circuit shown below, switch S was closed for a long time. If the switch is opened at $t = 0$, the maximum magnitude of the voltage $V_R$ in volts, is

Explanation

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q24

MCQ[2 Marks]

The switch $S_1$ was closed and $S_2$ was open for a long time. At $t = 0$, switch $S_1$ is opened and $S_2$ is closed, simultaneously. The value of $i_c(0^+)$, in amperes, is

(A)

-0.8

(B)

-1

(C)

0.2

(D)

0.8

Explanation

GATE→2023→Networks, Signals and Systems→Discrete-time Signals

Q25

MCQ[2 Marks]

Consider a discrete-time periodic signal with period $N = 5$. Let the discrete-time Fourier series (DTFS) representation be $x[n] = \sum_{k=0}^4 a_k e^{j \frac{k 2\pi n}{5}}$, where $a_0 = 1$, $a_1 = 3j$, $a_2 = 2j$, $a_3 = -2j$ and $a_4 = -3j$. The value of the sum $\sum_{n=0}^4 x[n] \sin \frac{4\pi n}{5}$ is

(A)

-10

(B)

10

(C)

-2

(D)

2

Explanation

GATE→2023→Networks, Signals and Systems→Discrete-time Signals

Q26

MCQ[2 Marks]

Let an input $x[n]$ having discrete time Fourier transform $X(e^{j\Omega}) = 1 - e^{-j\Omega} + 2e^{-3j\Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H(e^{j\Omega}) = 1 - \frac{1}{2}e^{-j2\Omega}$. The output $y[n]$ of the system is

(A)

Option A

(B)

Option B

(C)

$\delta[n] - \delta[n-1] - \frac{1}{2}\delta[n-2] + \frac{5}{2}\delta[n-3] - \delta[n-5]$

(D)

Option D

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q27

MCQ[2 Marks]

Let $x(t) = 10 \cos(10.5Wt)$ be passed through an LTI system having impulse response $h(t) = \pi \left(\frac{\sin Wt}{\pi t}\right)^2 \cos 10Wt$. The output of the system is

(A)

$(\frac{15W}{4}) \cos(10.5Wt)$

(B)

$(\frac{15W}{2}) \cos(10.5Wt)$

(C)

$(\frac{15W}{8}) \cos(10.5Wt)$

(D)

$(15W) \cos(10.5Wt)$

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q28

NAT[2 Marks]

Let $x_1(t) = u(t+1.5) - u(t-1.5)$ and $x_2(t)$ is shown in the figure below. For $y(t) = x_1(t) * x_2(t)$, the $\int_{-\infty}^{\infty} y(t) dt$ is _______ (rounded off to the nearest integer).

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q29

NAT[2 Marks]

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $\mu$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ $\mu$s (rounded off to two decimal places).

Explanation

Electronic Devices

6 Questions

GATE→2023→Electronic Devices→Semiconductor Physics and Carrier Transport

Q30

MCQ[1 Mark]

In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

(A)

degenerate n-type.

(B)

degenerate p-type.

(C)

non-degenerate n-type.

(D)

non-degenerate p-type.

Explanation

GATE→2023→Electronic Devices→Semiconductor Physics and Carrier Transport

Q31

MCQ[1 Mark]

For an intrinsic semiconductor at temperature $T = 0$ K, which of the following statement is true?

(A)

All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty of electrons.

(B)

All energy states in the valence band are empty of electrons and all energy states in the conduction band are filled with electrons.

(C)

All energy states in the valence and conduction band are filled with holes.

(D)

All energy states in the valence and conduction band are filled with electrons.

Explanation

GATE→2023→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q32

MCQ[1 Mark]

For a MOS capacitor, $V_{fb}$ and $V_t$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width ($W_{dep}$) for varying gate voltage ($V_g$) is best represented by

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Electronic Devices→Semiconductor Physics and Carrier Transport

Q33

NAT[2 Marks]

In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_i$ where $n_i$ is the intrinsic carrier concentration of $1 \times 10^{10} \text{ cm}^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as _______ (rounded off to two decimal places).

Explanation

GATE→2023→Electronic Devices→Semiconductor Physics and Carrier Transport

Q34

NAT[2 Marks]

In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at $T = 300$ K is $1 \times 10^{19} \text{ cm}^{-3}$. The thermal equilibrium hole concentration in silicon at 400 K is _______ $\times 10^{13} \text{ cm}^{-3}$ (rounded off to two decimal places). Given $kT$ at 300 K is 0.026 eV.

Explanation

GATE→2023→Electronic Devices→Semiconductor Physics and Carrier Transport

Q35

NAT[2 Marks]

A non-degenerate n-type semiconductor has 5% neutral dopant atoms. Its Fermi level is located at 0.25 eV below the conduction band ($E_C$) and the donor energy level ($E_D$) has a degeneracy of 2. Assuming the thermal voltage to be 20 mV, the difference between $E_C$ and $E_D$ (in eV, rounded off to two decimal places) is

Explanation

Analog Circuits

6 Questions

GATE→2023→Analog Circuits→BJT and MOSFET Amplifiers

Q36

MCQ[1 Mark]

In the circuit shown below, $V_1$ and $V_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a

(A)

voltage controlled voltage source.

(B)

voltage controlled current source.

(C)

current controlled voltage source.

(D)

current controlled current source.

Explanation

GATE→2023→Analog Circuits→Op-amp Circuits and Compensation

Q37

MCQ[1 Mark]

A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

(A)

the closed loop gain is less than 1 and the phase shift is less than $180^\circ$.

(B)

the closed loop gain is greater than 1 and the phase shift is less than $180^\circ$.

(C)

the closed loop gain is less than 1 and the phase shift is greater than $180^\circ$.

(D)

the closed loop gain is greater than 1 and the phase shift is greater than $180^\circ$.

Explanation

GATE→2023→Analog Circuits→Op-amp Circuits and Compensation

Q38

MCQ[2 Marks]

The $\frac{V_{OUT}}{V_{IN}}$ of the circuit shown below is

(A)

$-\frac{R_4}{R_3}$

(B)

$\frac{R_4}{R_3}$

(C)

$1 + \frac{R_4}{R_3}$

(D)

$1 - \frac{R_4}{R_3}$

Explanation

GATE→2023→Analog Circuits→Diode Circuits

Q39

MCQ[2 Marks]

In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of 0.7 V. $V_{IN}$ and $V_{OUT}$ are input and output voltages in volts. The transfer characteristic is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Analog Circuits→BJT and MOSFET Amplifiers

Q40

MCQ[2 Marks]

The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{V_{out}}{V_s}$ is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Analog Circuits→BJT and MOSFET Amplifiers

Q41

NAT[2 Marks]

In the circuit below, the voltage $V_L$ is _______ V (rounded off to two decimal places).

Explanation

Digital Circuits

4 Questions

GATE→2023→Digital Circuits→Number Representations and Combinatorial Circuits

Q42

MCQ[1 Mark]

In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

(A)

$Y = PQ$

(B)

$Y = P + Q$

(C)

$Y = \overline{PQ}$

(D)

$Y = P \oplus Q$

Explanation

GATE→2023→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q43

MCQ[1 Mark]

The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are

(A)

1000, 3

(B)

333.33, 1

(C)

2000, 3

(D)

333.33, 3

Explanation

GATE→2023→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q44

NAT[1 Mark]

The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is _______ bits (rounded off to the nearest integer).

Explanation

GATE→2023→Digital Circuits→Number Representations and Combinatorial Circuits

Q45

NAT[1 Mark]

For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is

Explanation

Control Systems

7 Questions

GATE→2023→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q46

MCQ[1 Mark]

The open loop transfer function of a unity negative feedback system is $G(s) = \frac{k}{s(1+sT_1)(1+sT_2)}$, where k, $T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in rad/s, is

(A)

$\frac{1}{\sqrt{T_1 T_2}}$

(B)

$\frac{1}{T_1 T_2}$

(C)

$\frac{1}{T_1 \sqrt{T_2}}$

(D)

$\frac{1}{T_2 \sqrt{T_1}}$

Explanation

GATE→2023→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q47

MCQ[2 Marks]

Consider a unity negative feedback control system with forward path gain $G(s) = \frac{K}{(s+1)(s+2)(s+3)}$ as shown. The impulse response of the closed-loop system decays faster than $e^{-t}$ if

(A)

$1 \le K \le 5$

(B)

$7 \le K \le 21$

(C)

$-4 \le K \le -1$

(D)

$-24 \le K \le -6$

Explanation

GATE→2023→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q48

MCQ[2 Marks]

A satellite attitude control system... has a plant with transfer function $G(s) = \frac{1}{s^2}$ cascaded with a compensator $C(s) = \frac{K(s+\alpha)}{s+4}$ where K and $\alpha$ are positive real constants. In order for the closed-loop system to have poles at $-1 \pm j\sqrt{3}$, the value of $\alpha$ must be

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2023→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q49

MCQ[2 Marks]

A closed loop system is shown in the figure where $k > 0$ and $\alpha > 0$. The steady state error due to a ramp input ($R(s) = \alpha/s^2$) is given by

(A)

$\frac{2\alpha}{k}$

(B)

$\frac{\alpha}{k}$

(C)

$\frac{\alpha}{2k}$

(D)

$\frac{\alpha}{4k}$

Explanation

GATE→2023→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q50

MCQ[2 Marks]

In the following block diagram, $R(s)$ and $D(s)$ are two inputs. The output $Y(s)$ is expressed as $Y(s) = G_1(s)R(s) + G_2(s)D(s)$. $G_1(s)$ and $G_2(s)$ are given by

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q51

MCQ[2 Marks]

The state equation of a second order system is $\dot{x}(t) = A x(t)$, $x(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of A and $v_1$ and $v_2$ are the corresponding eigenvectors. For constants $\alpha_1$ and $\alpha_2$, the solution, $x(t)$, of the state equation is

(A)

$\sum_{i=1}^2 \alpha_i e^{\lambda_i t} v_i$

(B)

$\sum_{i=1}^2 \alpha_i e^{2\lambda_i t} v_i$

(C)

$\sum_{i=1}^2 \alpha_i e^{3\lambda_i t} v_i$

(D)

$\sum_{i=1}^2 \alpha_i e^{4\lambda_i t} v_i$

Explanation

GATE→2023→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q52

NAT[2 Marks]

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $G(s) = \frac{k(s+z)^a}{s^b(s+p)^c}$, where k, z, p, a, b and c are positive constants. The value of $(a+b+c)$ is _______ (rounded off to the nearest integer).

Explanation

Communications

6 Questions

GATE→2023→Communications→Random Processes and Analog Communications

Q53

MCQ[1 Mark]

Let $m(t)$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $\omega_0 = 10B$, the energy in the signal $m(t) \cos \omega_0 t$ is

(A)

$\frac{E}{4}$

(B)

$\frac{E}{2}$

(C)

E

(D)

2E

Explanation

GATE→2023→Communications→Random Processes and Analog Communications

Q54

MSQ[1 Mark]

For a real signal, which of the following is/are valid power spectral density/densities?

(A)

$S_x(\omega) = \frac{2}{9 + \omega^2}$

(B)

$S_x(\omega) = e^{-\omega^2} \cos^2 \omega$

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Communications→Random Processes and Analog Communications

Q55

MCQ[2 Marks]

Let a frequency modulated (FM) signal $x(t) = A \cos(\omega_c t + k_f \int_{-\infty}^t m(\lambda)d\lambda)$, where $m(t)$ is a message signal of bandwidth W. It is passed through a non-linear system with output $y(t) = 2x(t) + 5(x(t))^2$. Let $B_T$ denote the FM bandwidth. The minimum value of $\omega_c$ required to recover $x(t)$ from $y(t)$ is

(A)

$B_T + W$

(B)

$\frac{3}{2} B_T$

(C)

$2B_T + W$

(D)

$\frac{5}{2} B_T$

Explanation

GATE→2023→Communications→Random Processes and Analog Communications

Q56

MCQ[2 Marks]

Let $x_1(t)$ and $x_2(t)$ be two band-limited signals having bandwidth $B = 4\pi \times 10^3$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s required to sample $y(t)$, is

(A)

$20\pi \times 10^3$

(B)

$40\pi \times 10^3$

(C)

$8\pi \times 10^3$

(D)

$32\pi \times 10^3$

Explanation

GATE→2023→Communications→Random Processes and Analog Communications

Q57

NAT[2 Marks]

Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2}$ W/Hz. If $X(t)$ is input to an LTI system with impulse response $e^{-t} u(t)$, the average power of the system output is W (rounded off to two decimal places).

Explanation

GATE→2023→Communications→Information Theory and Digital Communications

Q58

NAT[2 Marks]

The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is

Explanation

Electromagnetics

7 Questions

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q59

MCQ[1 Mark]

Consider a narrow band signal, propagating in a lossless dielectric medium $(\epsilon_r = 4, \mu_r = 1)$, with phase velocity $v_p$ and group velocity $v_g$. Which of the following statement is true? (c is the velocity of light in vacuum.)

(A)

$v_p > c$, $v_g > c$

(B)

$v_p < c$, $v_g > c$

(C)

$v_p > c$, $v_g < c$

(D)

$v_p < c$, $v_g < c$

Explanation

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q60

MCQ[2 Marks]

A uniform plane wave with electric field $\vec{E}(x) = A_y \hat{a}_y e^{-j\frac{2\pi x}{3}} \text{ V/m}$ is travelling in the air. It is incident normally on an ideal electric conductor at $x = 0$. The position of the first null of the total magnetic field in the air (measured from $x = 0$ in metres) is

(A)

$-\frac{3}{4}$

(B)

$-\frac{3}{2}$

(C)

-6

(D)

-3

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q61

MCQ[2 Marks]

The S-parameters of a two port network is given as $[S] = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix}$ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1 = \beta l_1$ and $\theta_2 = \beta l_2$ are added to the input and output ports. The S-parameters $[S']$ of the resultant two port network is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q62

MSQ[2 Marks]

The standing wave ratio on a $50~\Omega$ lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance $R_m$ of the same line. The value of $R_m$ and $l_m$, respectively, are

(A)

$R_m = 100~\Omega$, $l_m = 20$ cm

(B)

$R_m = 25~\Omega$, $l_m = 20$ cm

(C)

$R_m = 100~\Omega$, $l_m = 5$ cm

(D)

$R_m = 25~\Omega$, $l_m = 5$ cm

Explanation

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q63

MSQ[2 Marks]

The electric field of a plane electromagnetic wave is $E = a_x C_{1x} \cos(\omega t - \beta z) + a_y C_{1y} \cos(\omega t - \beta z + \theta)$ V/m. Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

(A)

$C_{1x} = 1$, $C_{1y} = 1$, $\theta = \pi/4$

(B)

$C_{1x} = 2$, $C_{1y} = 1$, $\theta = \pi/2$

(C)

$C_{1x} = 1$, $C_{1y} = 2$, $\theta = 3\pi/2$

(D)

$C_{1x} = 2$, $C_{1y} = 1$, $\theta = 3\pi/4$

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q64

MSQ[2 Marks]

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q65

NAT[2 Marks]

A transparent dielectric coating is applied to glass $(\epsilon_r = 4, \mu_r = 1)$ to eliminate the reflection of red light $(\lambda_0 = 0.75~\mu\text{m})$. The minimum thickness of the dielectric coating, in $\mu\text{m}$, that can be used is _______ (rounded off to two decimal places).

Explanation