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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Networks, Signals and Systems(9)Electronic Devices(7)Analog Circuits(8)Digital Circuits(6)Control Systems(5)Communications(7)Electromagnetics(4)

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '$\rightarrow$' denotes increasing order of intensity, then the meaning of the words [charm $\rightarrow$ enamor $\rightarrow$ bewitch] is analogous to [bored $\rightarrow$ ______ $\rightarrow$ weary]. Which one of the given options is appropriate to fill the blank?

(A)

jaded

(B)

baffled

(C)

dead

(D)

worsted

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. Given the valid room allocations, which one of the given options is the siblings?

(A)

P and T

(B)

P and S

(C)

T and Q

(D)

T and [Option D text]

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5. What was his father's age when Aman was born?

(A)

28 years

(B)

30 years

(C)

35 years

(D)

32 years

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

For a real number $x > 1$, $\frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} = 1$. The value of $x$ is

(A)

3

(B)

11

(C)

24

(D)

12

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

The greatest prime factor of $(3^{199} - 3^{196})$ is

(A)

13

(B)

17

(C)

3

(D)

11

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Sequence the following sentences (P, Q, R, S) in a coherent passage: P: Shifu's student exclaimed, "Why do you run since the bull is an illusion?" Q: Shifu said, "Surely my running away from the bull is also an illusion." R: Shifu once proclaimed that all life is illusion. S: One day, when a bull gave him chase, Shifu began running for his life.

(A)

SPRQ

(B)

SRPQ

(C)

RSPQ

(D)

QPRS

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Four identical cylindrical chalk-sticks, each of radius $r = 0.5$ cm and length $l = 10$ cm, are bound tightly together using a duct tape as shown in the following figure. The width of the duct tape is equal to the length of the chalk-stick. The area (in $\text{cm}^2$) of the duct tape required to wrap the bundle of chalk-sticks once, is

(A)

$20(4+\pi)$

(B)

$20(8+\pi)$

(C)

$10(8+\pi)$

(D)

$10(4+\pi)$

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023. Based on the data provided, which one of the following options is INCORRECT?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

An object appears as a specific image after first reflecting in a mirror and then reflecting on water. The original object is

(A)

62.5

(B)

Option B

(C)

Option C

(D)

6.25

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Two identical sheets A and B, of dimensions $24 \text{ cm} \times 16 \text{ cm}$, can be folded into half using two distinct operations, FO1 or FO2. In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge. If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is

(A)

14:11

(B)

11:14

(C)

18:11

(D)

11:18

Explanation

Engineering Mathematics

9 Questions

GATE→2024→Engineering Mathematics→Differential Equations

Q11

MCQ[1 Mark]

The general form of the complementary function of a differential equation is given by $y(t) = (At + B)e^{-2t}$, where A and B are real constants determined by the initial condition. The corresponding differential equation is

(A)

$\frac{d^2 y}{dt^2} + 4\frac{dy}{dt} + 4y = f(t)$

(B)

$\frac{d^2 y}{dt^2} + 4y = f(t)$

(C)

$\frac{d^2 y}{dt^2} + 3\frac{dy}{dt} + 2y = f(t)$

(D)

$\frac{d^2 y}{dt^2} + 5\frac{dy}{dt} + 6y = f(t)$

Explanation

GATE→2024→Engineering Mathematics→Vector Analysis

Q12

MSQ[1 Mark]

Let $\rho(x,y,z,t)$ and $u(x,y,z,t)$ represent density and velocity. Which of the following equations is/are equivalent to $\frac{\partial\rho}{\partial t} + \nabla \cdot (\rho u) = 0$?

(A)

$\int_V \frac{\partial\rho}{\partial t} dv = - \iint_S \rho u \cdot \hat{n} ds$

(B)

$\int_V \frac{\partial\rho}{\partial t} dv = \iint_S \rho u \cdot \hat{n} ds$

(C)

$\int_V \frac{\partial\rho}{\partial t} dv = - \int_V \nabla \cdot (\rho u) dv$

(D)

$\int_V \frac{\partial\rho}{\partial t} dv = \int_V \nabla \cdot (\rho u) dv$

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q13

NAT[1 Mark]

$x^2 - 12x + 37 = 0$. In a number system of base r, the equation has $x = 8$ as one of its solutions. The value of r is

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q14

NAT[1 Mark]

Let $\mathbb{R}$ and $\mathbb{R}^3$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors $\{[2 \quad -3 \quad \alpha], [3 \quad -1 \quad 3], [1 \quad -5 \quad 7]\}$ does not form a basis of $\mathbb{R}^3$ is

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that $X \ge Y$ is

Explanation

GATE→2024→Engineering Mathematics→Vector Analysis

Q16

MCQ[2 Marks]

Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the $60^{\circ}\text{N}$ latitude circle, that contains the north pole in its interior is

(A)

$(2 - \sqrt{3})\pi R^2$

(B)

$\frac{(\sqrt{2}-1)\pi R^2}{2}$

(C)

$\frac{2\pi R^2}{3}$

(D)

$\frac{(2+\sqrt{3})\pi R^2}{8\sqrt{2}}$

Explanation

GATE→2024→Engineering Mathematics→Complex Analysis

Q17

MCQ[2 Marks]

Let z be a complex variable. If $f(z) = \frac{\sin(\pi z)}{z^2(z-2)}$ and C is the circle in the complex plane with $|z| = 3$, then $\oint_C f(z)dz$ is

(A)

$\pi^2 j$

(B)

$j\pi(\frac{1}{2} - \pi)$

(C)

$j\pi(\frac{1}{2} + \pi)$

(D)

$-\pi^2 j$

Explanation

GATE→2024→Engineering Mathematics→Vector Analysis

Q18

MSQ[2 Marks]

Let $F_1, F_2,$ and $F_3$ be functions of $(x,y,z)$. Suppose that for every given pair of points A and B in space, the line integral is path-independent. Then which of the following is/are true?

(A)

For every closed path $\Gamma$, we have $\oint_\Gamma (F_1 dx + F_2 dy + F_3 dz) = 0$.

(B)

There exists a differentiable scalar function $f(x,y,z)$ such that $F_1 = \frac{\partial f}{\partial x}, F_2 = \frac{\partial f}{\partial y}, F_3 = \frac{\partial f}{\partial z}$.

(C)

$\frac{\partial F_1}{\partial x} + \frac{\partial F_2}{\partial y} + \frac{\partial F_3}{\partial z} = 0$.

(D)

$\frac{\partial F_3}{\partial y} = \frac{\partial F_2}{\partial z}, \frac{\partial F_1}{\partial z} = \frac{\partial F_3}{\partial x}, \frac{\partial F_2}{\partial x} = \frac{\partial F_1}{\partial y}$.

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q19

MSQ[2 Marks]

Consider the matrix $\begin{bmatrix} 1 & k \\ 2 & 1 \end{bmatrix}$, where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

(A)

$\begin{bmatrix} 1 \\ -\sqrt{2/k} \end{bmatrix}$

(B)

$\begin{bmatrix} 1 \\ \sqrt{2/k} \end{bmatrix}$

(C)

$\begin{bmatrix} \sqrt{2k} \\ 1 \end{bmatrix}$

(D)

$\begin{bmatrix} \sqrt{2k} \\ -1 \end{bmatrix}$

Explanation

Networks, Signals and Systems

9 Questions

GATE→2024→Networks, Signals and Systems→LTI Systems

Q20

MCQ[1 Mark]

A causal and stable LTI system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5t)$ is applied to another causal and stable LTI system with impulse response $h(0.5t)$. The resulting output is

(A)

$2y(0.5t)$

(B)

$4y(0.5t)$

(C)

$0.25y(2t)$

(D)

$0.25y(0.25t)$

Explanation

GATE→2024→Networks, Signals and Systems→Discrete-time Signals

Q21

MSQ[1 Mark]

For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2 + 3}{(z + 1/3)(z - 1/3)}$, which of the following statements is/are true?

(A)

The system is stable.

(B)

The system is a minimum phase system.

(C)

The initial value of the impulse response is 2.

(D)

The final value of the impulse response is 0.

Explanation

GATE→2024→Networks, Signals and Systems→Circuit Analysis

Q22

NAT[1 Mark]

In the given circuit, the current $I_x$ (in mA) is

Explanation

GATE→2024→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q23

NAT[1 Mark]

In the circuit given below, the switch has been open for a long time and is closed at time $t = 0$. The time constant (in seconds) of the circuit for $t > 0$ is

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q24

MCQ[2 Marks]

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below. If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q25

MCQ[2 Marks]

A continuous time signal $x(t) = 2 \cos(8\pi t + \pi/3)$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response $h(t) = \left(\frac{\sin 2\pi t}{\pi t}\right) \cos(38\pi t - \pi/2)$ produces $x_o(t)$.

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q26

MSQ[2 Marks]

The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are

(A)

$0.05\pi$

(B)

Option B

(C)

$0.3\pi$

(D)

$0.45\pi$

Explanation

GATE→2024→Networks, Signals and Systems→Discrete-time Signals

Q27

NAT[2 Marks]

Another sequence $y[n]$ is formed as below $y[n] = \mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\}$. For the sequence $x[n] = \{1, 2, 1, 3\}$, the value of $Y[0]$ is

Explanation

GATE→2024→Networks, Signals and Systems→Circuit Analysis

Q28

NAT[2 Marks]

In the network shown below, maximum power is to be transferred to the load $R_L$. The value of $R_L$ (in $\Omega$) is

Explanation

Electronic Devices

7 Questions

GATE→2024→Electronic Devices→Semiconductor Physics and Carrier Transport

Q29

MCQ[1 Mark]

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (T) dependence of free electron concentration (n)?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→Electronic Devices→Semiconductor Physics and Carrier Transport

Q30

MSQ[1 Mark]

The free electron concentration profile $n(x)$ in a doped semiconductor at equilibrium is shown in the figure. Which of the following statements is/are true?

(A)

For x between B and C, the electron diffusion current is directed from C to B.

(B)

For x between B and A, the electron drift current is directed from B to A.

(C)

For x between B and C, the electric field is directed from B to C.

(D)

For x between B and A, the electric field is directed from A to B.

Explanation

GATE→2024→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q31

MSQ[2 Marks]

Which of the following statements is/are true for a BJT with respect to its DC current gain $\beta$?

(A)

Under high-level injection condition in forward active mode, $\beta$ will decrease with increase in the magnitude of collector current.

(B)

Under low-level injection condition in forward active mode, where the current at the emitter-base junction is dominated by recombination-generation process, $\beta$ will decrease with increase in the magnitude of collector current.

(C)

$\beta$ will be lower when the BJT is in saturation region compared to when it is in active region.

(D)

A higher value of $\beta$ will lead to a lower value of the collector-to-emitter breakdown voltage.

Explanation

GATE→2024→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q32

NAT[2 Marks]

Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of 100 nm, a fixed positive oxide charge of $10^{-8}\text{ C/cm}^2$ at the oxide-silicon interface, and a metal work function of 4.6 eV. Assume that the relative permittivity of the oxide is 4 and absolute permittivity of free space is $8.85 \times 10^{-14}\text{ F/cm}$. If the flatband voltage is 0 V, the work function of the p-type silicon (in eV, rounded off to two decimal places) is

Explanation

GATE→2024→Electronic Devices→Semiconductor Physics and Carrier Transport

Q33

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

GATE→2024→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q34

NAT[2 Marks]

An NMOS transistor operating in the linear region has $I_{DS} = 5~\mu\text{A}$ at $V_{DS} = 0.1$ V. Keeping $V_{GS}$ constant, the $V_{DS}$ is increased to 1.5 V. Given that $\mu_n C_{ox} \frac{W}{L} = 50~\mu\text{A/V}^2$, the transconductance at the new operating point is

Explanation

GATE→2024→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q35

NAT[2 Marks]

The photocurrent of a PN junction diode solar cell is 1 mA. The voltage corresponding to its maximum power point is 0.3 V. If the thermal voltage is 30 mV, the reverse saturation current of the diode (in nA, rounded off to two decimal places) is

Explanation

Analog Circuits

8 Questions

GATE→2024→Analog Circuits→BJT and MOSFET Amplifiers

Q36

MCQ[1 Mark]

In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal input impedance $Z_{in}(j\omega)$ is

(A)

$\frac{-g_m}{C_1 C_L \omega^2} + \frac{1}{j\omega C_1} + \frac{1}{j\omega C_L}$

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Analog Circuits→BJT and MOSFET Amplifiers

Q37

MCQ[1 Mark]

For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is 40. The closed loop low frequency small signal voltage gain $\frac{v_{out}}{v_{in}}$ is

(A)

0.976

(B)

1.000

(C)

1.025

(D)

0.488

Explanation

GATE→2024→Analog Circuits→Diode Circuits

Q38

MCQ[1 Mark]

In the circuit shown, the n:1 step-down transformer and the diodes are ideal. If the input voltage (in Volts) is $V_s(t) = 10\sin\omega t$ and the average value of load voltage $V_L(t)$ (in Volts) is $2.5/\pi$, the value of n is

(A)

4

(B)

8

(C)

12

(D)

16

Explanation

GATE→2024→Analog Circuits→Diode Circuits

Q39

NAT[1 Mark]

As shown in the circuit, the initial voltage across the capacitor is 10 V, with the switch being open. The switch is then closed at $t = 0$. The total energy dissipated in the ideal Zener diode ($V_Z = 5$ V) after the switch is closed (in mJ, rounded off to three decimal places) is

Explanation

GATE→2024→Analog Circuits→Op-amp Circuits and Compensation

Q40

MCQ[2 Marks]

The opamps in the circuit shown are ideal, but have saturation voltages of $\pm 10$ V. Which of the following statements is true?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Analog Circuits→Op-amp Circuits and Compensation

Q41

MCQ[2 Marks]

In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of $R_1$ and the corresponding frequency of oscillation are

(A)

$29R$ and $1/(2\pi\sqrt{6}RC)$

(B)

$2R$ and $1/(2\pi RC)$

(C)

$29R$ and $1/(2\pi RC)$

(D)

$2R$ and $1/(2\pi\sqrt{6}RC)$

Explanation

GATE→2024→Analog Circuits→BJT and MOSFET Amplifiers

Q42

MCQ[2 Marks]

In the circuit shown below, the transistors $M_1$ and $M_2$ are biased in saturation. Assuming that capacitor $C_1$ is a short circuit at signal frequencies, the magnitude of small signal voltage gain $|v_{out}/v_{in}|$ is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Analog Circuits→Diode Circuits

Q43

NAT[2 Marks]

For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is

Explanation

Digital Circuits

6 Questions

GATE→2024→Digital Circuits→Number Representations and Combinatorial Circuits

Q44

MCQ[1 Mark]

For the Boolean function $F(A, B, C, D) = \sum m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15)$, the essential prime implicants are

(A)

$BD, \overline{B}\overline{D}$

(B)

$BD, AB$

(C)

$AB, \overline{B}\overline{D}$

(D)

$BD, \overline{B}\overline{D}, AB$

Explanation

GATE→2024→Digital Circuits→Computer Organization

Q45

NAT[1 Mark]

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is

Explanation

GATE→2024→Digital Circuits→Number Representations and Combinatorial Circuits

Q46

MCQ[2 Marks]

A 4-bit priority encoder has inputs $D_3, D_2, D_1,$ and $D_0$ in descending order of priority. The two-bit output AB is generated as 00, 01, 10, and 11 corresponding to inputs $D_3, D_2, D_1,$ and $D_0$, respectively. The Boolean expression of the output bit B is

(A)

$\overline{D_3} D_2$

(B)

$\overline{D_3} D_2 + \overline{D_3} \overline{D_1}$

(C)

$D_3 \overline{D_2} + \overline{D_3} D_1$

(D)

$D_3 \overline{D_1}$

Explanation

GATE→2024→Digital Circuits→Number Representations and Combinatorial Circuits

Q47

MCQ[2 Marks]

The propagation delay of the $2 \times 1$ MUX shown in the circuit is 10 ns. If S is set to 1 then the output Y is

(A)

a square wave of frequency 100 MHz

(B)

a square wave of frequency 50 MHz

(C)

constant at 0

(D)

constant at 1

Explanation

GATE→2024→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q48

MCQ[2 Marks]

The sequence of states $(Q_1 Q_0)$ of the given synchronous sequential circuit is

(A)

$00 \to 10 \to 11 \to 00$

(B)

$11 \to 00 \to 10 \to 01 \to 00$

(C)

$01 \to 10 \to 11 \to 00 \to 01$

(D)

$00 \to 01 \to 10 \to 00$

Explanation

GATE→2024→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q49

MCQ[2 Marks]

A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is $10~\mu\text{W}$. The effective number of bits (rounded off to the nearest integer) of the ADC is

(A)

7

(B)

8

(C)

9

(D)

10

Explanation

Control Systems

5 Questions

GATE→2024→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q50

MCQ[1 Mark]

In the context of Bode magnitude plots, 40 dB/decade is the same as ______

(A)

12 dB/octave

(B)

6 dB/octave

(C)

20 dB/octave

(D)

10 dB/octave

Explanation

GATE→2024→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q51

MCQ[1 Mark]

In the feedback control system shown in the figure below $G(s) = \frac{6}{s(s+1)(s+2)}$. If the input $r(t)$ is a unit step function, then

(A)

$\lim_{t\to\infty} e(t) = 0$

(B)

$\lim_{t\to\infty} e(t) = \frac{1}{3}$

(C)

$\lim_{t\to\infty} e(t) = \frac{1}{4}$

(D)

$\lim_{t\to\infty} e(t)$ does not exist, $e(t)$ is oscillatory

Explanation

GATE→2024→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q52

MCQ[2 Marks]

Consider a unity negative feedback control system with forward path gain $G(s) = \frac{K}{(s+1)(s+2)(s+3)}$. 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→2024→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q53

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→2024→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q54

MSQ[2 Marks]

Consider a system S represented in state space as given. Which of the state space representations given below has/have the same transfer function as that of S?

(A)

$\frac{dx}{dt} = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix} x + \begin{bmatrix} 0 \\ 1 \end{bmatrix} r$, $y = \begin{bmatrix} 1 & 2 \end{bmatrix} x$

(B)

Option B

(C)

$\frac{dx}{dt} = \begin{bmatrix} -1 & 0 \\ 0 & -2 \end{bmatrix} x + \begin{bmatrix} -1 \\ 3 \end{bmatrix} r$, $y = \begin{bmatrix} 1 & 1 \end{bmatrix} x$

(D)

Option D

Explanation

Communications

7 Questions

GATE→2024→Communications→Information Theory and Digital Communications

Q55

MCQ[1 Mark]

A digital communication system transmits through a noiseless bandlimited channel [-W, W]. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Communications→Random Processes and Analog Communications

Q56

MCQ[1 Mark]

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t = t_k$, the variance of the random variable $n(t_k)$ is

(A)

$\frac{N_0}{4RC}$

(B)

$\frac{N_0}{2RC}$

(C)

$\frac{N_0}{RC}$

(D)

$\frac{2N_0}{RC}$

Explanation

GATE→2024→Communications→Random Processes and Analog Communications

Q57

NAT[1 Mark]

An amplitude modulator has output (in Volts) $s(t) = A\cos(400\pi t) + B\cos(360\pi t) + B\cos(440\pi t)$. The carrier power normalized to $1~\Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is $1/9$. The value of B (in Volts, rounded off to two decimal places) is

Explanation

GATE→2024→Communications→Information Theory and Digital Communications

Q58

NAT[1 Mark]

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is

Explanation

GATE→2024→Communications→Information Theory and Digital Communications

Q59

MCQ[2 Marks]

A source transmits a symbol s, taken from $\{-4, 0, 4\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol r is given by $r = s + w$ where noise w is zero mean with variance 4. Using $Q(x)$, the optimum symbol error probability is

(A)

$\frac{2}{3} Q(2)$

(B)

$\frac{4}{3} Q(1)$

(C)

$\frac{2}{3} Q(1)$

(D)

$\frac{4}{3} Q(2)$

Explanation

GATE→2024→Communications→Information Theory and Digital Communications

Q60

MCQ[2 Marks]

The information bit sequence {111010101} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is

(A)

{1110101011100}

(B)

{1110101011101}

(C)

{1110101011110}

(D)

{1110101010100}

Explanation

GATE→2024→Communications→Random Processes and Analog Communications

Q61

NAT[2 Marks]

Let $X(t) = A \cos(2\pi f_0 t + \theta)$ be a random process... The signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of an 8-bit uniform mid-rise quantizer is

Explanation

Electromagnetics

4 Questions

GATE→2024→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q62

MCQ[1 Mark]

Consider a lossless transmission line terminated with a short circuit. As one moves towards the generator from the load, the normalized impedances at intervals of $\lambda/8$ are evaluated.

(A)

$Z_{inA} = +1j~\Omega$, $Z_{inB} = \infty$, $Z_{inC} = -1j~\Omega$, $Z_{inD} = 0$

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Electromagnetics→Maxwell's Equations and Plane Waves

Q63

MCQ[1 Mark]

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for the vector fields $\vec{F}_1 = A(\hat{i}y + \hat{j}x)$ and $\vec{F}_2 = A(\hat{i}y - \hat{j}x)$?

(A)

Both $\vec{F}_1$ and $\vec{F}_2$ are electrostatic fields.

(B)

Only $\vec{F}_1$ is an electrostatic field.

(C)

Only $\vec{F}_2$ is an electrostatic field.

(D)

Neither $\vec{F}_1$ nor $\vec{F}_2$ is an electrostatic field.

Explanation

GATE→2024→Electromagnetics→Maxwell's Equations and Plane Waves

Q64

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 in the +x direction. 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→2024→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q65

NAT[2 Marks]

A lossless transmission line with characteristic impedance $Z_0 = 50~\Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma| = 0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$) is

Explanation