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Type:ALLMCQNATMSQ

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

General Aptitude

10 Questions

GATE→2022→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Mr. X speaks ________ Japanese ________ Chinese.

(A)

neither/or

(B)

either/nor

(C)

neither / nor

(D)

also / but

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

A sum of money is to be distributed among P, Q, R, and S in the proportion 5:2:4:3, respectively. If R gets 1000 more than S, what is the share of Q (in ₹)?

(A)

500

(B)

1000

(C)

1500

(D)

2000

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, $PQ = 11$ cm, $QR = 4$ cm, $RS = 6$ cm and $SP = 3$ cm. What is the shortest distance between PQ and SR (in cm)?

(A)

1.80

(B)

2.40

(C)

4.20

(D)

5.76

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a 'hole in the interior' that can be formed within the $4 \times 4$ grid using the unit squares as building blocks?

(A)

15

(B)

20

(C)

21

(D)

26

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery... which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.

(A)

P and Q

(B)

Q

(C)

Q and S

(D)

R and S

Explanation

GATE→2022→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Mosquitoes pose a threat to human health... Which one of the following is the correct logical inference based on the information in the above passage?

(A)

Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous

(B)

Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects

(C)

Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous

(D)

Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Consider the following inequalities: (i) $2x - 1 > 7$ (ii) $2x - 9 < 1$ Which one of the following expressions below satisfies the above two inequalities?

(A)

$x \le -4$

(B)

$-4 < x \le 4$

(C)

$4 < x < 5$

(D)

$x \ge 5$

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Four points $P(0,1)$, $Q(0,-3)$, $R(-2,-1)$, and $S(2,-1)$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

(A)

4

(B)

$4\sqrt{2}$

(C)

8

(D)

$8\sqrt{2}$

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. Based on the information given above, the person who has copied in the exam is

(A)

R

(B)

P

(C)

Q

(D)

T

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively... Which one of the following statements is correct as per the information provided above?

(A)

The sequence of operations (1) and (2) are equivalent

(B)

The sequence of operations (1) and (3) are equivalent

(C)

The sequence of operations (2) and (3) are equivalent

(D)

The sequence of operations (1), (2) and (3) are equivalent

Explanation

Engineering Mathematics

10 Questions

GATE→2022→Engineering Mathematics→Vector Analysis

Q11

MCQ[1 Mark]

Consider the two-dimensional vector field $\vec{F}(x,y) = x\vec{i} + y\vec{j}$. A contour C in the x-y plane... The value of the closed path integral $\oint_C \vec{F}(x,y) \cdot (dx\vec{i} + dy\vec{j})$ is

(A)

0

(B)

1

(C)

$8 + 2\pi$

(D)

-1

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

Consider a system of linear equations $Ax = b$, where $A = \begin{bmatrix} 1 & -\sqrt{2} & 3 \\ -1 & \sqrt{2} & -3 \end{bmatrix}$, $b = \begin{bmatrix} 1 \\ 3 \end{bmatrix}$. This system of equations admits

(A)

a unique solution for x

(B)

infinitely many solutions for x

(C)

no solutions for x

(D)

exactly two solutions for x

Explanation

GATE→2022→Engineering Mathematics→Differential Equations

Q13

MSQ[1 Mark]

Consider the following partial differential equation (PDE) $a \frac{\partial^2 f(x,y)}{\partial x^2} + b \frac{\partial^2 f(x,y)}{\partial y^2} = f(x,y)$, where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters $\xi$ and $\eta$ such that $f(x,y) = e^{\xi x + \eta y}$ is a solution of the given PDE.

(A)

$\xi = \frac{1}{\sqrt{2a}}, \eta = \frac{1}{\sqrt{2b}}$

(B)

$\xi = \frac{1}{\sqrt{a}}, \eta = 0$

(C)

$\xi = 0, \eta = 0$

(D)

$\xi = \frac{1}{\sqrt{a}}, \eta = \frac{1}{\sqrt{b}}$

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q14

NAT[1 Mark]

The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. The median number of wickets taken by the bowler in a match is _______ (rounded off to one decimal place).

Explanation

GATE→2022→Engineering Mathematics→Complex Analysis

Q15

NAT[1 Mark]

A simple closed path C in the complex plane is shown in the figure. If $\oint_C \frac{2^z}{z^2-1} dz = -i\pi A$, where $i = \sqrt{-1}$, then the value of A is _______ (rounded off to two decimal places).

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

The function $f(x) = 8 \log_e x - x^2 + 3$ attains its minimum over the interval $[1, e]$ at $x =

(A)

2

(B)

1

(C)

e

(D)

$\frac{1+e}{2}$

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q17

MCQ[2 Marks]

Let $\alpha, \beta$ be two non-zero real numbers and $v_1, v_2$ be two non-zero real vectors of size $3 \times 1$. Suppose that $v_1^T v_2 = 0$, $v_1^T v_1 = 1$, and $v_2^T v_2 = 1$. Let A be the $3 \times 3$ matrix given by: $A = \alpha v_1 v_1^T + \beta v_2 v_2^T$. The eigenvalues of A are

(A)

$0, \alpha, \beta$

(B)

$0, \alpha+\beta, \alpha-\beta$

(C)

$\alpha, \frac{\alpha+\beta}{2}, \sqrt{\alpha\beta}$

(D)

$0, 0, \sqrt{\alpha^2+\beta^2}$

Explanation

GATE→2022→Engineering Mathematics→Complex Analysis

Q18

MSQ[2 Marks]

Consider the following series: $\sum_{n=1}^{\infty} \frac{n^d}{c^n}$. For which of the following combinations of c, d values does this series converge?

(A)

$c = 1, d = -1$

(B)

$c = 2, d = 1$

(C)

$c = 0.5, d = -10$

(D)

$c = 1, d = -2$

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q19

NAT[2 Marks]

The value of the integral $\iint_D 3(x^2 + y^2) dx dy$, where D is the shaded triangular region shown in the diagram, is _______ (rounded off to the nearest integer).

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q20

NAT[2 Marks]

Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, $f(x)$ as shown in the figure... If $\alpha^*$ and $\beta^*$ are the respective choices for $\alpha$ and $\beta$ that minimize the mean square quantization error, then $(\alpha^* - \beta^*) =$ _______ (rounded off to two decimal places).

Explanation

Networks, Signals and Systems

9 Questions

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q21

MCQ[1 Mark]

The current I in the circuit shown is

(A)

$10^{-3}$ A

(B)

$1.25 \times 10^{-3}$ A

(C)

$0.75 \times 10^{-3}$ A

(D)

$-0.5 \times 10^{-3}$ A

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q22

MCQ[1 Mark]

Consider the circuit shown in the figure. The current I flowing through the $10~\Omega$ resistor is

(A)

1 A

(B)

0 A

(C)

0.1 A

(D)

-0.1 A

Explanation

GATE→2022→Networks, Signals and Systems→Continuous-time Signals

Q23

MCQ[1 Mark]

The Fourier transform $X(j\omega)$ of the signal $x(t) = \frac{t}{(1+t^2)^2}$ is

(A)

$\frac{\pi}{2j} \omega e^{-|\omega|}$

(B)

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

(C)

$\frac{\pi}{2j} e^{-|\omega|}$

(D)

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

Explanation

GATE→2022→Networks, Signals and Systems→Continuous-time Signals

Q24

NAT[1 Mark]

Let $x_1(t) = e^{-t} u(t)$ and $x_2(t) = u(t) - u(t-2)$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_1(t)$ and $x_2(t)$, then $\lim_{t \to \infty} y(t) =$

Explanation

GATE→2022→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q25

MCQ[2 Marks]

For the circuit shown, the locus of the impedance $Z(j\omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_1$ and $R_2$ are:

(A)

$R_1 = 2~\text{k}\Omega, R_2 = 3~\text{k}\Omega$

(B)

$R_1 = 5~\text{k}\Omega, R_2 = 2~\text{k}\Omega$

(C)

$R_1 = 5~\text{k}\Omega, R_2 = 2.5~\text{k}\Omega$

(D)

$R_1 = 2~\text{k}\Omega, R_2 = 5~\text{k}\Omega$

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q26

MCQ[2 Marks]

Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically... The circuit element Z can be

(A)

a capacitor of 1 F

(B)

an inductor of 1 H

(C)

a capacitor of $\sqrt{3}$ F

(D)

an inductor of $\sqrt{3}$ H

Explanation

GATE→2022→Networks, Signals and Systems→LTI Systems

Q27

MSQ[2 Marks]

The outputs of four systems ($S_1, S_2, S_3,$ and $S_4$) corresponding to the input signal $\sin(t)$, for all time t, are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?

(A)

$S_1$

(B)

$S_2$

(C)

$S_3$

(D)

$S_4$

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q28

NAT[2 Marks]

A linear 2-port network is shown in Fig. (a)... When the variable resistance R at Port 2 is replaced by the load shown in Fig. (c), the current $I_2$ is _______ mA (rounded off to one decimal place).

Explanation

GATE→2022→Networks, Signals and Systems→Discrete-time Signals

Q29

NAT[2 Marks]

For a vector $\bar{x} = [x[0], x[1], \dots, x[7]]$ the 8-point discrete Fourier transform (DFT)... If $\bar{x} = [1, 0, 0, 0, 2, 0, 0, 0]$ and $\bar{y} = \text{DFT}(\text{DFT}(\bar{x}))$, then the value of $y[0]$ is _______ (rounded off to one decimal place).

Explanation

Electronic Devices

5 Questions

GATE→2022→Electronic Devices→Semiconductor Physics and Carrier Transport

Q30

MCQ[1 Mark]

Consider a long rectangular bar of direct bandgap p-type semiconductor... The steady state electron density at $x=2~\mu\text{m}$ is

(A)

$0.37 \times 10^{14}~\text{cm}^{-3}$

(B)

$0.63 \times 10^{13}~\text{cm}^{-3}$

(C)

$3.7 \times 10^{14}~\text{cm}^{-3}$

(D)

$10^3~\text{cm}^{-3}$

Explanation

GATE→2022→Electronic Devices→Semiconductor Physics and Carrier Transport

Q31

MCQ[1 Mark]

In a non-degenerate bulk semiconductor with electron density $n = 10^{16}~\text{cm}^{-3}$, the value of $E_C - E_{Fn} = 200$ meV... For $n = 0.5 \times 10^{16}~\text{cm}^{-3}$, the closest approximation of the value of $(E_C - E_{Fn})$, among the given options, is

(A)

226 meV

(B)

174 meV

(C)

218 meV

(D)

182 meV

Explanation

GATE→2022→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q32

NAT[1 Mark]

An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with $V_G = 2$ V. The corresponding inversion charge density $(Q_{IN})$ is $2.2~\mu\text{C/cm}^2$. Assume oxide capacitance per unit area as $C_{ox} = 1.7~\mu\text{F/cm}^2$. For $V_G = 4$ V, the value of $Q_{IN}$ is _______ $\mu\text{C/cm}^2$ (rounded off to one decimal place).

Explanation

GATE→2022→Electronic Devices→Semiconductor Physics and Carrier Transport

Q33

MSQ[2 Marks]

Select the CORRECT statement(s) regarding semiconductor devices.

(A)

Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.

(B)

Collector region is generally more heavily doped than Base region in a BJT.

(C)

Total current is spatially constant in a two terminal electronic device in dark under steady state condition.

(D)

Mobility of electrons always increases with temperature in Silicon beyond 300 K.

Explanation

GATE→2022→Electronic Devices→Semiconductor Physics and Carrier Transport

Q34

NAT[2 Marks]

A p-type semiconductor with zero electric field is under illumination... The magnitude of the current density due to the photo-generated electrons at $x = +2l_n$ is _______ $\text{mA/cm}^2$ (rounded off to two decimal places).

Explanation

Analog Circuits

9 Questions

GATE→2022→Analog Circuits→BJT and MOSFET Amplifiers

Q35

MCQ[1 Mark]

Consider the CMOS circuit shown in the figure. The steady state output voltage $V_0$ is

(A)

equal to 0 V

(B)

more than 2 V

(C)

less than 2 V

(D)

equal to 2 V

Explanation

GATE→2022→Analog Circuits→BJT and MOSFET Amplifiers

Q36

MCQ[1 Mark]

The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and -1 V, respectively... For the applied voltages as shown, the steady state voltages are

(A)

$V_1 = 5~\text{V}, V_2 = 5~\text{V}$

(B)

$V_1 = 5~\text{V}, V_2 = 4~\text{V}$

(C)

$V_1 = 4~\text{V}, V_2 = 5~\text{V}$

(D)

$V_1 = 4~\text{V}, V_2 = -5~\text{V}$

Explanation

GATE→2022→Analog Circuits→Op-amp Circuits and Compensation

Q37

MSQ[1 Mark]

An ideal OPAMP circuit with a sinusoidal input is shown in the figure... Which of the options is/are correct?

(A)

The circuit is a low pass filter.

(B)

The circuit is a high pass filter.

(C)

The 3 dB frequency is $1000~\text{rad/s}$

(D)

The 3 dB frequency is $\frac{1000}{3}~\text{rad/s}$.

Explanation

GATE→2022→Analog Circuits→BJT and MOSFET Amplifiers

Q38

MCQ[2 Marks]

Consider an ideal long channel MOSFET (enhancement-mode)... For $V_{GS} = [2 - \sin(2t)]$ V and $V_{DS} = 1$ V, the maximum value of the drain-to-source current is

(A)

40 mA

(B)

20 mA

(C)

15 mA

(D)

5 mA

Explanation

GATE→2022→Analog Circuits→Op-amp Circuits and Compensation

Q39

MCQ[2 Marks]

For the following circuit with an ideal OPAMP, the difference between the maximum and the minimum values of the capacitor voltage ($V_c$) is

(A)

15 V

(B)

27 V

(C)

13 V

(D)

14 V

Explanation

GATE→2022→Analog Circuits→Op-amp Circuits and Compensation

Q40

MCQ[2 Marks]

A circuit with an ideal OPAMP is shown. The Bode plot for the magnitude (in dB) of the gain transfer function is also provided. The values of R and C are

(A)

$R = 3~\text{k}\Omega, C = 1~\mu\text{F}$

(B)

$C = 3~\mu\text{F}, R = 1~\text{k}\Omega$

(C)

$R = 4~\text{k}\Omega, C = 1~\mu\text{F}$

(D)

$R = 3~\text{k}\Omega, C = 2~\mu\text{F}$

Explanation

GATE→2022→Analog Circuits→Diode Circuits

Q41

NAT[2 Marks]

A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{out}}{\partial V_{in}}$ is _______ (rounded off to two decimal places).

Explanation

GATE→2022→Analog Circuits→Op-amp Circuits and Compensation

Q42

NAT[2 Marks]

Consider the circuit shown with an ideal OPAMP. The output voltage $V_0$ is _______ V (rounded off to two decimal places).

Explanation

GATE→2022→Analog Circuits→BJT and MOSFET Amplifiers

Q43

NAT[2 Marks]

Consider the circuit shown with an ideal long channel nMOSFET... The value of $\frac{v_A}{v_B}$ is _______ (rounded off to one decimal place).

Explanation

Digital Circuits

5 Questions

GATE→2022→Digital Circuits→Number Representations and Combinatorial Circuits

Q44

MCQ[1 Mark]

Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for $A_0, A_1, A_2,$ and $A_3$ are

(A)

$A_0 = 0, A_1 = 0, A_2 = 1, A_3 = 1$

(B)

$A_0 = 1, A_1 = 0, A_2 = 1, A_3 = 0$

(C)

$A_0 = 0, A_1 = 1, A_2 = 1, A_3 = 0$

(D)

$A_0 = 1, A_1 = 1, A_2 = 0, A_3 = 0$

Explanation

GATE→2022→Digital Circuits→Number Representations and Combinatorial Circuits

Q45

MSQ[1 Mark]

Select the Boolean function(s) equivalent to $x+yz$, where x, y, and z are Boolean variables, and + denotes logical OR operation.

(A)

$x + z + xy$

(B)

$(x+y)(x+z)$

(C)

$x + xy + yz$

(D)

$x + xz + xy$

Explanation

GATE→2022→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q46

MSQ[1 Mark]

Select the correct statement(s) regarding CMOS implementation of NOT gates.

(A)

Noise Margin High $(NM_H)$ is always equal to the Noise Margin Low $(NM_L)$, irrespective of the sizing of transistors.

(B)

Dynamic power consumption during switching is zero.

(C)

For a logical high input under steady state, the nMOSFET is in the linear regime of operation.

(D)

Mobility of electrons always influences the switching speed of the NOT gate.

Explanation

GATE→2022→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q47

MCQ[2 Marks]

For the circuit shown, the clock frequency is $f_0$ and the duty cycle is 25%. For the signal at the Q output of the Flip-Flop,

(A)

frequency is $f_0/4$ and duty cycle is 50%

(B)

frequency is $f_0/4$ and duty cycle is 25%

(C)

frequency is $f_0/2$ and duty cycle is 50%

(D)

frequency is $f_0$ and duty cycle is 25%

Explanation

GATE→2022→Digital Circuits→Number Representations and Combinatorial Circuits

Q48

MSQ[2 Marks]

Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, $Y = A + \overline{B}$, where + denotes logical OR operation. The Boolean inputs '0' and '1' are also available separately. Using instances of only D gates and inputs '0' and '1', (select the correct option(s)).

(A)

NAND logic can be implemented

(B)

OR logic cannot be implemented

(C)

NOR logic can be implemented

(D)

AND logic cannot be implemented

Explanation

Control Systems

5 Questions

GATE→2022→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q49

MCQ[1 Mark]

Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path, where the gain $K=2$. The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure... The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2022→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q50

MCQ[1 Mark]

The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure... Select the transfer function $G(s)$ that results in the root-locus plot of the closed-loop system as shown in the figure.

(A)

$G(s) = \frac{1}{(s+1)^5}$

(B)

$G(s) = \frac{1}{s^5+1}$

(C)

$G(s) = \frac{s-1}{(s+1)^6}$

(D)

$G(s) = \frac{s+1}{s^6+1}$

Explanation

GATE→2022→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q51

MCQ[2 Marks]

Consider an even polynomial $p(s)$ given by $p(s) = s^4 + 5s^2 + 4 + K$, where K is an unknown real parameter. The complete range of K for which $p(s)$ has all its roots on the imaginary axis is

(A)

$-4 \le K \le \frac{9}{4}$

(B)

$-3 \le K \le \frac{9}{2}$

(C)

$-6 \le K \le \frac{5}{4}$

(D)

$-5 \le K \le 0$

Explanation

GATE→2022→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q52

MSQ[2 Marks]

Two linear time-invariant systems with transfer functions $G_1(s) = \frac{10}{s^2 + s + 1}$ and $G_2(s) = \frac{10}{s^2 + s\sqrt{10} + 10}$ have unit step responses $y_1(t)$ and $y_2(t)$, respectively. Which of the following statements is/are true?

(A)

$y_1(t)$ and $y_2(t)$ have the same percentage peak overshoot.

(B)

$y_1(t)$ and $y_2(t)$ have the same steady-state value.

(C)

$y_1(t)$ and $y_2(t)$ have the same damped frequency of oscillation.

(D)

$y_1(t)$ and $y_2(t)$ have the same 2% settling time.

Explanation

GATE→2022→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q53

NAT[2 Marks]

The block diagram of a closed-loop control system is shown in the figure... Assuming the reference input $r(t) = 0$ for all t, the steady-state error $e(\infty)$, due to a unit step disturbance $d(t)$ is _______ (rounded off to two decimal places).

Explanation

Communications

8 Questions

GATE→2022→Communications→Random Processes and Analog Communications

Q54

MCQ[1 Mark]

The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure... Which one of the following combinations is true?

(A)

Statement I is correct, Statement II is correct

(B)

Statement I is correct, Statement II is incorrect

(C)

Statement I is incorrect, Statement II is correct

(D)

Statement I is incorrect, Statement II is incorrect

Explanation

GATE→2022→Communications→Information Theory and Digital Communications

Q55

MSQ[1 Mark]

Let $H(X)$ denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?

(A)

$H(X) \le \log_2 K$ bits

(B)

$H(X) \le H(2X)$

(C)

$H(X) \le H(X^2)$

(D)

$H(X) \le H(2^X)$

Explanation

GATE→2022→Communications→Information Theory and Digital Communications

Q56

NAT[1 Mark]

A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _______ mega-bits per second (rounded off to two decimal places).

Explanation

GATE→2022→Communications→Random Processes and Analog Communications

Q57

MSQ[2 Marks]

A state transition diagram with states A, B, and C, and transition probabilities $p_1, p_2, \dots, p_7$ is shown in the figure. For this state diagram, select the statement(s) which is/are universally true.

(A)

$p_2 + p_3 = p_5 + p_6$

(B)

$p_1 + p_3 = p_4 + p_6$

(C)

$p_1 + p_4 + p_7 = 1$

(D)

$p_2 + p_5 + p_7 = 1$

Explanation

GATE→2022→Communications→Random Processes and Analog Communications

Q58

MSQ[2 Marks]

Consider an FM broadcast that employs the pre-emphasis filter response $H_{pe}(\omega) = 1 + \frac{j\omega}{\omega_0}$ where $\omega_0 = 10^4$ rad/sec. For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R, C) values is/are

(A)

$R = 1~\text{k}\Omega, C = 0.1~\mu\text{F}$

(B)

$R = 2~\text{k}\Omega, C = 1~\mu\text{F}$

(C)

$R = 1~\text{k}\Omega, C = 2~\mu\text{F}$

(D)

$R = 2~\text{k}\Omega, C = 0.5~\mu\text{F}$

Explanation

GATE→2022→Communications→Information Theory and Digital Communications

Q59

NAT[2 Marks]

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure... The parameter $\alpha$ lies in the interval $[0.25, 1]$. The value of $\alpha$ for which the capacity of this channel is maximized, is _______ (rounded off to two decimal places).

Explanation

GATE→2022→Communications→Information Theory and Digital Communications

Q60

NAT[2 Marks]

Consider communication over a memoryless binary symmetric channel using a $(7, 4)$ Hamming code. Each transmitted bit is received correctly with probability $(1-\epsilon)$ and flipped with probability $\epsilon$. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error. For $\epsilon = 0.1$, the probability that a transmitted codeword is decoded correctly is _______ (rounded off to two decimal places).

Explanation

GATE→2022→Communications→Information Theory and Digital Communications

Q61

NAT[2 Marks]

Consider a channel over which either symbol $x_A$ or symbol $x_B$ is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for Y given $x_A$ and $x_B$ are given... The probability of symbol error for this system is _______ (rounded off to two decimal places).

Explanation

Electromagnetics

4 Questions

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q62

MCQ[1 Mark]

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is $2 \sin(t + \pi/2)$. The displacement current (in Amperes) through the capacitor is

(A)

$2 \sin(t)$

(B)

$2 \sin(t + \pi)$

(C)

$2 \sin(t + \pi/2)$

(D)

0

Explanation

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q63

MSQ[1 Mark]

Consider the following wave equation, $\frac{\partial^2 f(x,t)}{\partial t^2} = 10000 \frac{\partial^2 f(x,t)}{\partial x^2}$. Which of the given options is/are solution(s) to the given wave equation?

(A)

$f(x,t) = e^{-(x-100t)^2} + e^{-(x+100t)^2}$

(B)

$f(x,t) = e^{-(x-100t)} + 0.5 e^{-(x+1000t)}$

(C)

$f(x,t) = e^{-(x-100t)} + \sin(x+100t)$

(D)

$f(x,t) = e^{j100\pi(-100x+t)} + e^{j100\pi(100x+t)}$

Explanation

GATE→2022→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q64

MSQ[2 Marks]

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4}$ cm, with air as the dielectric. Assume the speed of light in air to be $3 \times 10^8$ m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are

(A)

$6 \times 10^{15}$ Hz

(B)

$0.5 \times 10^{12}$ Hz

(C)

$8 \times 10^{14}$ Hz

(D)

$1 \times 10^{13}$ Hz

Explanation

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q65

NAT[2 Marks]

In an electrostatic field, the electric displacement density vector, $\vec{D}$, is given by $\vec{D}(x,y,z) = (x^3\vec{i} + y^3\vec{j} + xy^2\vec{k})~\text{C/m}^2$... The electric charge enclosed within R is _______ C (rounded off to two decimal places).

Explanation