Electronics and Communication Gate 2022 Questions with Answer

Ques 14 GATE 2022

A state transition diagram with states A, B, and C, and transition probabilities p₁, p₂, …, p₇ is shown in the figure (e.g., p₁ denotes the probability of transition from state A to B). For this state diagram, select the statement(s) which is/are universally true.

p₂ + p₃ = p₅ + p₆

p₁ + p₃ = p₄ + p₆

p₁ + p₄ + p₇ = 1

p₂ + p₅ + p₇ = 1

Ques 15 GATE 2022

Consider an FM broadcast that employs the pre-emphasis filter with frequency response
H_pe(ω) = 1 + jω/ω₀,
where ω₀ = 10⁴ 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 ________.

R = 1 kΩ, C = 0.1 μF

R = 2 kΩ, C = 1 μF

R = 1 kΩ, C = 2 μF

R = 2 kΩ, C = 0.5 μF

(a) is the correct answer.

Ques 16 GATE 2022

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

(0.50) is the correct answer.

Ques 17 GATE 2022

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability (1 − ε), and flipped with probability ε. 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 ε = 0.1, the probability that a transmitted codeword is decoded correctly is _________ (rounded off to two decimal places).

(0.85) is the correct answer.

Ques 18 GATE 2022

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:
f_{Y|x_A}(y) = e^−(y+1)u(y + 1),
f_{Y|x_B}(y) = e^(y−1)(1 − u(y − 1)),
where u(⋅) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).

(0.27) is the correct answer.

Ques 19 GATE 2022

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.

Consider a 1 bit quantizer that maps positive samples to value α and others to value β. If α* and β* are the respective choices for α and β that minimize the mean square quantization error, then (α* − β*) = _________ (rounded off to two decimal places).

(1.33) is the correct answer.

Ques 20 GATE 2022

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?

H(X) ≤ log₂ K bits

H(X) ≤ H(2X)

H(X) ≤ H(X²)

H(X) ≤ H(2^X)

(a) is the correct answer.

Ques 21 GATE 2022

Two linear time-invariant systems with transfer functions
G₁(s) = 10/(s² + s + 1) and G₂(s) = 10/(s² + s√10 + 10)
have unit step responses y₁(t) and y₂(t), respectively. Which of the following statements is/are true?

y₁(t) and y₂(t) have the same percentage peak overshoot.

y₁(t) and y₂(t) have the same steady-state value.

y₁(t) and y₂(t) have the same damped frequency of oscillation.

y₁(t) and y₂(t) have the same 2% settling time.

(b) is the correct answer.

Ques 22 GATE 2022

The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r(t), y(t), and d(t), respectively. Let the error signal be defined as e(t) = r(t) − y(t). Assuming the reference input r(t) = 0 for all t, the steady-state error e(∞), due to a unit step disturbance d(t), is _________ (rounded off to two decimal places).

(0.10) is the correct answer.

Ques 23 GATE 2022

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. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________

(2) is the correct answer.

Ques 24 GATE 2022

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. Note that K is varied from 0 to ∞.
Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

G(s) = 1/(s + 1)⁵

G(s) = 1/(s⁵ + 1)

G(s) = (s − 1)/(s + 1)⁶

G(s) = (s + 1)/(s⁶ + 1)

(a) is the correct answer.

Ques 25 GATE 2022

Consider an even polynomial p(s) given by
p(s) = s⁴ + 5s² + 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 ________.

−4 ≤ K ≤ 9/4

−3 ≤ K ≤ 9/2

−6 ≤ K ≤ 5/4

−5 ≤ K ≤ 0

(a) is the correct answer.

Ques 26 GATE 2022

Consider a Boolean gate (D) where the output Y is related to the inputs A and B as,
Y = A + B̄, 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)).

NAND logic can be implemented

OR logic cannot be implemented

NOR logic can be implemented

AND logic cannot be implemented

(a) is the correct answer.

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