Electronics and Communication GATE 2024 Questions with Answer

Ques 1 Communication Systems

A digital communication system transmits through a noiseless bandlimited channel [-W W].
The received signal $z(t)$ at the output of the receiving filter is given by $z(t)=\sum_{n}b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol.
The received signal is sampled at $t=mT$. The Fourier transform of $x(t)$ is $X(f)$.
The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is

$\sum_{m=-\infty}^{\infty}X(f+\frac{m}{T})=T$

$\sum_{m=-\infty}^{\infty}X(f+\frac{m}{T})=\frac{1}{T}$

$\sum_{m=-\infty}^{\infty}X(f+mT)=T$

$\sum_{m=-\infty}^{\infty}X(f+mT)=\frac{1}{T}$

Ques 2 Communication Systems

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

$\frac{N_{0}}{4RC}$

$\frac{N_{0}}{2RC}$

$\frac{N_{0}}{RC}$

$\frac{2N_{0}}{RC}$

Ques 3 Communication Systems

An amplitude modulator has output (in Volts)
s(t) = A cos(400πt) + B cos(360πt) + B cos(440πt).
The carrier power normalized to 1Ω 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

1 is the correct answer.

Ques 4 Communication Systems

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 the noise w is zero mean with variance 4 and is independent of s.
Using $Q(x) = \frac{1}{√2π} ∫_x^∞ e^{-\frac{t^2}{2}} dt$, the optimum symbol error probability is

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

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

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

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

Ques 5 Communication Systems

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) = x⁴ + x + 1.
The encoded sequence of bits is

{1110101011100}

{1110101011101}

{1110101011110}

{1110101010100}

Ques 6 Communication Systems

Let X(t) = A cos(2πf0t + θ) be a random process, where amplitude A and phase θ are independent of each other, and are uniformly distributed in the intervals [-2, 2] and [0, 2π], respectively.
X(t) is fed to an 8-bit uniform mid-rise type quantizer.
Given that the autocorrelation of X(t) is $R_x(τ) = \frac{2}{3} cos(2πf_0 τ)$, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is

45.84 is the correct answer.

Ques 7 Computer Organization

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

16383 is the correct answer.

Ques 8 Control Systems

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

12 dB/octave

6 dB/octave

20 dB/octave

10 dB/octave

Ques 9 Control Systems

In the feedback control system shown in the figure below $G(s)=\frac{6}{s(s+1)(s+2)}$
$R(s)$, $Y(s)$, and $E(s)$ are the Laplace transforms of $r(t)$, $y(t)$, and $e(t)$, respectively.
If the input $r(t)$ is a unit step function, then

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

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

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

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

Ques 10 Control Systems

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

$1≤K≤5$

$7≤K≤21$

$-4≤K<-1$

$-24≤K≤-6$

Ques 11 Control Systems

A satellite attitude control system, as shown below, has a plant with transfer function $G(s)=\frac{1}{s^2}$ cascaded with a compensator $C(s)=\frac{K(s+α)}{s+4}$ where K and α are positive real constants.