GATE Electronics and Communication 2019

Question 1
Which one of the following functions is analytic over the entire complex plane?
A
ln(z)
B
e^{1/z}
C
\frac{1}{1-z}
D
cos(z)
Engineering Mathematics   Complex Analysis
Question 1 Explanation: 
f(z) = \cos z is analytic every where.
Question 2
The families of curves represented by the solution of the equation

\frac{dy}{dx}=-\left (\frac{x}{y} \right )^n

for n = -1 and n = +1, respectively, are
A
Parabolas and Circles
B
Circles and Hyperbolas
C
Hyperbolas and Circles
D
Hyperbolas and Parabolas
Engineering Mathematics   Differential Equations
Question 2 Explanation: 
\begin{aligned} \frac{d y}{d x} &=-\left(\frac{x}{y}\right)^{n} \\ n=-1\quad\quad \frac{d y}{d x} &=-\frac{y^{\prime}}{x} \\ \frac{d y}{y} &=-\frac{d x}{x} \\ \int \frac{1}{y} d y &=-\int \frac{1}{x} d x \\ \ln y &=-\ln x+\ln c \\ \ln (y x) &=\ln c \end{aligned}
x y=c \quad (Represents rectangular hyporbola)
\begin{aligned} n=1, \quad \frac{d y}{d x}&=-\frac{x}{y} \\ y d y &=-x d x \\ y d y &=-\int x d x \\ \frac{y^{2}}{2} &=-\frac{x^{2}}{2}+c \end{aligned}
x^{2}+y^{2}=2 c \quad (Represents family of circles)
Question 3
Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z)=H(z)H\left (\frac{1}{z} \right ) has a zero at z=\frac{1}{2}+\frac{1}{2}j, and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?
A
A
B
B
C
C
D
D
Signals and Systems   Z-Transform
Question 3 Explanation: 
P(Z)=H(Z)H\left ( \frac{1}{Z} \right )
(i) h(n) is real. Som p(n) will be also real
(ii) P(z)=P(z^{-1})
From (i) : if z_1 is a zero of P(z), then z_1^* will be also a zero of P(z).
From (ii): If z_1 is a zero of P(z), then \frac{1}{z_1} will be also a zero of P(z).
So, the 4 zeros are,
\begin{aligned} z_1&= \frac{1}{2}+\frac{1}{2}j\\ z_2&= z_1^*=\frac{1}{2}-\frac{1}{2}j\\ z_3&=\frac{1}{z_1}=\frac{1}{\frac{1}{2}-\frac{1}{2}j}=1-j \\ z_4&=\left ( \frac{1}{z_1} \right )^*=z_3^*=1+j \end{aligned}
Question 4
Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).
Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see(b) in the figure), what is the current through the short circuit at Port 1?
A
0.5 A
B
1.0 A
C
2.0 A
D
2.5 A
Network Theory   Network Theorems
Question 4 Explanation: 
According to reciprocity theorem,
In a linear bilateral single source network the ratio of response to excitation remains the same even after their positions get interchanged.
\therefore \quad \frac{I}{5}=\frac{1}{5} \Rightarrow I=1 \mathrm{A}
Question 5
Let Y(s) be the unit-step response of a causal system having a transfer function
G(s)=\frac{3-s}{(s+1)(s+3)}

that is, Y(s)=\frac{G(s)}{s}. The forced response of the system is
A
u(t)-2e^{-t}u(t)+e^{-3t}u(t)
B
2u(t)-2e^{-t}u(t)+e^{-3t}u(t)
C
2u(t)
D
u(t)
Signals and Systems   Laplace Transform
Question 5 Explanation: 
Given, \quad G(s)=\frac{3-s}{(s+1)(s+3)}
\therefore \quad Y(s)=\frac{G(s)}{s}=\frac{3-s}{s(s+1)(s+3)}
Using partial fractions, we get,
\begin{aligned} Y(s)&=\frac{A}{s}+\frac{B}{(s+1)}+\frac{C}{(s+3)} \\ A\left(s^{2}+4 s+3\right)&+B\left(s^{2}+3 s\right)+C\left(s^{2}+s\right)=3-s \\ A+B+C&=0\\ 4 A+3 B+C&=-1 \\ \text{and }3 A&=3 \\ \text{Therefore, }&\text{we get,}\\ A=1, B&=-2 \text { and } C=1\\ \text{So, }\quad Y(s)&=\frac{1}{s}-\frac{2}{(s+1)}+\frac{1}{(s+3)} \\ \text{and}\quad \mathrm{y}(t)&=u(t)-2 e^{-t} u(t)+e^{-3 t} u(t) \\ \end{aligned}
Forced response,
y_{t}(t)=u(t) \Rightarrow \text { option }(D)
Question 6
For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N_p and the number of system zeros N_z in the frequency range 1Hz\leq f\leq 10^7Hz is
A
N_p=5,N_z=2
B
N_p=6,N_z=3
C
N_p=7,N_z=4
D
N_p=4,N_z=2
Control Systems   Frequency Response Analysis
Question 6 Explanation: 


Number of poles (N_{P})= 6
Number of zeros (N_{Z}) = 3
Question 7
A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to
A
10011
B
1100001
C
1111000
D
1111111
Communication Systems   Information Theory and Coding
Question 7 Explanation: 


Question 8
Which one of the following options describes correctly the equilibrium band diagram at T=300 K of a Silicon pnp^+p^{++} configuration shown in the figure?
A
A
B
B
C
C
D
D
Electronic Devices   PN-Junction Diodes and Special Diodes
Question 9
The correct circuit representation of the structure shown in the figure is
A
A
B
B
C
C
D
D
Electronic Devices   IC Fabrication
Question 9 Explanation: 


Question 10
The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with \Phi _{ms}=0V and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points
A
P, Q, R
B
Q, R, P
C
R, P, Q
D
Q, P, R
Electronic Devices   BJT and FET Basics
Question 10 Explanation: 
Since \phi_{ms}= 0, the MOS-capacitor is ideal.
Point P Represents accumulation
Point Q Represents flat band
Point R Represents Inversion
There are 10 questions to complete.
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