GATE Electrical Engineering 2019

Question 1
The inverse Laplace transform of
H(s)=\frac{s+3}{s^2+2s+1} \; for \; t\geq 0 is
A
3te^{-t}+e^{-t}
B
3e^{-t}
C
2te^{-t}+e^{-t}
D
4te^{-t}+e^{-t}
Signals and Systems   Laplace Transform
Question 1 Explanation: 
\begin{aligned} L^{-1}\left ( \frac{s+3}{s^2+2s+1} \right )&=L^{-1}\left ( \frac{s+1+2}{(s+1)^2} \right )\\ &=L^{-1}\left ( \frac{1}{s+1}+\frac{2}{(s+1)^2} \right )\\ &=e^{-t}+2te^{-t} \end{aligned}
Question 2
M is a 2x2 matrix with eigenvalues 4 and 9. The eigenvalues of M^2 are
A
4 and 9
B
2 and 3
C
-2 and -3
D
16 and 81
Engineering Mathematics   Linear Algebra
Question 2 Explanation: 
M is 2 x 2 matrix with eigen values 4 and 9. The eigen values of M^2 are 16 and 81.
Question 3
The partial differential equation
\frac{\partial^2 u}{\partial t^2}-c^2\left ( \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} \right )=0; where c\neq 0
is known as
A
heat equation
B
wave equation
C
Poisson's equation
D
Laplace equation
Engineering Mathematics   Differential Equations
Question 4
Which one of the following functions is analytic in the region |z|\leq 1?
A
\frac{z^2-1}{z}
B
\frac{z^2-1}{z+2}
C
\frac{z^2-1}{z-0.5}
D
\frac{z^2-1}{z+j0.5}
Engineering Mathematics   Complex Variables
Question 4 Explanation: 


By Cauchy integral theorem,
\int \frac{z^2-1}{z+2}dz=0
Therefore, \frac{z^2-1}{z+2} is analytic in the region |z|\leq 1.
Question 5
The mean-square of a zero-mean random process is \frac{kT}{C}, where k is Boltzmann's constant, T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is
A
\frac{kT}{C}
B
\sqrt{\frac{kT}{C}}
C
\frac{C}{kT}
D
\frac{\sqrt{kT}}{C}
Engineering Mathematics   Probability and Statistics
Question 5 Explanation: 
Given that,
\begin{aligned} E(x^2)&=\frac{kT}{C}\\ E(x)&=0\\ &=E(x^2)-(E(x))^2\\ Var(x)&=\frac{kT}{C}-0=\frac{kT}{C} \end{aligned}
Standard deviation =\sqrt{\frac{kT}{C}}
Question 6
A system transfer function is H(s)=\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}. If a_1=b_1=0, and all other coefficients are positive, the transfer function represents a
A
low pass filter
B
high pass filter
C
band pass filter
D
notch filter
Signals and Systems   Laplace Transform
Question 6 Explanation: 
\begin{aligned} H(s)&=\frac{c_1}{a_2s^2+b_2s+c_2}\\ & as \;\; a_1=b_1=0\\ &=\frac{c_1}{(1+s\tau _1)(1+s\tau _2)}\\ \text{Put }s&=0,\; H(0)=\frac{c_1}{c_2}\\ \text{Put }s&=\infty ,\; H(\infty )=0 \end{aligned}

which represents second order low pass filter.
Question 7
The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?
A
e^{+at}u(t)
B
e^{-a(t+T)}u(t)
C
1+e^{-at}u(t)
D
e^{-a(t-T)}u(t)
Signals and Systems   Introduction of C.T. and D.T. signals
Question 7 Explanation: 
a and T represents positive quantities.
u(t) is unit step function.
h(t)=1+e^{-at}u(t), is non-causal
Here '1' is a constant and two sided so the system will be non-causal, because for causal system,
h(t)=0,\;\;\; t \lt 0
h(t) \neq 0,\;\;\; t \gt 0
Question 8
A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is
A
4.50%
B
9%
C
5%
D
1%
Electrical Machines   Transformers
Question 8 Explanation: 
\begin{aligned} \text{Voltage regulation } &=\frac{V_{NL}-V_{FL}}{V_{NL}} \times 100 \\ &= \frac{100-95}{100} \times 100=5\% \end{aligned}
Question 9
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is
A
100Hz
B
150Hz
C
250Hz
D
300Hz
Power Electronics   Phase Controlled Rectifiers
Question 9 Explanation: 
For 6 pulse converter harmonics present in AC current are 6k\pm 1
Lowest order harmonic =5
Lowest harmonic frequency = 5 x 50 =250Hz
Question 10
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is
A
rotor resistance
B
rotor leakage reactance
C
magnetizing reactance
D
stator resistance
Electrical Machines   Three Phase Induction Machines
There are 10 questions to complete.
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