# 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.