# GATE Electrical Engineering 2022

 Question 1
The transfer function of a real system, $H(s)$, is given as:
$H(s)=\frac{As+B}{s^2+Cs+D}$
where A, B, C and D are positive constants. This system cannot operate as
 A low pass filter. B high pass filter C band pass filter. D an integrator.
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 1 Explanation:
Put $s=0, H(0)=\frac{A \times 0+B}{0+C \times 0+D}=\frac{B}{D}$
So, the system pass low frequency component. Put $s=\infty , H(\infty )=0$
For high pass filter, high frequency component should be non zero. Hence this system cannot be operated as high pass filter.
 Question 2
For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is
 A 0 B 1 C 100 D infinite
Analog Electronics   Small Signal Analysis
Question 2 Explanation:
For ideal MOSFET, $i_G=0$
Therefore, Current gain, $A_I=\frac{i_s}{i_G}=\infty$
 Question 3
The most commonly used relay, for the protection of an alternator against loss of excitation, is
 A offset Mho relay. B over current relay. C differential relay D Buchholz relay.
Power Systems   Switch Gear and Protection
 Question 4
The geometric mean radius of a conductor, having four equal strands with each strand of radius $'r'$, as shown in the figure below, is

 A $4r$ B $1.414r$ C $2r$ D $1.723r$
Power Systems   Performance of Transmission Lines, Line Parameters and Corona
Question 4 Explanation:
Redraw the configuration:

$\therefore \; GMR=(r' \times 2r\times 2r\times 2\sqrt{2}r)^{1/4}$
Where, $r'=0.7788r$
Hence, $GMR=1.723r$
 Question 5
The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are
 A 1.1, 0.15 and 0.08 B 0.15, 0.15 and 0.35 C 0.2, 0.2 and 0.2 D 0.1, 0.3 and 0.1
Power Systems   Fault Analysis
Question 5 Explanation:
We have,
$X_0 \gt X_1=X_2$
(for $3-\phi$ transposed transmission line)
 Question 6
The steady state output ($V_{out}$), of the circuit shown below, will

 A saturate to $+V_{DD}$ B saturate to $-V_{EE}$ C become equal to 0.1 V D become equal to -0.1 V
Analog Electronics   Operational Amplifiers
Question 6 Explanation:
Redraw the circuit:

From circuit,
\begin{aligned} V_{out} &=-\frac{1}{C_1}\int I\cdot dt \\ &= -\frac{1}{R_1C_1}\int 0 \cdot 1dt \\ \\ &=-\frac{0.1}{R_1C_1}\int dt \\ \\ &= -\frac{0.1}{R_1C_1}t \end{aligned}

Hence, $V_{out}=-V_{EE}$
 Question 7
The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is $-180^{\circ}$. This system has

 A one LHP pole and one RHP zero at the same frequency B one LHP pole and one LHP zero at the same frequency C two LHP poles and one RHP zero D two RHP poles and one LHP zero.
Control Systems   Frequency Response Analysis
Question 7 Explanation:
The given system is non-minimum phase system Therefore, transfer function, $T.F=\frac{s-1}{s+1}$
Hence, one LHP pole and one RHP zero at the same frequency.
 Question 8
A balanced Wheatstone bridge $ABCD$ has the following arm resistances:
$R_{AB}=1k\Omega \pm 2.1%; R_{BC}=100\Omega \pm 0.5%, R_{CD}$ is an unknown resistance; $R_{DA}=300\Omega \pm 0.4%;$. The value of $R_{CD}$ and its accuracy is
 A $30\Omega \pm 3\Omega$ B $30\Omega \pm 0.9\Omega$ C $3000\Omega \pm 90\Omega$ D $3000\Omega \pm 3\Omega$
Electrical and Electronic Measurements   A.C. Bridges
Question 8 Explanation:
The condition for balanced bridge
\begin{aligned} R_{AB}R_{CD}&=R_{DA}R_{BC} \\ R_{CD} &=\frac{300 \times 100}{1000}=30\Omega \\ %Error &=\pm (2.1+0.5+0.4)=\pm 3% \\ \therefore \; R_{CD}&=30\pm 30 \times \frac{3}{100}=30\pm 0.9\Omega \end{aligned}
 Question 9
The open loop transfer function of a unity gain negative feedback system is given by $G(s)=\frac{k}{s^2+4s-5}$.
The range of $k$ for which the system is stable, is
 A $k \gt 3$ B $k \lt 3$ C $k \gt 5$ D $k \lt 5$
Control Systems   Root Locus Techniques
Question 9 Explanation:
Characteristic equation:
\begin{aligned} 1+G(s)H(s)&=0\\ 1+\frac{k}{s^2+4s-5}&=0\\ s^2+4s+k-5&=0 \end{aligned}
R-H criteria:
$\left.\begin{matrix} s^2\\ s^1\\ s^0 \end{matrix}\right| \begin{matrix} 1 & k-5\\ 4 & 0\\ k-5 & \end{matrix}$
Hence, for stable system,
$k-5 \gt 0 \;\; \Rightarrow \; k \gt 5$
 Question 10
Consider a 3 x 3 matrix A whose (i,j)-th element, $a_{i,j}=(i-j)^3$. Then the matrix A will be
 A symmetric. B skew-symmetric. C unitary D null.
Engineering Mathematics   Linear Algebra
Question 10 Explanation:
$for \; i=j\Rightarrow a_{ij}=(i-i)^3=0\forall i$
$for \; i\neq j\Rightarrow a_{ij}=(i-j)^3=(-(j-i))^3=-(j-i)^3=-a_{ji}$
$\therefore \; A_{3 \times 3 }$ is skew symmetric matrix.
There are 10 questions to complete.