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GATE2019 EE: 24
The Rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
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GATE2019 EE: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $2$ and $3$ $16$ and $81$
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3
GATE2019 EE: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1} for \quad t \geq0$ $3te^{t}+e^{t}$ $3e^{t}$ $2te^{t}+e^{t}$ $4te^{t}+e^{t}$
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4
GATE2019 EE: 3
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}} C^{2}(\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}})=0; where \quad c \neq 0$ heat equation wave equation Poisson’s equation Laplace equation
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5
GATE2019 EE: 4
Which one of the following functions is analytic in the region $z \leq 1$ ? $\frac{z^{2}1}{z}$ $\frac{z^{2}1}{z+2}$ $\frac{z^{2}1}{z0.5}$ $\frac{z^{2}1}{z+j0.5}$
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6
GATE2019 EE: 5
The meansquare of a zeromean 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 $\frac{kT}{c}$ $\sqrt{\frac{kT}{c}}$ $\frac{c}{kT}$ $\frac{\sqrt{kT}}{c}$
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7
GATE2019 EE: 6
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfer function represents a low pass filter high pass filter band pass filter notch filter
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8
GATE2019 EE: 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 timeinvariant system? $e^{+at}u(t)$ $e^{a(t+T)}u(t)$ $1+e^{at}u(t)$ $e^{a(tT)}u(t)$
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9
GATE2019 EE: 8
A $5kVA, 50V/100V,$ singlephase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is $4.5\%$ $9\%$ $5\%$ $1\%$
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10
GATE2019 EE: 9
A sixpulse thyristor bridge rectifier is connected to a balanced threephase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is $100 Hz$ $150 Hz$ $250 Hz$ $300 Hz$
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11
GATE2019 EE: 10
The parameter of an equivalent circuit of a threephase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is rotor resistance rotor leakage reactance magnetizing reactance stator resistance
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12
GATE2019 EE: 11
A threephase synchronous motor draws $200 A$ from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of $0.5$ leading is $100 A$ $200 A$ $300 A$ $400 A$
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13
GATE2019 EE: 12
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which whill give the maximum value of DC offset of the current at the time of switching is $60$ $45$ $90$ $30$
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14
GATE2019 EE: 13
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$ The steady state value of $y(t)$ is $\frac{1}{10 \sqrt{2}}$ $10 \sqrt{2}$ $\frac{1}{100 \sqrt{2}}$ $100 \sqrt{2}$
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15
GATE2019 EE: 14
The open loop transfer function of a unity feedback system is given by $G(s)=\frac{\pi e^{0.25s}}{s}$ In G(s) plane, the Nyquist plot of $G(s)$ passes through the negative real axis at the point $(0.5,j0)$ $(0.75,j0)$ $(1.25,j0)$ $(1.5,j0)$
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16
GATE2019 EE: 15
The characteristics equation of a linear timeinvariant (LTI) system is given by $\Delta(s)=s^{4}+3s^{3}+3s^{2}+s+k=0$ The system is BIBO stable if $0<K<\frac{12}{9}$ $k>3$ $0<k<\frac{8}{9}$ $k>6$
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17
GATE2019 EE: 16
Given $V_{gs}$ is the gatesource voltage, $V_{ds}$ is the drain source voltage, and $V_{th}$ is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are $V_{gs}<V_{th};V_{ds}\geq V_{gs}V_{th}$ ... $V_{gs}>V_{th};V_{ds}\leq V_{gs}V_{th}$ $V_{gs}<V_{th};V_{ds}\leq V_{gs}V_{th}$
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18
GATE2019 EE: 17
A current controlled current source (CCCS) has an input impedance of $10 \Omega$ and output impedance of $100k\Omega$. When this CCCS is used in a negative feedback closed loop with a loop gain of $9$, the closed loop output impedance is $10 \Omega$ $100 \Omega$ $100 k\Omega$ $1000 k\Omega$
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19
GATE2019 EE: 18
If $f=2x^{3}+3y^{2}+4z,$ the value of line integral $\int_{c}$ grad$f.dr$ evaluated over contour $C$ formed by the segments $(3,3,2)\rightarrow(2,3,2)\rightarrow(2,6,2) \rightarrow(2,6,1) $ is___________.
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20
GATE2019 EE: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _____
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21
GATE2019 EE: 20
A coaxial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\epsilon_{r1} = 2.$. When one – fourth portion of the dielectric is replaced with another dielectric of relative permittivity $\epsilon_{r2}$, as shown in the Figure(ii), the capacitance is doubled. The value of $\epsilon_{r2}$ is _________.
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22
GATE2019 EE: 21
The $Y_{bus}$ matrix of a twobus power system having two identical parallel lines connected between them in pu is given as $Y_{bus} = \begin{bmatrix} j8 & j20 \\ j20& j8 \end{bmatrix}$ The magnitudde of the series reactance of each line in pu (round off upto one decimal place) is__________.
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23
GATE2019 EE: 22
Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short circuit level in MVA at the busbar is ____________.
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24
GATE2019 EE: 23
The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 $\Omega$. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is_________.
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25
GATE2019 EE: 25
The output voltage of a singlephase fullbridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of the output voltage to be 75% of DC voltage, The required pulse width in degrees (round off up to one decimal place) is ___________.
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26
GATE2019 EE: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are the row ... Statement 1 is True and Statement 2 is false Statement 2 is true and Statement 1 is false Both the Statements are true Both the statements are false
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27
GATE2019 EE: 27
The closedloop line integral $\oint_{z = 5} \frac{z^3 + z^2 + 8}{z+2}dz$ Evaluated Counterclockwise is $+8j\pi$ $8j\pi$ $4j\pi$ $+4\pi$
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28
GATE2019 EE: 28
A periodic function $\large{f(t)},$ with a period of 2$\pi$, is represented as its fourier series, $\large{f(t)} = a_0 + \sum_{n=1}^{\infty }a_n cos nt + \sum_{n=1}^{\infty} b_n sin nt.$}$ If $\large{f(t)} = \left\{\begin{matrix} Asint, & 0 \le t\le \pi\\ 0, & \pi ... $a_1 = \frac{A}{2}; b_1 = 0$ $a_1 = 0;b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
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29
GATE2019 EE: 29
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30
GATE2019 EE: 30
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31
GATE2019 EE: 31
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32
GATE2019 EE: 32
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GATE2019 EE: 33
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GATE2019 EE: 34
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35
GATE2019 EE: 35
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36
GATE2019 EE: 36
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37
GATE2019 EE: 37
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38
GATE2019 EE: 38
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39
GATE2019 EE: 39
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40
GATE2019 EE: 40
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