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361
GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ?$\frac{z^{2}-1}{z} \\ $$\frac{z^{2}-1}{z+2} \\ $$\frac{z^{2}-1}{z-0.5} \\ $$\frac{z^...
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363
GATE Electrical 2019 | Question: 6
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfer function represents a low pass filter high pass filter band pass filter notch filter
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfe...
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364
GATE Electrical 2019 | Question: 7
The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system? $e^{+at}u(t)$ $e^{-a(t+T)}u(t)$ $1+e^{-at}u(t)$ $e^{-a(t-T)}u(t)$
The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal ...
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365
GATE Electrical 2019 | Question: 8
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is $4.5\%$ $9\%$ $5\%$ $1\%$
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is$4.5\%$$9\%$$5\%$$1\%$
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366
GATE Electrical 2019 | 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 $100 Hz$ $150 Hz$ $250 Hz$ $300 Hz$
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 low...
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367
GATE Electrical 2019 | 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 rotor resistance rotor leakage reactance magnetizing reactance stator resistance
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 isrotor resistance...
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368
GATE Electrical 2019 | Question: 11
A three-phase 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 $100 \: A$ $200 \: A$ $300 \: A$ $400 \: A$
A three-phase 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 f...
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369
GATE Electrical 2019 | Question: 12
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching is $60$ $-45$ $90$ $-30$
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of s...
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371
GATE Electrical 2019 | Question: 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 $(-0.5,j0)$ $(-0.75,j0)$ $(-1.25,j0)$ $(-1.5,j0)$
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 nega...
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372
GATE Electrical 2019 | Question: 15
The characteristic equation of a linear time-invariant (LTI) system is given by $\Delta(s)=s^{4}+3s^{3}+3s^{2}+s+k=0$ The system is BIBO stable if $0<K<\frac{12}{9}$ $k>3$ $0<k<\frac{8}{9}$ $k>6$
The characteristic equation of a linear time-invariant (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}$$k>3$$...
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375
GATE Electrical 2019 | Question: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-3,2)\rightarrow(2,6,2) \rightarrow(2,6,-1) $ is___________.
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-...
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376
GATE Electrical 2019 | Question: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
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379
GATE Electrical 2019 | Question: 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 ____________
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 bus...
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380
GATE Electrical 2019 | Question: 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_________
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,...
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381
GATE Electrical 2019 | Question: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
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384
GATE Electrical 2019 | Question: 27
The closed-loop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counter-clockwise, is $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
The closed-loop line integral $$\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$$evaluated Counter-clockwise, is $+8 j \pi$$-8 j \pi$$-4 j \pi$$+4 j \pi$
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385
GATE Electrical 2019 | Question: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $$f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin ...
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387
GATE Electrical 2019 | Question: 30
The transfer function of a phase lead compensator is given by $D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$ The frequency (in rad/sec), at which $\angle D(j \omega)$ is maximum, is $\sqrt{\frac{3}{T^2}}$ $\sqrt{\frac{1}{3T^2}}$ $\sqrt{3T}$ $\sqrt{3T^2}$
The transfer function of a phase lead compensator is given by$$D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$$The frequency (in rad/sec), a...
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390
GATE Electrical 2019 | Question: 33
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu _nC_{ox} =100 \: \mu A /V^2$, the threshold voltage $(V_T)$ is $500$ mV. Ignore channel length modulation. The output voltage $V_{\text{out}}$ is $100$ mV $500$ mV $600$ mV $2$ V
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu _nC_{ox} =100 \: \mu A /V^2$, the threshold voltage $(V_T)$ is $500$ mV. Ignor...
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391
GATE Electrical 2019 | Question: 34
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is $100$ mV $400$ mV $500$ mV $600$ mV
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is$100$ mV$400$ mV$500$ mV$600$ mV
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392
GATE Electrical 2019 | Question: 35
The output expression for the Karnaugh map shown below is $Q \bar{R} +S$ $Q \bar{R} + \bar{S}$ $QR+S$ $Q R +\bar{S}$
The output expression for the Karnaugh map shown below is$Q \bar{R} +S$$Q \bar{R} + \bar{S}$$QR+S$$Q R +\bar{S}$
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393
GATE Electrical 2019 | Question: 36
In the circuit shown below, $X$ and $Y$ are digital inputs, and $Z$ is a digital output. The Equivalent circuit is a NAND gate NOR gate XOR gate XNOR gate
In the circuit shown below, $X$ and $Y$ are digital inputs, and $Z$ is a digital output. The Equivalent circuit is aNAND gateNOR gateXOR gateXNOR gate
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394
GATE Electrical 2019 | Question: 37
A DC-DC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of the converter is $250$ Hz. If switch-on duration is $1$ ms, the load power is $6$ W $12$ W $24$ W $48$ W
A DC-DC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of th...
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395
GATE Electrical 2019 | Question: 38
The line currents of a three-phase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to each other. The rms value of neutral current is $0$ A $\frac{100}{\sqrt{3}}$ A $100$ A $300$ A
The line currents of a three-phase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to ea...
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396
GATE Electrical 2019 | Question: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
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397
GATE Electrical 2019 | Question: 40
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is _______________
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (r...
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398
GATE Electrical 2019 | Question: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage acr...
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399
GATE Electrical 2019 | Question: 42
The current $I$ flowing in the circuit shown in amperes is ____________
The current $I$ flowing in the circuit shown in amperes is ____________
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400
GATE Electrical 2019 | Question: 43
The voltage across and the current through a load are expressed as follows $v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load is _________.
The voltage across and the current through a load are expressed as follows$v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$$i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \b...
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