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161
GATE 2024 Electrical | GA Question: 9
The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks ... . Object $\mathrm{R}$ rotates in the anticlockwise direction. Object $\mathrm{Q}$ rotates in the clockwise direction.
The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinion...
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GATE 2024 Electrical | GA Question: 10
A surveyor has to measure the horizontal distance from her position to a distant reference point $\text{C}$. Using her position as the center, a $200 \mathrm{~m}$ horizontal line segment is drawn with the two endpoints $\text{A}$ ... $\mathrm{m}$ ) of the reference point $\mathrm{C}$ from her position is nearest to $2603$ $2606$ $2306$ $2063$
A surveyor has to measure the horizontal distance from her position to a distant reference point $\text{C}$. Using her position as the center, a $200 \mathrm{...
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GATE Electrical 2023 | GA Question: 10
A square with sides of length $6 \mathrm{~cm} $ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is_______ $\mathrm{cm}^2.$ $6 \pi$ $18$ $20$ $9 \pi$
A square with sides of length $6 \mathrm{~cm} $ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as...
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May 20, 2023
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GATE Electrical 2023 | Question: 1
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \mathbf{x}=1$ ... $\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^T$
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \math...
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GATE Electrical 2023 | Question: 2
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is $\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}{s+1}$
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is$\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}...
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GATE Electrical 2023 | Question: 3
In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s+5}{s-1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at $G(s)H(s) = \infty$ $G(s)H(s) = 0$ $G(s)H(s) = 3$ $G(s)H(s) = -5$
In the Nyquist plot of the open-loop transfer function$$G(s)H(s) = \frac{3s+5}{s-1}$$corresponding to the feedback loop shown in the figure, the infinite semi-circular ar...
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GATE Electrical 2023 | Question: 4
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral gain be $3$ and $1,$ respectively. For a unit step reference input, the final values of the controller output and ... respectively, are $G(s)=\frac{1}{s-1}$ $\infty, \infty$ $1,0$ $1,-1$ $-1,1$
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral...
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GATE Electrical 2023 | Question: 5
The following columns present various modes of induction machine operation and the ranges of slip ... $a-r, b-q$, and $c-p$ $a-p, b-r$, and $c-q$ $a-q, b-p$, and $c-r$
The following columns present various modes of induction machine operation and the ranges of slip$$\begin{array}{ll} \qquad \qquad\textbf{A} & \qquad \textbf{B} \\ \quad...
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GATE Electrical 2023 | Question: 7
A continuous-time system that is initially at rest is described by $ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$ where$x(t)$ is the input voltage and $y(t)$ is the output voltage. The impulse response of the system is $3 e^{-2 t}$ $\frac{1}{3} e^{-2 t} u(t)$ $2 e^{-3 t} u(t)$ $2 e^{-3 t}$
A continuous-time system that is initially at rest is described by $$ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$$ where$x(t)$ is the input voltage and $y(t)$ is the output voltag...
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GATE Electrical 2023 | Question: 8
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by $\begin{aligned} X(\omega) & =1, \text { for }|\omega|<W_o \\ & =0, \text { for }|\omega|>W_0 \end{aligned}$ Which one of the following statements is true? $x(t)$ tends to be an impulse as ... At $t=\frac{\pi}{2 W_0}, x(t)=-\frac{1}{\pi}$ At $t=\frac{\pi}{2 W_0}, x(t)=\frac{1}{\pi}$
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by$$\begin{aligned}X(\omega) & =1, \text { for }|\omega|<W_o \\& =0, \text { for }|\omega|>W_0\end{aligned...
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GATE Electrical 2023 | Question: 9
The $\text{Z}$-transform of a discrete signal $\text{x[n]}$ is $\text{X(z)}=\frac{4 z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}$ with $\text{ROC=R}$ Which one of the following statements is true? Discrete-time Fourier ... transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is such that $ \mathrm{x}[\mathrm{n}]$ is a right-sided sequence
The $\text{Z}$-transform of a discrete signal $\text{x[n]}$ is$\text{X(z)}=\frac{4 z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}$ with $\text{ROC=R}$ Whic...
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GATE Electrical 2023 | Question: 10
For the three-bus power system shown in the figure, the trip signals to the circuit breakers $\text{B}_1$ to $\text{B}_9$ are provided by overcurrent relays $\text{R}_1$ to $\text{R}_9$, respectively, some of which have directional ... $\text{R}_4$ are directional overcurrent relays blocking faults towards Line $1$ and Line $2,$ respectively.
For the three-bus power system shown in the figure, the trip signals to the circuit breakers $\text{B}_1$ to $\text{B}_9$ are provided by overcurrent relays $\text{R}_1$ ...
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GATE Electrical 2023 | Question: 11
The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G 1}$ and $P_{G 2}$ ... Both $P_{G 1}$ and $F$ will increase $P_{G 1}$ will increase and $F$ will decrease Both $P_{G 1}$ and $F$ will decrease
The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G 1}$ and $P_{G 2}$ are given as $F_{1}\left(P_{G 1}\rig...
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GATE Electrical 2023 | Question: 12
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{DC}$ currents of the same value, the directions of which are shown in the figure (i). The rotor coils ... with $E_{a-a^{\prime}}$ leading $E_{b-b^{\prime}}$ $E_{a-a^{\prime}}=E_{b-b^{\prime}}=0$
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{D...
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GATE Electrical 2023 | Question: 13
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ ... $10 \mathrm{~V}$ $6 \mathrm{~V}$ $12 \mathrm{~V}$ $20 \mathrm{~V}$
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ All the...
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GATE Electrical 2023 | Question: 14
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ ... $\left[\begin{array}{ll}\frac{4}{5} & -\frac{3}{5} \\ \frac{3}{5} & -\frac{4}{5}\end{array}\right]$
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ is$\le...
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GATE Electrical 2023 | Question: 15
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_o$. The $\sigma_o$ is estimated by randomly drawing out $10,000$ numbers of samples $\left(x_n\right)$. The ... $E\left(\hat{\sigma}_1\right)=E\left(\hat{\sigma}_2\right)$
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_o$.The $\sigma...
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GATE Electrical 2023 | Question: 16
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ during OFF state as shown in figure (i) and carry current in both directions during $\text{ON}$ state as shown in figure (ii). Which of the following switch combination(s) will realize the same?
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ duringOFF state as shown in figure (i) and carry current in both directions d...
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GATE Electrical 2023 | Question: 17
Which of the following statement(s) is/are true? If an $\text{LTI}$ system is causal, it is stable A discrete time $\text{LTI}$ system is causal if and only if its response to a step input $u[n]$ is $0$ for $n<0$ ... the system is stable If the impulse response $0<|h[n]|<1$ for all $n$, then the $\text{LTI}$ system is stable.
Which of the following statement(s) is/are true? If an $\text{LTI}$ system is causal, it is stableA discrete time $\text{LTI}$ system is causal if and only if its respons...
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GATE Electrical 2023 | Question: 18
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below. Considering that there is no shunt inductor connected to any of the buses, which of the following can $\text{NOT}$ be true? Line charging ... capacitor of finite value is present in line$ 2-3$ only and shunt capacitor of finite value is present in bus $3$ only
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below.Considering that there is no shunt inductor connected to any of the bus...
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GATE Electrical 2023 | Question: 19
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t<0$ ... value of the voltage across the inductor $\left(V_{L}\right)$ at $t=0^{+}$in Volts is________ (Round off to $1$ decimal place).
The value of parameters of the circuit shown in the figure are $\qquad R_{1}=2 \Omega, R_{2}=2 \Omega, R_{3}=3 \Omega, L=10 \mathrm{mH}, C=100 \mu \mathrm{F}$ For time $t...
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GATE Electrical 2023 | Question: 20
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm{~V}$ $\text{DC}$ supply drawing rated current. The armature ... field current unaltered then the resultant speed of the motor in $\mathrm{~ RPM}$ is_________ (Round off to the nearest integer).
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm...
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GATE Electrical 2023 | Question: 21
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
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GATE Electrical 2023 | Question: 22
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to $1$ decimal place).
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to...
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GATE Electrical 2023 | Question: 23
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mathrm{mH} / \mathrm{km} ;$ ... $2$ decimal places).
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mat...
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GATE Electrical 2023 | Question: 24
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-\alpha t}}{2+\alpha t}, \quad \alpha=0.01$ and $y(0)=0$
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-...
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GATE Electrical 2023 | Question: 25
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round off to $2$ decimal places)
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round o...
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GATE Electrical 2023 | Question: 26
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$ $\frac{e^{-2.514 s}}{s+1}$ $1.04 e^{-2.514 s}$ $2.51 e^{-1.047 s}$
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$$\frac{e^{-2.514 s}}{s+1}$$1.04...
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GATE Electrical 2023 | Question: 27
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components are ideal and the breakdown voltage of the Zener is $5 \mathrm{~V}.$ Which of the ... minimum values of the output voltage $\text{V}_{O} $ are $+5 \mathrm{~V}$ and $-10 \mathrm{~V}$, respectively.
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components a...
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GATE Electrical 2023 | Question: 28
Consider a lead compensator of the form $K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$ The frequency at which this compensator produces maximum phase lead is $ 4 \mathrm{rad} / \mathrm{s}.$ At this frequency, the gain amplification provided ... $6 \mathrm{~dB}$. The values of $\alpha, \beta,$ respectively, are $1,16$ $2,4$ $3,5$ $2.66,2.25$
Consider a lead compensator of the form $$K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$$The frequency at which this compensator produces maximum phase lea...
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GATE Electrical 2023 | Question: 29
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in the figure. If the wattmeter reading is $-400 \mathrm{~W}$ and the line ... $0.5$ leading $0.866$ leading $0.707$ lagging
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in ...
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GATE Electrical 2023 | Question: 30
An $8$-bit $\text{ADC}$ converts analog voltage in the range of $0$ to $+5 \mathrm{~V}$ to the corresponding digital code as per the conversion characteristics shown in figure. For $V_{\text {in }}=1.9922 \mathrm{~V}$, which of the following digital output, given in hex, is true? $64 \mathrm{H}$ $65 \mathrm{H}$ $66 \mathrm{H}$ $67 \mathrm{H}$
An $8$-bit $\text{ADC}$ converts analog voltage in the range of $0$ to $+5 \mathrm{~V}$ to the corresponding digital code as per the conversion characteristics shown in f...
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GATE Electrical 2023 | Question: 31
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bus having a voltage of magnitude $\left|V_3\right|=1.0$ p.u. and angle of $-15^{\circ}$. A ... $3 \quad$ Slack bus Bus $1 \quad P-|V|$ bus Bus $2 \quad P-Q$ bus Bus $3 \quad$ Slack bus
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bu...
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GATE Electrical 2023 | Question: 32
Consider the following equation in a $2-\text{D}$ real-space. $\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ Which of the following statement(s) is/are true? When $p=2$, the area enclosed by the curve is $\pi$. When $p$ ... $p$ tends to $0,$ the area enclosed by the curve is $1.$ When $p=1$, the area enclosed by the curve is $2.$
Consider the following equation in a $2-\text{D}$ real-space. $\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ Which of the following statement(s) is/a...
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GATE Electrical 2023 | Question: 33
In the figure, the electric field $\boldsymbol{E}$ and the magnetic field $\boldsymbol{B}$ point to $\mathrm{x}$ and $\mathrm{z}$ directions, respectively, and have constant magnitudes. A positive charge q' is released from rest at the origin ... plane only. The trajectory of the charge will be a circle. The charge will progress in the direction of $\mathbf{y}$.
In the figure, the electric field $\boldsymbol{E}$ and the magnetic field $\boldsymbol{B}$ point to $\mathrm{x}$ and $\mathrm{z}$ directions, respectively, and have cons...
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GATE Electrical 2023 | Question: 34
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true? When switch $\text{S}$ is $\mathrm{ON}$, both $D_{1}$ and $D_{2}$ conducts and $D_{3}$ is reverse biased When switch $\text{S}$ ... conduct When switch $\text{S}$ is $\mathrm{OFF}, D_{1}$ conducts, $D_{2}$ is reverse biased and $D_{3}$ conducts
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true? When switch $\text{S}$ is $\mathrm{ON}$, both $D_{...
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GATE Electrical 2023 | Question: 36
Consider the state-space description of an $\text{LTI}$ ... for which the steady-state output of the system will be zero, is ________(Round off to the nearest integer).
Consider the state-space description of an $\text{LTI}$ system with matrices$\qquad A=\left[\begin{array}{cc}0 & 1 \\-1 & -2\end{array}\right], B=\left[\begin{array}{l}0 ...
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GATE Electrical 2023 | Question: 37
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ The corresponding excitation voltage in per unit is _________ (Round off to $2$ decimal places).
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ ...
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GATE Electrical 2023 | Question: 38
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the ... in $\text { RPM}$ (neglecting the stator leakage impedance and rotational losses) is ________ (Round off to the nearest integer).
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed oper...
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GATE Electrical 2023 | Question: 39
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer). $x[n]=1+3 \sin \left(\frac{15 \pi}{8} n+\frac{3 \pi}{4}\right)-5 \sin \left(\frac{\pi}{3} n-\frac{\pi}{4}\right)$
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer).$$x[n]=1+3 \sin \left(\frac{15 \pi}{8} n...
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