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41
GATE Electrical 2024 | Question: 42
The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ represent the unit vectors along $r$ and $\theta$, respectively. The value of $\text{P}$ in the ... bar{H}(r, \theta, \phi)=\frac{1}{r^{3}}(\hat{r} P \cos \theta+\hat{\theta} \sin \theta) \]
The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ r...
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42
GATE Electrical 2024 | Question: 43
If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal place).
If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal pla...
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43
GATE Electrical 2024 | Question: 44
A $3$-phase star connected slip ring induction motor has the following parameters referred to the stator: \[ R_{s}=3 \Omega, X_{s}=2 \Omega, X_{r}^{\prime}=2 \Omega, R_{r}^{\prime}=2.5 \Omega \] The per phase stator to rotor ... to the rotor side) to be connected in series with each phase of the rotor winding is ____________ (rounded off to $2$ decimal places).
A $3$-phase star connected slip ring induction motor has the following parameters referred to the stator:\[R_{s}=3 \Omega, X_{s}=2 \Omega, X_{r}^{\prime}=2 \Omega, R_{r}^...
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44
GATE Electrical 2024 | Question: 45
A $5 \mathrm{~kW}, 220 \mathrm{~V}$ $\text{DC}$ shunt motor has $0.5 \Omega$ armature resistance including brushes. The motor draws a no-load current of $3 \mathrm{~A}$. The field current is constant at $1 \mathrm{~A}$ ... ) drawn by the motor while delivering the rated load, for the best possible efficiency, is _____________ (rounded off to $2$ decimal places).
A $5 \mathrm{~kW}, 220 \mathrm{~V}$ $\text{DC}$ shunt motor has $0.5 \Omega$ armature resistance including brushes. The motor draws a no-load current of $3 \mathrm{~A}$. ...
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GATE Electrical 2024 | Question: 46
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{\max } \sin \delta$, where $\delta$ is the load angle ... , the accelerating area on the power angle curve is __________ times $P_{\max }$ (rounded off to $2$ decimal places).
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the ge...
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46
GATE Electrical 2024 | Question: 47
Consider the closed-loop system shown in the figure with \[ G(s)=\frac{K\left(s^{2}-2 s+2\right)}{\left(s^{2}+2 s+5\right)} . \] The root locus for the closed-loop system is to be drawn for $0 \leq K<\infty$. The angle of ... $(-1+j 2)$, in degrees, is ___________(rounded off to the nearest integer).
Consider the closed-loop system shown in the figure with\[G(s)=\frac{K\left(s^{2}-2 s+2\right)}{\left(s^{2}+2 s+5\right)} .\]The root locus for the closed-loop system is ...
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GATE Electrical 2024 | Question: 48
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20 \mathrm{~dB} /$ decade at least till $100 \mathrm{rad} / \mathrm{sec}$ with the gain crossover frequency ... . The steadystate error of the closed-loop system for a unit ramp input is (rounded off to 2 decimal places).
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20 \mathrm{~dB} /$ decade at least till...
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48
GATE Electrical 2024 | Question: 49
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of the gain $K_{I}(>0)$ for a $50^{\circ}$ phase margin is __________ (rounded off to $2$ ... -80 \\ \hline 2.0 & -18 & -130 \\ \hline 10.0 & -40 & -200 \\ \hline \end{array}
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of...
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49
GATE Electrical 2024 | Question: 50
In the given circuit, the diodes are ideal. The current $\text{I}$ through the diode $\text{D} 1$ in milliamperes is __________(rounded off to two decimal places).
In the given circuit, the diodes are ideal. The current $\text{I}$ through the diode $\text{D} 1$ in milliamperes is __________(rounded off to two decimal places).
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GATE Electrical 2024 | Question: 51
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded off to $2$ decimal places).
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded of...
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GATE Electrical 2024 | Question: 52
A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is $60^{\circ}$. The ratio of the rms value of the fundamental component of the input current to the rms value of the total input current of the bridge is _____________ (rounded off to $3$ decimal places).
A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is $60^{\circ}$. The ratio...
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GATE Electrical 2024 | Question: 53
A single-phase full bridge voltage source inverter $\text{(VSI)}$ feeds a purely inductive load. The inverter output voltage is a square wave in $180^{\circ}$ ... is $20 \mathrm{mH}$, the peak-topeak load current in amperes is _____________ (rounded off to the nearest integer).
A single-phase full bridge voltage source inverter $\text{(VSI)}$ feeds a purely inductive load. The inverter output voltage is a square wave in $180^{\circ}$ conduction ...
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GATE Electrical 2024 | Question: 54
In the $\mathrm{DC}-\mathrm{DC}$ converter shown in the figure, the current through the inductor is continuous. The switching frequency is $500 \mathrm{~Hz}$. The voltage $\left(V_{o}\right)$ across the load is assumed to be constant and ripple free. The peak inductor current in amperes is ______________ (rounded off to the nearest integer).
In the $\mathrm{DC}-\mathrm{DC}$ converter shown in the figure, the current through the inductor is continuous. The switching frequency is $500 \mathrm{~Hz}$. The voltage...
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GATE Electrical 2024 | Question: 55
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited $\text{DC}$ motor with the following specifications: Rated armature voltage $210 \mathrm{~V}$ ... the triggering angle of the converter bridge in degrees should be ____________ (rounded off to $2$ decimal places).
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited $\text{DC}$ motor with the following specifications:Rat...
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GATE 2024 Electrical | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [talk $\rightarrow$ shout $\rightarrow$ scream] is analogous to [please $\rightarrow$ __________ $\rightarrow$ pander]. Which one of the given options is appropriate to fill the blank? flatter flutter fritter frizzle
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [talk $\rightarrow$ shout $\rightarrow$ scream] is analogous to [...
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GATE 2024 Electrical | GA Question: 2
$\text{P}$ and $\text{Q}$ have been allotted a hostel room with two beds, a study table, and an almirah. $\mathrm{P}$ is an avid bird-watcher and wants to sit at the table and watch birds outside the window. $\text{Q}$ does not mind that as long as his bed is close to the ceiling fan. Which one of the following arrangements suits them the most?
$\text{P}$ and $\text{Q}$ have been allotted a hostel room with two beds, a study table, and an almirah. $\mathrm{P}$ is an avid bird-watcher and wants to ...
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GATE 2024 Electrical | GA Question: 3
The decimal number system uses the characters $0,1,2, \ldots, 8,9$, and the octal number system uses the characters $0,1,2, \ldots, 6,7$. For example, the decimal number $12\left(=1 \times 10^{1}+2 \times 10^{0}\right)$ is expressed ... $108$ in the octal number system is $168$ $108$ $150$ $154$
The decimal number system uses the characters $0,1,2, \ldots, 8,9$, and the octal number system uses the characters $0,1,2, \ldots, 6,7$.For example, the deci...
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GATE 2024 Electrical | Question: 4
A shopkeeper buys shirts from a producer and sells them at $20 \%$ profit. A customer has to pay ₹ $3,186.00$ including $18 \%$ taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer? ₹ $2,500.00$ ₹ $1,975.40$ ₹ $2,250.00$ ₹ $2,548.80$
A shopkeeper buys shirts from a producer and sells them at $20 \%$ profit. A customer has to pay ₹ $3,186.00$ including $18 \%$ taxes, per shirt. At what pr...
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GATE 2024 Electrical | GA Question: 5
If, for non-zero real variables $x, y$, and real parameter $a>1$, \[ x: y=(a+1):(a-1) \text {, } \] then, the ratio $\left(x^{2}-y^{2}\right):\left(x^{2}+y^{2}\right)$ is $2 a:\left(a^{2}+1\right)$ $a:\left(a^{2}+1\right)$ $2 a:\left(a^{2}-1\right)$ $a:\left(a^{2}-1\right)$
If, for non-zero real variables $x, y$, and real parameter $a>1$,\[x: y=(a+1):(a-1) \text {, }\]then, the ratio $\left(x^{2}-y^{2}\right):\left(x^{2}+y^{2}\right)$ ...
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GATE 2024 Electrical | GA Question: 6
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks. Following a row $\text{(i)}$ the shopkeeper $\text{(ii)}$_the price of a frying pan, the cook stood $\text{(iii)}$ a row to withdraw cash $\text{(iv)}$ ... $\text{(iv)}$ at $\text{(i)}$ over $\text{(ii)}$ with $\text{(iii)}$ over $\text{(iv)}$ at
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.Following a row $\text{(i)}$ the shopkeeper $\text{...
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GATE 2024 Electrical | GA Question: 7
In the following figure, \[ \begin{array}{c} \mathrm{CD}=5 \mathrm{~cm}, \mathrm{BE}=10 \mathrm{~cm}, \mathrm{AE}=12 \mathrm{~cm}, \\ \angle \mathrm{DAB}=\angle \mathrm{DCB} \text {, and } \angle \mathrm{DAE}=\angle \mathrm{DBC}=90^{\circ} \end ... } \] Points $\text{AFCD}$ create a rhombus. The length of $\mathrm{BF}$ (in $\mathrm{cm}$ ) is $3$ $2$ $4$ $6$
In the following figure,\[\begin{array}{c}\mathrm{CD}=5 \mathrm{~cm}, \mathrm{BE}=10 \mathrm{~cm}, \mathrm{AE}=12 \mathrm{~cm}, \\\angle \mathrm{DAB}=\angle \...
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GATE 2024 Electrical | GA Question: 8
The chart below shows the data of the number of cars bought by Millennials and Gen $\text{X}$ people in a country from the year $2010$ to $2020$ as well as the yearly fuel consumption of the country (in Million liters). Considering the data ... buyers from $2015$ to $2020$ is more than the increase in the number of Millennial car buyers from $2010$ to $2015$.
The chart below shows the data of the number of cars bought by Millennials and Gen $\text{X}$ people in a country from the year $2010$ to $2020$ as well as the yearly ...
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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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