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Questions by Arjun
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281
GATE Electrical 2018 | Question: 45
The capacitance of an air-filled parallel-plate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes $86$ pF. Neglecting the fringing effects, the relative permittivity of the dielectric is ___________ (up to $2$ decimal places)
The capacitance of an air-filled parallel-plate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of ...
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Feb 19, 2018
new
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numerical-answers
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282
GATE Electrical 2018 | Question: 44
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$...
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Feb 19, 2018
Linear Algebra
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
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283
GATE Electrical 2018 | Question: 43
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
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Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
maxima-minima
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284
GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$...
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Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
definite-integral
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285
GATE Electrical 2018 | Question: 41
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The base-emitter voltage drop is a constant, $V_{BE}=0.7 \: V$. The value of the Thevenin equivalent resistance $R_{Th}$ (in $\Omega$) as shown in the figure is _________ (up to $2$ decimal places)
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The base-emitter voltage drop is a constant, $V_{BE}=0.7 \: V$...
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Feb 19, 2018
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286
GATE Electrical 2018 | Question: 40
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\om...
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Feb 19, 2018
Transform Theory
gate2018-ee
numerical-answers
transform-theory
fourier-transform
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287
GATE Electrical 2018 | Question: 39
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is $11/3$ $7/3$ $1/3$ $5/3$
The signal energy of he continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is$11/3$$7/3$$1/3$$5/3$
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Feb 19, 2018
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288
GATE Electrical 2018 | Question: 38
Consider the two continuous-time signals defined below: ... than the energy of $x_1[n]$ $x_1[n]$ and $x_2[n]$ have equal energies Neither $x_1[n]$ nor $x_2[n]$ is a finite-energy signal
Consider the two continuous-time signals defined below:$$x_1(t) = \begin{cases} \mid t \mid, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases} \\ x_2(t) = \begin{ca...
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Feb 19, 2018
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289
GATE Electrical 2018 | Question: 37
Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function $F=m_0+m_2+m_3+m_5+m_7$, where $m_i$ denotes the $i$ th minterm. In addition, $F$ has a don't care for $m_1$. The simplified expression for $F$ is given by ... $\overline{A}+C$ $\overline{C}+A$ $\overline{A} C + BC + A \overline{C}$
Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function $F=m_0+m_2+m_3+m_5+m_7$, where $m_i$ denotes the $i$ th minterm...
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Feb 19, 2018
Analog and Digital Electronics
gate2018-ee
analog-and-digital-electronics
boolean-algebra
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290
GATE Electrical 2018 | Question: 36
Which one of the following statements is true about the digital circuit shown in the figure It can be used for dividing input frequency by $3$ It can be used for dividing input frequency by $5$ It can be used for dividing input frequency by $7$ It cannot be reliably used as a frequency divider due to disjoint internal cycles
Which one of the following statements is true about the digital circuit shown in the figureIt can be used for dividing input frequency by $3$It can be used for dividing i...
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Feb 19, 2018
Analog and Digital Electronics
gate2018-ee
analog-and-digital-electronics
sequential-circuit
counters
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291
GATE Electrical 2018 | Question: 35
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $-1$ $-2$
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is$1$$0$$-1$$-2$
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Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
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292
GATE Electrical 2018 | Question: 34
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is$3$$4$$5$$6$
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Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
complex-valued-functions
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293
GATE Electrical 2018 | Question: 33
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$
Consider a system governed by the following equations $$ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$$ The initial conditions are such that $...
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Feb 19, 2018
Differential Equations
gate2018-ee
differential-equations
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294
GATE Electrical 2018 | Question: 32
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is $\text{j} 12 \: \Omega$ $\text{-j} 12 \: \Omega$ $\text{j} 13 \: \Omega$ $13 \: \Omega$
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is$\text{j} 12 \: \Omega$$\text{-j} 12 \: \Omega$$\text{j} 13 \: \Omega$$13 \: \Omeg...
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Feb 19, 2018
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295
GATE Electrical 2018 | Question: 31
A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?
A DC voltage source is connected to a series $L-C$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the fo...
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Feb 19, 2018
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296
GATE Electrical 2018 | Question: 30
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $\delta$ is the load angle. Newton-Raphson method is used to calculate the value of $\delta$ ... at the end of the first iteration is $15^{\circ}$ $28.28^{\circ}$ $28.74^{\circ}$ $31.20^{\circ}$
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $...
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Feb 19, 2018
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GATE Electrical 2018 | Question: 29
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$, and line ... $6.34, \: 11.34, \: 2.68$ $5.00, \: 11.34, \: 1.34$
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by gene...
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Feb 19, 2018
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GATE Electrical 2018 | Question: 28
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$, the fault current is $I_{f1}= kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation ... $Z_f=\frac{(Z_1+Z_2)k}{1-k} \\$ $Z_f=\frac{(Z_1+Z_2)k}{1+k}$
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$,...
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Feb 19, 2018
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299
GATE Electrical 2018 | Question: 27
A $0-1$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $0-10$ Ampere for all operating frequencies. The time constant in milliseconds and resistance in $m \Omega$ of the shunt coil respectively are $2, \: 5.55$ $2, \: 1$ $2.18, \: 0.55$ $11.1, \: 2$
A $0-1$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $0-10$ A...
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Feb 19, 2018
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300
GATE Electrical 2018 | Question: 26
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius $r < < R$, and neglecting any leakage flux, the best estimate for the mean radius $R$ ... $\frac{\mu V r^2 N_P^2 \omega}{2I} \\ $ $\frac{\mu I r^2 N_P^2 \omega}{2V} $
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius $r < < R$, a...
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Feb 19, 2018
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GATE Electrical 2018 | Question: 25
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steady-state error in the output of the system for a unit-step input is _______ (up to $2$ decimal places).
Consider a unity feedback system with forward transfer function given by $$G(s) = \frac{1}{(s+1)(s+2)}$$ The steady-state error in the output of the system for a unit-ste...
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Feb 19, 2018
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302
GATE Electrical 2018 | Question: 24
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the no- ... motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produ...
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Feb 19, 2018
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numerical-answers
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303
GATE Electrical 2018 | Question: 23
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of the current is ________ A (up to $2$ decimal places).
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of...
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Feb 19, 2018
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numerical-answers
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304
GATE Electrical 2018 | Question: 22
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers)...
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Feb 19, 2018
new
gate2018-ee
numerical-answers
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305
GATE Electrical 2018 | Question: 21
The positive, negative and zero sequence impedances of a $125$ MVA, three-phase, $15.5$ kV, star-gounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respectively on the machine rating base. The machine is unloaded and working ... then the magnitude of fault current for a $b$-phase to ground fault (in kA) is __________ (up to $2$ decimal places).
The positive, negative and zero sequence impedances of a $125$ MVA, three-phase, $15.5$ kV, star-gounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respe...
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Feb 19, 2018
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numerical-answers
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306
GATE Electrical 2018 | Question: 20
The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$ ... $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).
The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{b...
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Feb 19, 2018
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numerical-answers
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307
GATE Electrical 2018 | Question: 19
In the two-port nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
In the two-port nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
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Feb 19, 2018
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308
GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0...
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Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
definite-integral
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309
GATE Electrical 2018 | Question: 17
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textb...
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Feb 19, 2018
Linear Algebra
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
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310
GATE Electrical 2018 | Question: 16
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is$k \: x(t)$, where $k$ is an eigenvalue$k \: e^{j \omega t} \: x(t)$, where $k...
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Feb 19, 2018
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311
GATE Electrical 2018 | Question: 15
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by $Z \frac{R_1}{R_2}$ $ – Z \frac{R_2}{R_1}$ $Z$ $ – Z \frac{R_1}{R_1 + R_2}$
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by$Z \frac{R_1}{R_2}$$ – Z \frac{R_2}{R_1}$$Z$$ – Z \frac{...
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Feb 19, 2018
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312
GATE Electrical 2018 | Question: 14
In the logic circuit shown in the figure, $Y$ is given by $Y=ABCD$ $Y=(A+B)(C+D)$ $Y=A+B+C+D$ $Y=AB+CD$
In the logic circuit shown in the figure, $Y$ is given by$Y=ABCD$$Y=(A+B)(C+D)$$Y=A+B+C+D$$Y=AB+CD$
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Feb 19, 2018
Analog and Digital Electronics
gate2018-ee
analog-and-digital-electronics
logic-gates
boolean-algebra
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313
GATE Electrical 2018 | Question: 13
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $-2 \pi i$
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is$\frac{\pi i}...
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Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
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314
GATE Electrical 2018 | Question: 12
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2...
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Feb 19, 2018
Calculus
gate2018-ee
calculus
directional-derivatives
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315
GATE Electrical 2018 | Question: 11
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true? $f(x)$ is discontinuous at $x=0$ $f(x)$ ... is differentiable but its first derivative is not continuous at $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true?$f(x)$...
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Feb 19, 2018
Calculus
gate2018-ee
calculus
continuity-and-differentiability
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316
GATE Electrical 2018 | Question: 10
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{-12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $-899.18$ V/m $999.09$ V/m $-999.09$ V/m
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85...
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Feb 19, 2018
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317
GATE Electrical 2018 | Question: 9
Match the transfer functions of the second-order systems with the nature of the systems given below. ... P-I, Q-II, R-III P-II, Q-I, R-III P-III, Q-II, R-I P-III, Q-I, R-II
Match the transfer functions of the second-order systems with the nature of the systems given below.$\begin{array} {} \underline{\textit{Transfer functions}} & \underline...
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Feb 19, 2018
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GATE Electrical 2018 | Question: 8
In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinusoidal steady state, and $R< < \omega L$. $P_1$, $P_2$ and $P_3$ are the ... $P_1 <0$, $P_2>0$, $P_3>0$ $P_1 <0$, $P_2>0$, $P_3<0$ $P_1 > 0$, $P_2<0$, $P_3>0$
In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinuso...
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Feb 19, 2018
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319
GATE Electrical 2018 | Question: 7
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is $11$ $12$ $13$ $14$
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is$11$$12$$13$$14$
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Feb 19, 2018
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GATE Electrical 2018 | Question: 6
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be greater ... $ \begin{vmatrix} \frac{V_1V_2}{Z} \end{vmatrix} \\ $
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the...
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Feb 19, 2018
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