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361
GATE Electrical 2012 | Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
The state variable description of an LTI system is given by$$\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 & a_1 & 0 \\ 0 & 0 & a_2 \\ a_3 & 0 & 0 \...
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362
GATE Electrical 2012 | Question: 40
Assuming both the voltages sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is $0.8 \: \Omega$ $1.4 \: \Omega$ $2 \: \Omega$ $2.8 \: \Omega$
Assuming both the voltages sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is$0.8 \: \Omega$$1.4 \: \Omega$$2 \: \...
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363
GATE Electrical 2012 | Question: 39
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t=0^-} =0$. The numerical value of $\dfrac{dy}{dt} \bigg \vert _{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t...
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364
GATE Electrical 2012 | Question: 38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of ...
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365
GATE Electrical 2012 | Question: 37
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
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367
GATE Electrical 2012 | Question: 35
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, the peak current in $S$ is $6.6$ A $5.0$ A $5.8$ A $4.2$ A
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, th...
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369
GATE Electrical 2012 | Question: 33
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor $(Q_{G2})$ connected at bus $2$ is $0.2$ pu $0.268$ pu $0.312$ pu $0.4$ pu
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor...
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371
GATE Electrical 2012 | Question: 31
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n u[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=1/2$, then $g[1]$ equals $0$ $1/2$ $1$ $3.2$
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n u[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y =1/2$, then $g $ equals$0$$1/2$$1$$3...
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372
GATE Electrical 2012 | Question: 30
The state transition diagram for the logic circuit shown is
The state transition diagram for the logic circuit shown is
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373
GATE Electrical 2012 | Question: 29
The voltage gain $A_V$ of the circuit shown below is $\mid A_V \mid \approx 200$ $\mid A_V \mid \approx 100$ $\mid A_V \mid \approx 20$ $\mid A_V \mid \approx 10$
The voltage gain $A_V$ of the circuit shown below is$\mid A_V \mid \approx 200$$\mid A_V \mid \approx 100$$\mid A_V \mid \approx 20$$\mid A_V \mid \approx 10$
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374
GATE Electrical 2012 | Question: 28
If $V_A – V_B =6$ V, then $V_C – V_D $ is $-5$ V $2$ V $3$ V $6$ V
If $V_A – V_B =6$ V, then $V_C – V_D $ is$-5$ V$2$ V$3$ V$6$ V
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375
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
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378
GATE Electrical 2012 | Question: 24
The typical ratio of latching current to holding current in a $20$ A thyristor is $5.0$ $2.0$ $1.0$ $0.5$
The typical ratio of latching current to holding current in a $20$ A thyristor is$5.0$$2.0$$1.0$$0.5$
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379
GATE Electrical 2012 | Question: 23
A half-controlled single-phase bridge rectifier is supplying an R-L load. It is operated at a firing angle $\alpha$ and the load current is continuous. The fraction of cycle that the freewheeling diode conduct is $1/2$ $\big( 1- \alpha/ \pi \big)$ $\alpha / 2 \pi $ $\alpha/ \pi$
A half-controlled single-phase bridge rectifier is supplying an R-L load. It is operated at a firing angle $\alpha$ and the load current is continuous. The fraction of cy...
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380
GATE Electrical 2012 | Question: 22
The sequence components of the fault current are as follows: $I_{\text{positive}} = j1.5$ pu, $I_{\text{negative}} =- j0.5$ pu, $I_{\text{zero}} = – j1$ pu. The type of fault in the system is LG LL LLG LLLG
The sequence components of the fault current are as follows: $I_{\text{positive}} = j1.5$ pu, $I_{\text{negative}} =- j0.5$ pu, $I_{\text{zero}} = – j1$ pu. The type of...
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382
GATE Electrical 2012 | Question: 20
Consider the given circuit. In this circuit, the race around does not occur occurs when $\text{CLK}=0$ occurs when $\text{CLK}=1$ and $A=B=1$ occurs when $\text{CLK}=1$ and $A=B=0$
Consider the given circuit. In this circuit, the race arounddoes not occuroccurs when $\text{CLK}=0$occurs when $\text{CLK}=1$ and $A=B=1$occurs when $\text{CLK}=1$ and $...
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383
GATE Electrical 2012 | Question: 19
The output $Y$ of a $2$-bit comparator is logic $1$ whenever the $2$-bit input A is greater than the $2$-bit input B. The number of combinations of which the output is logic $1$, is $4$ $6$ $8$ $10$
The output $Y$ of a $2$-bit comparator is logic $1$ whenever the $2$-bit input A is greater than the $2$-bit input B. The number of combinations of which the output is lo...
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384
GATE Electrical 2012 | Question: 18
The $i-v$ characteristics of the diode in the circuit given below are $i= \begin{cases} \dfrac{v-0.7}{500}A, & v \geq 0.7 \: V \\ 0 A, & v <0.7 \: V \end{cases}$ The current in the circuit is $10 \: mA$ $9.3\: mA$ $6.67\: mA$ $6.2\: mA$
The $i-v$ characteristics of the diode in the circuit given below are $$i= \begin{cases} \dfrac{v-0.7}{500}A, & v \geq 0.7 \: V \\ 0 A, & v <0.7 \: V \end{cases}$$ The cu...
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385
GATE Electrical 2012 | Question: 17
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12$ V before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is zero a step function an exponentially decaying function an impulse function
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12$ V before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all...
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386
GATE Electrical 2012 | Question: 16
The average power delivered to an impedance $(4-j3) \Omega$ by a current $5 \cos (100 \pi \:t +100)$A is $44.2$ W $50$ W $62.5$ W $125$ W
The average power delivered to an impedance $(4-j3) \Omega$ by a current $5 \cos (100 \pi \:t +100)$A is$44.2$ W$50$ W$62.5$ W$125$ W
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388
GATE Electrical 2012 | Question: 14
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is $x=t-\dfrac{1}{2} \\ $ $x=t^2-\dfrac{1}{2} \\ $ $x=\dfrac{t^2}{2} \\$ $x=\dfrac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is$x=t-\dfrac{1}{2} \\ $$x=t^2-\dfrac{1}{2} \\ $$x=\dfrac{t^2}{2} \\$$x...
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389
GATE Electrical 2012 | Question: 13
The bridge method commonly used for finding mutual inductance is Heaviside Campbell bridge Schering bridge De Sauty bridge Wien bridge
The bridge method commonly used for finding mutual inductance isHeaviside Campbell bridgeSchering bridgeDe Sauty bridgeWien bridge
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390
GATE Electrical 2012 | Question: 12
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permane magnet moving coil (PMMC) meter connected across the same load reads $4$V $5$ V $8$ V $10$ V
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permane magnet moving coil (PMMC) meter connected across the same load reads$4$V$5$ V$8$...
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391
GATE Electrical 2012 | Question: 11
A two-phase load draws the following phase currens: $i_1(t)=I_m \sin(\omega t – \phi_1), i_2(t) = I_m \cos(\omega t – \phi_2)$. These currents are balanced if $\phi_1$ is equal to $- \phi_2$ $\phi_2$ $\pi/2 - \phi_2$ $\pi/2 + \phi_2$
A two-phase load draws the following phase currens: $i_1(t)=I_m \sin(\omega t – \phi_1), i_2(t) = I_m \cos(\omega t – \phi_2)$. These currents are balanced if $\phi_1...
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392
GATE Electrical 2012 | Question: 10
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque core-loss component
The slip of an induction motor normally does not depend onrotor speedsynchronous speedshaft torquecore-loss component
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394
GATE Electrical 2012 | Question: 8
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be $\dfrac{1}{3} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid < \dfrac{1}{2} \\$ $\dfrac{1}{2} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid $
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be$\dfrac{1}{3} < \mid z \mid < 3 \\$$\...
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396
GATE Electrical 2012 | Question: 6
A system with transfer function $G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at $\omega = 1 \text{ rad/s}$ $\omega = 2\text{ rad/s}$ $\omega = 3 \text{ rad/s}$ $\omega = 4 \text{ rad/s}$
A system with transfer function $$G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at$\omega = ...
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397
GATE Electrical 2012 | Question: 5
The impedance looking into nodes $1$ and $2$ in the given circuit is $50 \: \Omega$ $100 \: \Omega$ $5 \: \Omega$ $10.1 \: \Omega$
The impedance looking into nodes $1$ and $2$ in the given circuit is$50 \: \Omega$$100 \: \Omega$$5 \: \Omega$$10.1 \: \Omega$
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398
GATE Electrical 2012 | Question: 4
In the circuit shown below, the current through the inductor is $\dfrac{2}{1+j} A\\ $ $\dfrac{-1}{1+j} A\\$ $\dfrac{1}{1+j} A \\$ $0 A$
In the circuit shown below, the current through the inductor is$\dfrac{2}{1+j} A\\ $$\dfrac{-1}{1+j} A\\$$\dfrac{1}{1+j} A \\$$0 A$
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399
GATE Electrical 2012 | Question: 3
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oint_c f(z) dz$ is $-2$ $-1$ $1$ $2$
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oi...
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400
GATE Electrical 2012 | Question: 2
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{- \pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{- \pi/2}$$e^{\pi/2}$$x$$1$
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