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201
GATE Electrical 2022 | Question: 19
The maximum clock frequency in $\text{MHz}$ of a $4$ – stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of $20\:ns$, is _______________. (round off to one decimal place)
The maximum clock frequency in $\text{MHz}$ of a $4$ – stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of $20\:ns$, is ______...
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202
GATE Electrical 2022 | Question: 20
If only $5\%$ of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ________________. (round off to nearest integer)
If only $5\%$ of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ________________. (round off to nearest integer)
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203
GATE Electrical 2022 | Question: 21
In the circuit shown below, the switch $S$ is closed at $t = 0$. The magnitude of the steady state voltage, in volts, across the $6 \Omega$ resistor is ________________. (round off to two decimal places)
In the circuit shown below, the switch $S$ is closed at $t = 0$. The magnitude of the steady state voltage, in volts, across the $6 \Omega$ resistor is ________________. ...
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204
GATE Electrical 2022 | Question: 22
A single-phase full-bridge diode rectifier feeds a resistive load of $50\; \Omega$ from a $200\:V$, $50\:Hz$ single phase $\text{AC}$ supply. If the diodes are ideal, then the active power, in watts, drawn by the load is __________________. (round off to nearest integer)
A single-phase full-bridge diode rectifier feeds a resistive load of $50\; \Omega$ from a $200\:V$, $50\:Hz$ single phase $\text{AC}$ supply. If the diodes are ideal, the...
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205
GATE Electrical 2022 | Question: 23
The voltage at the input of an $\text{AC-DC}$ rectifier is given by $v\left ( t \right ) = 230 \sqrt{2} \sin \omega t$ where $\omega = 2\pi \times 50$ ... . The input power factor, (rounded off to two decimal places), is, _______________________ lag.
The voltage at the input of an $\text{AC-DC}$ rectifier is given by $v\left ( t \right ) = 230 \sqrt{2} \sin \omega t$ where $\omega = 2\pi \times 50$ rad/s. The input cu...
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207
GATE Electrical 2022 | Question: 25
The frequencies of the stator and rotor currents flowing in a three-phase $8$-pole induction motor are $40\:Hz$ and $1\:Hz$, respectively. The motor speed, in $\text{rpm}$, is ________________. (round off to nearest integer)
The frequencies of the stator and rotor currents flowing in a three-phase $8$-pole induction motor are $40\:Hz$ and $1\:Hz$, respectively. The motor speed, in $\text{rpm}...
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208
GATE Electrical 2022 | Question: 26
The output impedance of a non-ideal operational amplifier is denoted by $Z_{out}$. The variation in the magnitude of $Z_{out}$ with increasing frequency, $f$, in the circuit shown below, is best represented by A. B. C. D.
The output impedance of a non-ideal operational amplifier is denoted by $Z_{out}$. The variation in the magnitude of $Z_{out}$ with increasing frequency, $f$, in the circ...
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213
GATE Electrical 2022 | Question: 31
Let $f\left ( x \right ) = \int_{0}^{x} e^{t}\left ( t-1 \right )\left ( t-2 \right )dt$. Then $f\left ( x \right )$ decreases in the interval $x \in \left ( 1,2 \right )$ $x \in \left ( 2,3 \right )$ $x \in \left ( 0, 1 \right )$ $x \in \left ( 0.5, 1 \right )$
Let $f\left ( x \right ) = \int_{0}^{x} e^{t}\left ( t-1 \right )\left ( t-2 \right )dt$. Then $f\left ( x \right )$ decreases in the interval$x \in \left ( 1,2 \right )$...
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214
GATE Electrical 2022 | Question: 32
Consider a matrix $A = \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & -2\\ 0 & 1 & 1 \end{bmatrix}$. The matrix $A$ satisfies the equation $6A^{-1} = A^{2} + cA + dl$, where $c$ and $d$ are scalars and $I$ is the identity matrix. Then $\left ( c + d \right )$ is equal to $5$ $17$ $-6$ $11$
Consider a matrix $A = \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & -2\\ 0 & 1 & 1 \end{bmatrix}$.The matrix $A$ satisfies the equation $6A^{-1} = A^{2} + cA + dl$, where $c$ and ...
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216
GATE Electrical 2022 | Question: 34
The current gain $( I_{\text{out}}/I_{\text{in}})$ in the circuit with an ideal current amplifier given below is $\dfrac{C_{f}}{C_{c}}$ $\dfrac{-C_{f}}{C_{c}}$ $\dfrac{C_{c}}{C_{f}}$ $\dfrac{-C_{c}}{C_{f}}$
The current gain $( I_{\text{out}}/I_{\text{in}})$ in the circuit with an ideal current amplifier given below is$\dfrac{C_{f}}{C_{c}}$$\dfrac{-C_{f}}{C_{c}}$$\dfrac{C_{c}...
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217
GATE Electrical 2022 | Question: 35
If the magnetic field intensity $(H)$ in a conducting region is given by the expression. $H = x^{2} \hat{i} + x^{2}y^{2}\hat{j} + x^{2}y^{2}z^{2}k$ $\text{A/m}$. The magnitude of the current density, in $A/m^{2}$, at $x = 1\;m, y = 2\; m$ and $z = 1\; m$, is $8$ $12$ $16$ $20$
If the magnetic field intensity $(H)$ in a conducting region is given by the expression. $H = x^{2} \hat{i} + x^{2}y^{2}\hat{j} + x^{2}y^{2}z^{2}k$ $\text{A/m}$. The magn...
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218
GATE Electrical 2022 | Question: 36
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)$ and $y(t)$ ... $8e^{-\frac{1}{4}t}u\left ( t \right )$ $8e^{-4t}u\left ( t \right )$
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)...
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219
GATE Electrical 2022 | Question: 37
Let an input $x\left ( t \right ) = 2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$ is passed through an $\text{LTI}$ ... $2 \sin \left ( 10 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$
Let an input $x\left ( t \right ) = 2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \righ...
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220
GATE Electrical 2022 | Question: 38
Consider the system as shown below Where $y(t)=x(e^t).$ The system is linear and casual linear and non-casual non-linear and casual non-linear and non-casual
Consider the system as shown belowWhere $y(t)=x(e^t).$ The system is linear and casuallinear and non-casualnon-linear and casualnon-linear and non-casual
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222
GATE Electrical 2022 | Question: 40
Let, $f\left ( x,y, z \right ) = 4x^{2} + 7xy + 3xz^{2}$. The direction in which the function $\text{f(x, y, z)}$ increases most rapidly at point $P = (1,0,2)$ is $20\hat{i} + 7\hat{j}$ $20\hat{i} + 7\hat{j} + 12\hat{k}$ $20\hat{i} + 12\hat{k}$ $20\hat{i}$
Let, $f\left ( x,y, z \right ) = 4x^{2} + 7xy + 3xz^{2}$. The direction in which the function $\text{f(x, y, z)}$ increases most rapidly at point $P = (1,0,2)$ is$20\hat{...
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224
GATE Electrical 2022 | Question: 42
Let $\vec{E}\left ( x, y, z \right ) = 2x^{2}\hat{i} + 5y\hat{j} + 3z\hat{k}$. The value of $\iiint_{V} \left ( \vec{\triangledown} . \vec{E} \right )dV$, where $V$ is the volume enclosed by the unit cube defined by $0\leq x\leq 1, 0\leq y\leq 1$ and $0\leq z\leq 1$, is $3$ $8$ $10$ $5$
Let $\vec{E}\left ( x, y, z \right ) = 2x^{2}\hat{i} + 5y\hat{j} + 3z\hat{k}$. The value of $\iiint_{V} \left ( \vec{\triangledown} . \vec{E} \right )dV$, where $V$ is th...
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225
GATE Electrical 2022 | Question: 43
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that the potential $\text{V(r)}$ at $r = c$ is $V_{1}$ and $\text{V(r)}$ at $r = d$ is $V_{2}$. Assume ...
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that ...
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226
GATE Electrical 2022 | Question: 44
Let the probability density function of a random variable $x$ be given as $f\left ( x \right ) = ae^{-2\left | x \right |}$ The value of $’a’$ is _________________.
Let the probability density function of a random variable $x$ be given as $$f\left ( x \right ) = ae^{-2\left | x \right |}$$ The value of $’a’$ is _________________....
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227
GATE Electrical 2022 | Question: 45
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
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238
gate ee
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239
Gate 2000 signals and systems
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240
GATE Electrical 2021 | Question: 1
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are $1$ and $1$ $1$ and $-1$ $j$ and $-j$ $pq$ and $-pq$
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are$1$ and $1$$1$ and $-1$$j$ and $...
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