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2401
GATE ECE 2015 Set 2 | Question: 2
The value of $x$ for which all the eigen-values of the matrix given below are real is $\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$ $5+j$ $5-j$ $1-5j$ $1+5j$
The value of $x$ for which all the eigen-values of the matrix given below are real is $$\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$$$5+j$$5-j$$1-5j$$1...
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2402
GATE ECE 2015 Set 2 | Question: 3
Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.
Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.
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2405
GATE ECE 2015 Set 2 | Question: 6
The voltage $(ܸV_{C})$ across the capacitor (in Volts) in the network shown is ______.
The voltage $(ܸV_{C})$ across the capacitor (in Volts) in the network shown is ______.
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2406
GATE ECE 2015 Set 2 | Question: 7
In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.
In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.
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2407
GATE ECE 2015 Set 2 | Question: 8
The $2$-port admittance matrix of the circuit shown is given by $\begin{bmatrix}0.3 &0.2 \\0.2 &0.3 \end{bmatrix}$ $\begin{bmatrix} 15&5 \\5 &15 \end{bmatrix}$ $\begin{bmatrix} 3.33&5 \\5 &3.33 \end{bmatrix}$ $\begin{bmatrix} 0.3&0.4 \\0.4 &0.3 \end{bmatrix}$
The $2$-port admittance matrix of the circuit shown is given by$\begin{bmatrix}0.3 &0.2 \\0.2 &0.3 \end{bmatrix}$$\begin{bmatrix} 15&5 \\5 &15 \end{bmatrix}$$\begin{bmatr...
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2410
GATE ECE 2015 Set 2 | Question: 11
If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period $T?$ $RC \ll T$ $RC = 0.35\: T$ $RC \approx T$ $RC \gg T$
If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period $T?$$RC \l...
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2411
GATE ECE 2015 Set 2 | Question: 12
In the circuit shown, $V_{0} = V_{0A}$ for switch $SW$ in position $A$ and $V_{0} = V_{0B}$ for $SW$ in position $B$. Assume that the opamp is ideal. The value of $\dfrac{V_{0B}}{V_{0A}}$ is ___________.
In the circuit shown, $V_{0} = V_{0A}$ for switch $SW$ in position $A$ and $V_{0} = V_{0B}$ for $SW$ in position $B$. Assume that the opamp is ideal. The value of $\dfrac...
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2412
GATE ECE 2015 Set 2 | Question: 13
In the bistable circuit shown, the ideal opamp has saturation levels of $\pm\: 5\: V.$ The value of $R_{1} \text{(in}\: k\Omega)$ that gives a hysteresis width of $500\: mV$ is ________.
In the bistable circuit shown, the ideal opamp has saturation levels of $\pm\: 5\: V.$ The value of $R_{1} \text{(in}\: k\Omega)$ that gives a hysteresis width of $500\: ...
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2413
GATE ECE 2015 Set 2 | Question: 14
In the figure shown, the output ܻ$Y = AB + \overline{C}\:\:\overline{D}$ is required to be ܻ The gates $G1$ and $G2$ must be, respectively, NOR, OR OR, NAND NAND, OR AND,NAND
In the figure shown, the output ܻ$Y = AB + \overline{C}\:\:\overline{D}$ is required to be ܻ The gates $G1$ and $G2$ must be, respectively,NOR, OROR, NANDNAND, ORAND,NA...
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2414
GATE ECE 2015 Set 2 | Question: 15
In an $8085$ microprocessor, which one of the following instructions changes the content of the accumulator? MOV B, M PCHL RNZ SBI BEH
In an $8085$ microprocessor, which one of the following instructions changes the content of the accumulator?MOV B, MPCHLRNZSBI BEH
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2415
GATE ECE 2015 Set 2 | Question: 16
A mod-$n$ counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of $n$ is _______.
A mod-$n$ counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of $n$ is _______.
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2417
GATE ECE 2015 Set 2 | Question: 18
Two causal discrete-time signals $x[n]$ and $y[n]$ are related as $y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]$. If the $z$-transform of $y[n]$ is $\dfrac{2}{z(z-1)^{2}},$ the value of $x[2]$ is _______.
Two causal discrete-time signals $x[n]$ and $y[n]$ are related as $y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]$. If the $z$-transform of $y[n]$ is $\dfrac{2}{z(z-1)^{2}},$...
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2420
GATE ECE 2015 Set 2 | Question: 21
A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.
A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________...
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2422
GATE ECE 2015 Set 2 | Question: 23
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ ... $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t - \dfrac{\pi}{2}\right)$
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ The sampled signal is passed through a filter with impulse ...
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2423
GATE ECE 2015 Set 2 | Question: 24
In a source free region in vacuum, if the electrostatic potential $\varphi = 2x^{2} + y^{2} + cz^{2},$ the value of constant ܿ$c$ must be _______.
In a source free region in vacuum, if the electrostatic potential $\varphi = 2x^{2} + y^{2} + cz^{2},$ the value of constant ܿ$c$ must be _______.
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2425
GATE ECE 2015 Set 2 | Question: 26
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is $2-e^{-0.2t}$ $2-e^{0.2t}$ $50-49e^{-0.2t}$ $50-49e^{0.2t}$
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is$2-e^{-0.2t}$$2-...
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2426
GATE ECE 2015 Set 2 | Question: 27
The value of the integral $\int_{-\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.
The value of the integral $\int_{-\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.
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2427
GATE ECE 2015 Set 2 | Question: 28
If $C$ denotes the counterclockwise unit circle, the value of the contour integral $\dfrac{1}{2\pi j}\oint_{C} Re\{z\}dz$ is __________.
If $C$ denotes the counterclockwise unit circle, the value of the contour integral $$\dfrac{1}{2\pi j}\oint_{C} Re\{z\}dz$$ is __________.
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2428
GATE ECE 2015 Set 2 | Question: 29
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _...
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2430
GATE ECE 2015 Set 2 | Question: 31
In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.
In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.
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2435
GATE ECE 2015 Set 2 | Question: 36
A function of Boolean variables $X, Y$ and $Z$ is expressed in terms of the min-terms as $F(X, Y, Z) = \Sigma (1, 2, 5, 6, 7)$ Which one of the product of sums given below is equal to the function $F(X, Y, Z)?$ ...
A function of Boolean variables $X, Y$ and $Z$ is expressed in terms of the min-terms as $$F(X, Y, Z) = \Sigma (1, 2, 5, 6, 7)$$Which one of the product of sums given bel...
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2436
GATE ECE 2015 Set 2 | Question: 37
The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a mod-$2$ counter mod-$4$ counter mod-$5$ counter mod-$6$ counter
The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a mod-$2$ counter mod-$4$ counter mod-$5$ counter mod-...
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2438
GATE ECE 2015 Set 2 | Question: 39
The diode in the circuit given below has $V_{ON} = 0.7\:V$ but is ideal otherwise. The current $(\text{in}\: mA)$ in the $4\: k\Omega$ resistor is _______.
The diode in the circuit given below has $V_{ON} = 0.7\:V$ but is ideal otherwise. The current $(\text{in}\: mA)$ in the $4\: k\Omega$ resistor is _______.
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2439
GATE ECE 2015 Set 2 | Question: 40
Assuming that the opamp in the circuit shown below is ideal, the output voltage ܸ$V_{o}$ (in volts) is________.
Assuming that the opamp in the circuit shown below is ideal, the output voltage ܸ$V_{o}$ (in volts) is________.
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