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1242
GATE ECE 2006 | Question: 49
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be $\overline{\mathrm{AB} \overline{\mathrm{C}}}$ $\overline{\mathrm{A}}$ $\mathrm{AB} \overline{\mathrm{C}}$ $\mathrm{A}$
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be$\overline{\mathrm{AB} \overline{\mathrm{C}}}$$\overline{\mathrm{A}}$$\mathrm{AB} \ove...
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1245
GATE ECE 2006 | Question: 52
A uniformly distributed random variable $X$ with probability density function \[ f_{\gamma}(x)=\frac{1}{10}(t r(x+5)-u(x-5)) \] where $u(.)$ is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random ...
A uniformly distributed random variable $X$ with probability density function\[ f_{\gamma}(x)=\frac{1}{10}(t r(x+5)-u(x-5)) \]where $u(.)$ is the unit step function is pa...
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1246
GATE ECE 2006 | Question: 53
A system with input $x[n]$ and output $y[n]$ is given as $y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)$. The system is linear, stable and invertible non-linear, stable and non-invertible linear, stable and non-invertible linear, unstable and invertible
A system with input $x[n]$ and output $y[n]$ is given as $y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)$.The system islinear, stable and invertiblenon-linear, stable and ...
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1247
GATE ECE 2006 | Question: 54
The unit-step response of a system starting from rest is given by $\qquad C(t)=1-t^{-2 t} \text { for } t \geq 0$ The transfer function of the system is $\frac{1}{1+2 s}$ $\frac{2}{2+s}$ $\frac{1}{2+s}$ $\frac{2 s}{1+2 s}$
The unit-step response of a system starting from rest is given by$\qquad C(t)=1-t^{-2 t} \text { for } t \geq 0$The transfer function of the system is$\frac{1}{1+2 s}$$\f...
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1248
GATE ECE 2006 | Question: 55
The Nyquist plot of $\mathrm{G}(j \omega) \mathrm{H}(j \omega)$ for a closed loop control system, passes through $(-1, j 0)$ point in the $\mathrm{GH}$ plane. The gain margin of the system in $\mathrm{dB}$ is equal to infinite greater than zero. less than zero zero
The Nyquist plot of $\mathrm{G}(j \omega) \mathrm{H}(j \omega)$ for a closed loop control system, passes through $(-1, j 0)$ point in the $\mathrm{GH}$ plane. The gain ma...
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1249
GATE ECE 2006 | Question: 56
The positive values of $\text{“K”}$ and “$a$” so that the system shown in the figure below oscillates at a frequency of $2 \mathrm{rad} / \mathrm{sec}$ respectively are $1,0.75$ $2, 0.75$ $1,1$ $2,2$
The positive values of $\text{“K”}$ and “$a$” so that the system shown in the figure below oscillates at a frequency of $2 \mathrm{rad} / \mathrm{sec}$ respective...
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1250
GATE ECE 2006 | Question: 57
The unit impulse response of a system is \[h(t)=e^{-t}, t \geq 0\] For this system, the steady-state value of the output for unit step input is equal to $-1$ $0$ $1$ $\infty$
The unit impulse response of a system is\[h(t)=e^{-t}, t \geq 0\]For this system, the steady-state value of the output for unit step input is equal to$-1$$0$$1$$\infty$
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1251
GATE ECE 2006 | Question: 58
The transfer function of a phase-lead compensator is given by \[G_{c}(s)=\frac{1+3 T s}{1+T s} \text { where } T>0\] The maximum phase-shift provided by such a compensator is $\frac{\pi}{2}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ $\frac{\pi}{6}$
The transfer function of a phase-lead compensator is given by\[G_{c}(s)=\frac{1+3 T s}{1+T s} \text { where } T>0\]The maximum phase-shift provided by such a compensator ...
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1252
GATE ECE 2006 | Question: 59
A linear system is described by the following state equation $X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc} 0 & 1 \\ -1 & 0\end{array}\right]$ ... $\left[\begin{array}{cc}\cos t & -\sin t \\ \cos t & \sin t\end{array}\right]$
A linear system is described by the following state equation$$X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$$The...
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1254
GATE ECE 2006 | Question: 61
A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t_{s}=0.03 \; \mathrm{msec}$. The samples so obtained would be correlated statistically independent uncorrelated orthogonal
A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t...
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1256
GATE ECE 2006 | Question: 63
The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here $W$ is message bandwidth and $\omega_{c}$ ... $\mathrm{RC}<\frac{1}{\omega_{c}}$ $\mathrm{RC}>\frac{1}{\omega_{c}}$
The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (...
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1257
GATE ECE 2006 | Question: 64
In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is $\Delta$ $\frac{\Delta}{2}$ $\frac{\Delta^{2}}{12}$ $\frac{\Delta}{\mathrm{L}}$
In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is$\Delta$$\frac{...
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1261
GATE ECE 2006 | Question: 68
When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by $\frac{8}{9}$ $\frac{1}{2}$ $\frac{1}{3}$ $\frac{5}{6}$
When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by$\...
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1263
GATE ECE 2006 | Question: 70
A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. The radiation resistance of the antenna in ohms is $\frac{2 \pi^{2}}{5}$ $\frac{\pi^{2}}{5}$ $\frac{4 \pi^{2}}{5}$ $20 \pi^{2}$
A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. ...
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1264
GATE ECE 2006 | Question: 71
Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: \[ \beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{ ... $4.8$ Volts $5.3$ Volts $6.0$ Volts $6.6$ Volts
Common Data for Questions 71, 72,73:In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:\[ \beta_{\mathrm{DC}}=60, ...
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1267
GATE ECE 2006 | Question: 74
Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function The impulse response of filter matched to the signal $s(t)=g(t)-\delta(t-2)^{*} g(t)$ is given as $s(1-t)$ $-s(1-t)$ $-s(t)$ $s(t)$
Common Data for Questions 74, 75:Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step functionThe impulse response...
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1273
GATE ECE 2006 | Question: 80
Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ \[x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t\] The average side-band power for the $\text{AM}$ signal given above is $25$ $12.5$ $6.25$ $3.125$
Statement for Linked Answer Questions 80 and 81Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$\[x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \...
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1275
GATE ECE 2006 | Question: 82
Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is \[G(s)=\frac{as+1}{s^{2}}\] The value of '$a$' so that the system has a phase-margin equal to $\frac{\pi}{4}$ is approximately equal to $2.40$ $1.40$ $0.84$ $0.74$
Statement for Linked Answer Questions 82 and 83Consider a unity-gain feedback control system whose open-loop transfer function is\[G(s)=\frac{as+1}{s^{2}}\]The value of '...
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1279
GATE ECE 1994 | Question 1.1
The Laplace transform of a unit ramp function starting at $t=a$, is $\frac{1}{(s+a)^{2}}$ $\frac{e^{-as}}{(s+a)^{2}}$ $\frac{e^{-as}}{s^{2}}$ $\frac{a}{s^{2}}$
The Laplace transform of a unit ramp function starting at $t=a$, is$\frac{1}{(s+a)^{2}}$$\frac{e^{-as}}{(s+a)^{2}}$$\frac{e^{-as}}{s^{2}}$$\frac{a}{s^{2}}$
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1280
GATE ECE 1994 | Question: 1.2
The Fourice Series of a odd periọdic function, contains only odd harmonics even harmonics cosine terms sine terms
The Fourice Series of a odd periọdic function, contains onlyodd harmonicseven harmonicscosine termssine terms
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