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961
GATE ECE 2004 | Question: 64
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state value is $2.7 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.1 \; \mathrm{sec}$
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state val...
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962
GATE ECE 2004 | Question: 65
The impulse response $h|n|$ ... $4 \sqrt{2} e^{j \pi n / 4}$ $4 e^{j \pi n / 4}$ $-4 e^{j \pi n / 4}$
The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...
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963
GATE ECE 2004 | Question: 66
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure. Then $Y(f)$ is $-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}$ $-\frac{1}{2} X(f / 2) e^{j 2 \pi f}$ $-X(f / 2) e^{j 2 \pi f}$ $-\mathrm{X}(f / 2) e^{-j2 \pi f}$
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...
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964
GATE ECE 2004 | Question: 67
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase of the system response at $20 \mathrm{~Hz}$ is $-90^{\circ}$ $0^{\circ}$ $90^{\circ}$ $-180^{\circ}$
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase...
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965
GATE ECE 2004 | Question: 68
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is $\frac{1-\left(b e+c f+d g\right)}{a b c}$ $\frac{b e d g}{1-(b e+c f+d g)}$ $\frac{a b c d}{1-\left(b e+c f+d g\right)+bedg}$ $\frac{1-\left(b e+cf+d g\right)+b ed g}{a b c d}$
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is$\frac{1-\left(b e+c f+d g\right)}{a b c}$$\frac{b e d g}{1-(b e+c f+d g)}$$\fr...
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966
GATE ECE 2004 | Question: 69
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ ...
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ is$\frac{1}{3}\left[\begin{array}{cc}\sin (-4 t)+2 \sin (-t) & -2 \sin (-4 t)+2 \sin (-t...
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967
GATE ECE 2004 | Question: 70
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$ The range of $\mathrm{K}$ for which the system is stable is $\frac{21}{44}>\mathrm{K}>0$ $13>\mathrm{K}>0$ $\frac{21}{4}<\mathrm{K}<\infty$ $-6<\mathrm{K}<\infty$
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$The range of $\mathrm{K}$ for which the system is stable is$\fr...
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968
GATE ECE 2004 | Question: 71
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is $4$ $2$ $3$ $1$
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is$4$$2$$3$$1$
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969
GATE ECE 2004 | Question: 72
The state variable equations of a system are: $\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$ The system is controllable but not observable observable but not controllable neither controllable nor observable controllable and observable
The state variable equations of a system are:$\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$The system iscontrollabl...
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970
GATE ECE 2004 | Question: 73
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by $\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{array}\right]$ ... $\left[\begin{array}{cc}0 & e^{t} \\ e^{t} & 0\end{array}\right]$
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by$\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{a...
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973
GATE ECE 2004 | Question: 76
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ ... $\sqrt{5 / 4+\cos \left(2 \pi \times 10^{6} t\right)}$
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ amplitude are fed to a balanced modulator. The...
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974
GATE ECE 2004 | Question: 77
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal frequency detector. The output of the detector is $0.1 \; \mathrm{kHz}$ sinusoid $20.1 \; \mathrm{kHz}$ sinusoid a linear function of time a constant
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal freq...
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976
GATE ECE 2004 | Question: 79
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ ... $\text{X}$. The root-mean square value of the quantization noise is $0.573$ $0.198$ $2.205$ $0.266$
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ is quantized as follows:$\begin{array}{ll} \qquad \text{If 0 < X < 0.3,} & \text{x}_{4} = 0...
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977
GATE ECE 2004 | Question: 80
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ ... $\text{1-S, 2-P, 3-U, 4-Q}$ $\text{1-U, 2-R, 3-S, 4-Q}$
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item i...
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980
GATE ECE 2004 | Question: 83
A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3.6 \; \mathrm{GHz}$ ... $10 \mathrm{~mA}$ $100 \mathrm{~mA}$ $10 \mathrm{~A}$ $1.59 \mathrm{~mA}$
A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3....
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983
GATE ECE 2004 | Question: 86
In a microwave test bench, why is the microwave signal amplitude modulated at $1 \; \mathrm{kHz}$? To increase the sensitivity of measurement To transmit the signal to a far-off place To study amplitude modulation Because crystal detector fails at microwave frequencies
In a microwave test bench, why is the microwave signal amplitude modulated at $1 \; \mathrm{kHz}$?To increase the sensitivity of measurementTo transmit the signal to a fa...
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985
GATE ECE 2004 | Question: 88
Consider an impedance $\mathrm{Z = R + j X }$ marked with point $\mathrm{P}$ in an impedance Smith chart as shown in the figure. The movement from point $\mathrm{P}$ ... series with $\mathrm{Z}$ adding an inductance in shunt across $\mathrm{Z}$ adding a capacitance in shunt across $\mathrm{Z}$
Consider an impedance $\mathrm{Z = R + j X }$ marked with point $\mathrm{P}$ in an impedance Smith chart as shown in the figure. The movement from point $\mathrm{P}$ alon...
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987
GATE ECE 2004 | Question: 90
A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is $2.$ The percentage of the power that is reflected back is $57.73$ $33.33$ $0.11$ $11.11$
A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is $2.$ The percentage of the power that is reflected ...
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988
GATE ECE 1995 | Question 3.8
(A) $\text{AM}$ system (B) $\text{DSB-SC}$ system (C) $\text{PAM}$ system Coherent detection Envelope detection Correlation detection $\text{PLL}$ $\text{LPF}$
(A) $\text{AM}$ system(B) $\text{DSB-SC}$ system(C) $\text{PAM}$ systemCoherent detectionEnvelope detectionCorrelation detection$\text{PLL}$$\text{LPF}$
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989
GATE ECE 2005 | Question: 1
The following differential equation has \[3 \frac{d^{2} y}{d t^{2}}+4\left(\frac{d y}{d t}\right)^{3}+y^{2}+2=x\] degree $=2$, order $=1$ degree $=3$, order $=2$ degree $=4$, order $=3$ degree $=2$, order $=3$
The following differential equation has\[3 \frac{d^{2} y}{d t^{2}}+4\left(\frac{d y}{d t}\right)^{3}+y^{2}+2=x\]degree $=2$, order $=1$degree $=3$, order $=2$degree $=4$,...
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990
GATE ECE 2005 | Question: 2
Choose the function $f(t); – \infty < 1 < \infty,$ for which a Fourier series cannot be defined. $3 \sin (25 t)$ $4 \cos (20 t+3)+2 \sin (710 t)$ $\exp (-|t|) \sin (25 t)$ $1$
Choose the function $f(t); – \infty < 1 < \infty,$ for which a Fourier series cannot be defined.$3 \sin (25 t)$$4 \cos (20 t+3)+2 \sin (710 t)$$\exp (-|t|) \sin (25 t)$...
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991
GATE ECE 2005 | Question: 3
A fair dice is rolled twice. The probability that an odd number will follow an even number is $\frac{1}{2}$ $\frac{1}{6}$ $\frac{1}{3}$ $\frac{1}{4}$
A fair dice is rolled twice. The probability that an odd number will follow an even number is$\frac{1}{2}$$\frac{1}{6}$$\frac{1}{3}$$\frac{1}{4}$
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992
GATE ECE 2005 | Question: 4
A solution of the following differential equation is given by \[\frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=0\] $y=e^{2 x}+e^{-3 x}$ $y=e^{2 x}+e^{3 x}$ $y=e^{-2 x}+e^{3 x}$ $y=e^{-2 x}+e^{-3 x}$
A solution of the following differential equation is given by\[\frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=0\]$y=e^{2 x}+e^{-3 x}$$y=e^{2 x}+e^{3 x}$$y=e^{-2 x}+e^{3 x}...
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993
GATE ECE 2005 | Question: 5
The function $x(t)$ is shown in the figure. Even and odd parts of a unit-step function $u(t)$ are respectively, $\frac{1}{2}, \frac{1}{2} x(t)$ $-\frac{1}{2}, \frac{1}{2} x(t)$ $\frac{1}{2},-\frac{1}{2} x(t)$ $-\frac{1}{2},-\frac{1}{2} x(t)$
The function $x(t)$ is shown in the figure. Even and odd parts of a unit-step function $u(t)$ are respectively,$\frac{1}{2}, \frac{1}{2} x(t)$$-\frac{1}{2}, \frac{1}{2} x...
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994
GATE ECE 2005 | Question: 6
The region of convergence of $Z$-transform of the sequence $\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be $|z|<\frac{5}{6}$ $|z|>\frac{6}{5}$ $\frac{5}{6}<|z|<\frac{6}{5}$ $\frac{6}{5}<|z|<\infty$
The region of convergence of $Z$-transform of the sequence$\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be$|z|<\frac{5}{6}$$|z|>\frac{6}{5...
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996
GATE ECE 2005 | Question: 8
The $\text{ABCD}$ parameters of an ideal $n: 1$ transformer shown in the figure are $\left[\begin{array}{ll}n & 0 \\ 0 & \mathrm{X}\end{array}\right]$. The value of $X$ will be $n$ $\frac{1}{n}$ $n^{2}$ $\frac{1}{n^{2}}$
The $\text{ABCD}$ parameters of an ideal $n: 1$ transformer shown in the figure are $\left[\begin{array}{ll}n & 0 \\ 0 & \mathrm{X}\end{array}\right]$. The value of $X$ w...
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997
GATE ECE 2005 | Question: 9
In a series $\mathrm{RLC}$ circuit, $\mathrm{R}=2 \; \mathrm{k} \Omega, \mathrm{L}=1 \; \mathrm{H}$, and $\mathrm{C} \frac{1}{400}=\mu \mathrm{F}$. The resonant frequency is $2 \times 10^{4} \mathrm{~Hz}$ $\frac{1}{\pi} \times 10^{4} \mathrm{~Hz}$ $10^{4} \mathrm{~Hz}$ $2 \pi \times 10^{4} \mathrm{~Hz}$
In a series $\mathrm{RLC}$ circuit, $\mathrm{R}=2 \; \mathrm{k} \Omega, \mathrm{L}=1 \; \mathrm{H}$, and $\mathrm{C} \frac{1}{400}=\mu \mathrm{F}$. The resonant frequency...
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998
GATE ECE 2005 | Question: 10
The maximum power that can be transferred to the load resistor $R_{L}$ from the voltage source in the figure is $1 \mathrm{~W}$ $10 \mathrm{~W}$ $0.25 \mathrm{~W}$ $0.5 \mathrm{~W}$
The maximum power that can be transferred to the load resistor $R_{L}$ from the voltage source in the figure is$1 \mathrm{~W}$$10 \mathrm{~W}$$0.25 \mathrm{~W}$$0.5 \math...
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999
GATE ECE 2005 | Question: 11
The bandgap of Silicon at room temperature is $1.3 \; \mathrm{eV}$ $0.7 \; \mathrm{eV}$ $1.1 \; \mathrm{eV}$ $1.4 \; \mathrm{eV}$
The bandgap of Silicon at room temperature is$1.3 \; \mathrm{eV}$$0.7 \; \mathrm{eV}$$1.1 \; \mathrm{eV}$$1.4 \; \mathrm{eV}$
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1000
GATE ECE 2005 | Question: 12
A Silicon PN junction at a temperature of $20^{\circ} \mathrm{C}$ has a reverse saturation current of $10$ picoAmperes $(\mathrm{pA})$. The reverse saturation current at $40^{\circ} \mathrm{C}$ for the same bias is approximately $30 \; \mathrm{pA}$. $40 \; \mathrm{pA}$. $50 \; \mathrm{pA}$ $60 \; \mathrm{pA}$.
A Silicon PN junction at a temperature of $20^{\circ} \mathrm{C}$ has a reverse saturation current of $10$ picoAmperes $(\mathrm{pA})$. The reverse saturation current at ...
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