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842
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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844
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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845
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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846
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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847
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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848
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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849
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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850
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)$$-\frac{1}{2}, \frac{1}{2} x...
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851
GATE ECE 2005 | Question: 6
The region of convergence of $Z$-transform of the sequence $\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be $|z|<\frac{5}{6}$ $|z|>\frac{6}{5}$ $\frac{5}{6}<|z|<\frac{6}{5}$ $\frac{6}{5}<|z|<\infty$
The region of convergence of $Z$-transform of the sequence$\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be$|z|<\frac{5}{6}$$|z|>\frac{6}{5...
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853
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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854
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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855
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}$$0.5 \math...
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856
GATE ECE 2005 | Question: 11
The bandgap of Silicon at room temperature is $1.3 \; \mathrm{eV}$ $0.7 \; \mathrm{eV}$ $1.1 \; \mathrm{eV}$ $1.4 \; \mathrm{eV}$
The bandgap of Silicon at room temperature is$1.3 \; \mathrm{eV}$$0.7 \; \mathrm{eV}$$1.1 \; \mathrm{eV}$$1.4 \; \mathrm{eV}$
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857
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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858
GATE ECE 2005 | Question: 13
The primary reason for the widespread use of Silicon in semiconductor device technology is aboundance of Silicon on the surface of the Earth. larger bandgap of Silicon in comparison to Germanium. favorable properties of Silicon-dioxide $\left(\mathrm{SiO}_{2}\right)$. lower melting point.
The primary reason for the widespread use of Silicon in semiconductor device technology isaboundance of Silicon on the surface of the Earth.larger bandgap of Silicon in c...
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859
GATE ECE 2005 | Question: 14
The effect of current shunt feedback in an amplifier is to increase the input resistance and decrease the output resistance. increase both input and output resistances. decrease both input and output resistances. decrease the input resistance and increase the output resistance.
The effect of current shunt feedback in an amplifier is toincrease the input resistance and decrease the output resistance.increase both input and output resistances.decr...
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860
GATE ECE 2005 | Question: 15
The input resistance $\text{R}_{\mathrm{i}}$ of the amplifier shown in the figure is $\frac{30}{4} \; \mathrm{k} \Omega$ $10 \; \mathrm{k} \Omega$ $40 \; \mathrm{k} \Omega$ infiinte
The input resistance $\text{R}_{\mathrm{i}}$ of the amplifier shown in the figure is$\frac{30}{4} \; \mathrm{k} \Omega$$10 \; \mathrm{k} \Omega$$40 \; \mathrm{k} \Omega$i...
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861
GATE ECE 2005 | Question: 16
The first and the last critical frequency of an $\text{RC}$-driving point impedance function must respectively be a zero and a pole a zero and a zero a pole and a pole a pole and a zero
The first and the last critical frequency of an $\text{RC}$-driving point impedance function must respectively bea zero and a polea zero and a zeroa pole and a polea pole...
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862
GATE ECE 2005 | Question: 17
The cascode amplifier is a multistage configuration of $\mathrm{CC}-\mathrm{CB}$ $\mathrm{CE}-\mathrm{CB}$ $\mathrm{CB}-\mathrm{CC}$ $\mathrm{CE}-\mathrm{CC}$
The cascode amplifier is a multistage configuration of$\mathrm{CC}-\mathrm{CB}$$\mathrm{CE}-\mathrm{CB}$$\mathrm{CB}-\mathrm{CC}$$\mathrm{CE}-\mathrm{CC}$
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863
GATE ECE 2005 | Question: 18
Decimal $43$ in Hexadecimal and $\text{BCD}$ number system is respectively $\text{B2, 01000011}$ $\text{2B, 01000011}$ $\text{2B, 00110100}$ $\text{B2, 0100 0100}$
Decimal $43$ in Hexadecimal and $\text{BCD}$ number system is respectively$\text{B2, 01000011}$$\text{2B, 01000011}$$\text{2B, 00110100}$$\text{B2, 0100 0100}$
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865
GATE ECE 2005 | Question: 20
Which of the following can be impulse response of a casual system?
Which of the following can be impulse response of a casual system?
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866
GATE ECE 2005 | Question: 21
Let $x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)$ and $\mathrm{Y}\left(e^{j i e}\right)$ be the Fourier transform of $y(n)$. Then $Y\left(e^{j i e}\right)$ is $\frac{1}{4}$ $2$ $4$ $\frac{4}{3}$
Let $x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)$ and $\mathrm{Y}\left(e^{j i e}\right)$ be the Fourier transform of $y(n)$. Then $Y\left(e^{j i e}\right)$ is$\...
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867
GATE ECE 2005 | Question: 22
Find the correct match between group $1$ and group $2.$ ... $\text{P - X, Q - W, R - Z, S - Y,}$ $\text{P - Y, Q - Z, R - W, S - X,}$
Find the correct match between group $1$ and group $2.$Group I$\begin{array}{l}\mathrm{P}-\{1+k m(t)\} \mathrm{A} \sin \left(\omega_{c} t\right) \\\mathrm{Q}-k m(t) \math...
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868
GATE ECE 2005 | Question: 23
The power in the signal $s(t)=8 \cos \left(20 \pi t-\frac{\pi}{2}\right)+$ $4 \sin (15 \pi t)$ is $40$ $41$ $42$ $82$
The power in the signal $s(t)=8 \cos \left(20 \pi t-\frac{\pi}{2}\right)+$ $4 \sin (15 \pi t)$ is$40$$41$$42$$82$
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869
GATE ECE 2005 | Question: 24
Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth? VSB DSB-SC SSB AM
Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth?VSBDSB-SCSSBAM
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871
GATE ECE 2005 | Question: 26
Which one of the following polar diagrams corresponds to a lag network?
Which one of the following polar diagrams corresponds to a lag network?
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872
GATE ECE 2005 | Question: 27
Despite the presence of negative feedback, control systems still have problems of instability because the components used have nonlinearities. dynamic equations of the subsystems are not known exactly. mathematical analysis involves approximations. system has large negative phase angle at high frequencies.
Despite the presence of negative feedback, control systems still have problems of instability because thecomponents used have nonlinearities.dynamic equations of the subs...
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873
GATE ECE 2005 | Question: 28
The magnetic field intensity vector of a plane wave is given by $\overline{\mathrm{H}}(x, y, z, t)=10 \sin \left(50000 t+0.004 x+30 \; \hat{a}_{y}\right)$, where $\hat{a}_{y}$ denotes the unit vector in $y$ ... $-1.25 \times 10^{7} \mathrm{~m} / \mathrm{s}$. $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$.
The magnetic field intensity vector of a plane wave is given by$\overline{\mathrm{H}}(x, y, z, t)=10 \sin \left(50000 t+0.004 x+30 \; \hat{a}_{y}\right)$,where $\hat{a}_{...
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874
GATE ECE 2005 | Question: 29
Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure represent unit circles. constant resistance circles. constant reactance circles. constant reflection coefficient circles.
Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure representunit circles.constant resistance circles.constan...
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875
GATE ECE 2005 | Question: 30
Refractive index of glass is $1.5.$ Find the wavelength of a beam of light with a frequency of $10^{14} \mathrm{~Hz}$ in glass. Assume velocity of light is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ in vacuum. $3 \; \mu \mathrm{m}$ $3 \mathrm{~mm}$ $2 \; \mu \mathrm{m}$ $1 \; \mu \mathrm{m}$
Refractive index of glass is $1.5.$ Find the wavelength of a beam of light with a frequency of $10^{14} \mathrm{~Hz}$ in glass. Assume velocity of light is $3 \times 10^{...
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876
GATE ECE 2005 | Question: 31
In what range should $\operatorname{Re}(s)$ remain so that the Laplace transform of the function $e^{(n+2)t+5}$ exits? $\operatorname{Re}(s)>a+2$ $\operatorname{Re}(\mathrm{s})>a+7$ $\operatorname{Re}(s)<2$ $\operatorname{Re}(s)>a+5$
In what range should $\operatorname{Re}(s)$ remain so that the Laplace transform of the function $e^{(n+2)t+5}$ exits?$\operatorname{Re}(s)>a+2$$\operatorname{Re}(\mathrm...
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877
GATE ECE 2005 | Question: 32
Given the matrix $\left[\begin{array}{cc}-4 & 2 \\ 4 & 3\end{array}\right]$, the eigenvector is $\left[\begin{array}{l}3 \\ 2\end{array}\right]$ $\left[\begin{array}{l}4 \\ 3\end{array}\right]$ $\left[\begin{array}{c}2 \\ -1\end{array}\right]$ $\left[\begin{array}{c}-2 \\ 1\end{array}\right]$
Given the matrix $\left[\begin{array}{cc}-4 & 2 \\ 4 & 3\end{array}\right]$, the eigenvector is$\left[\begin{array}{l}3 \\ 2\end{array}\right]$$\left[\begin{array}{l}4 \\...
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878
GATE ECE 2005 | Question: 33
Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right]$ Then $(a+b)=$ $\frac{7}{20}$ $\frac{3}{20}$ $\frac{19}{60}$ $\frac{11}{20}$
Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{a...
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879
GATE ECE 2005 | Question: 34
The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is $1$ $\pi$ $2$ $2 \pi$
The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is$1$$\pi$$2$$2 \pi$
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880
GATE ECE 2005 | Question: 35
The derivative of the symmetric function drawn in given figure will look like
The derivative of the symmetric function drawn in given figure will look like
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