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Recent questions tagged gateece-2023
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GATE ECE 2023 | Question: 31
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm{s}^2\right)$ is given by $\frac{2 \alpha}{\mathrm{k}}$ $\frac{\alpha}{\mathrm{k}}$ $\frac{\alpha}{2 \mathrm{k}}$ $\frac{\alpha}{4 \mathrm{k}}$
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm...
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GATE ECE 2023 | Question: 32
In the following block diagram, $\mathrm{R}(\mathrm{s})$ and $\mathrm{D}(\mathrm{s})$ are two inputs. The output $\mathrm{Y}(\mathrm{s})$ is expressed as $Y(s)=G_1(s) R(s)+G_2(s) D(s)$. $\mathrm{G}_1(\mathrm{~s})$ and $\mathrm{G}_2(\mathrm{~s})$ ...
In the following block diagram, $\mathrm{R}(\mathrm{s})$ and $\mathrm{D}(\mathrm{s})$ are two inputs. The output $\mathrm{Y}(\mathrm{s})$ is expressed as $Y(s)=G_1(s) R(s...
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GATE ECE 2023 | Question: 33
The state equation of a second order system is $\dot{\boldsymbol{x}}(t)=\mathrm{A} \boldsymbol{x}(t), \; \boldsymbol{x}(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of $\mathrm{A}$ and $v_1$ and $v_2$ are ... $\sum_{i=1}^2 \alpha_i e^{4 \lambda_i \mathrm{t}} \boldsymbol{v}_i$
The state equation of a second order system is$\dot{\boldsymbol{x}}(t)=\mathrm{A} \boldsymbol{x}(t), \; \boldsymbol{x}(0)$ is the initial condition.Suppose $\lambda_1$ an...
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GATE ECE 2023 | Question: 34
The switch $\mathrm{S}_{1}$ was closed and $\mathrm{S}_{2}$ was open for a long time. At $t=0$, switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed, simultaneously. The value of $\mathrm{i}_{\mathrm{c}}\left(0^{+}\right)$, in amperes, is $1$ $-1$ $0.2$ $0.8$
The switch $\mathrm{S}_{1}$ was closed and $\mathrm{S}_{2}$ was open for a long time. At $t=0$, switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed, simultan...
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GATE ECE 2023 | Question: 35
Let a frequency modulated $\text{(FM)}$ signal $x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of bandwidth $\text{W.}$ ... to recover $x(t)$ from $y(t)$ is $B_{T}+W$ $\frac{3}{2} B_{T}$ $2 B_{T}+W$ $\frac{5}{2} B_{T}$
Let a frequency modulated $\text{(FM)}$ signal$x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of b...
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GATE ECE 2023 | Question: 36
The $\text{h}$-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{\mathrm{V}_{\text {out }}}{\mathrm{V}_{\mathrm{s}}}$ is $\mathrm{h}_{11}=0, \mathrm{~h}_{12}=0, \mathrm{~h}_{21}=$ ... $\mathrm{h}_{11}=0, \mathrm{~h}_{12}=0, \mathrm{~h}_{21}=$ very high and $\mathrm{h}_{22}=$ very high
The $\text{h}$-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{\mathrm{V}_{\text {out }}}{\mathrm{V}_{\ma...
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GATE ECE 2023 | Question: 37
Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \pi n}{5}}$, where $a_0=1, a_1=$ $3 j, a_2=2 j, a_3=-2 j$ and $a_4=-3 j$. The value of the sum $\sum_{n=0}^4 x[n] \sin \frac{4 \pi n}{5}$ is $-10$ $10$ $-2$ $2$
Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \...
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GATE ECE 2023 | Question: 38
Let an input $x[n]$ having discrete-time Fourier transform $X\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H\left(e^{j \Omega}\right)=1-\frac{1}{2} e^{-j 2 \Omega}$. The ... $\delta[n]+\delta[n-1]+\frac{1}{2} \delta[n-2]+\frac{5}{2} \delta[n-3]+\delta[n-5]$
Let an input $x[n]$ having discrete-time Fourier transform$X\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega}$ be passed through an LTI system. The frequency re...
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GATE ECE 2023 | Question: 39
Let $x(t)=10 \cos (10.5 W t)$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt$. The output of the system is $\left(\frac{15 W}{4}\right) \cos (10.5 W t)$ $\left(\frac{15 W}{2}\right) \cos (10.5 W t)$ $\left(\frac{15 W}{8}\right) \cos (10.5 W t)$ $(15 W) \cos (10.5 W t)$
Let $x(t)=10 \cos (10.5 W t)$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt$. The output of the sys...
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GATE ECE 2023 | Question: 40
Let $\mathrm{x}_1(\mathrm{t})$ and $\mathrm{x}_2(\mathrm{t})$ be two band-limited signals having bandwidth $B=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s}$ each. In the figure below, the Nyquist sampling frequency, in $\mathrm{rad} / \mathrm{s}$, required to sample $y(\mathrm{t})$, is $20 \pi \times 10^3$ $40 \pi \times 10^3$ $8 \pi \times 10^3$ $32 \pi \times 10^3$
Let $\mathrm{x}_1(\mathrm{t})$ and $\mathrm{x}_2(\mathrm{t})$ be two band-limited signals having bandwidth $B=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s}$ each. In the...
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GATE ECE 2023 | Question: 41
The $S$-parameters of a two-port network is given as $ [S]=\left[\begin{array}{ll} S_{11} & S_{12} \\ S_{21} & S_{22} \end{array}\right] $ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1=\beta l_1$ ...
The $S$-parameters of a two-port network is given as$$[S]=\left[\begin{array}{ll}S_{11} & S_{12} \\S_{21} & S_{22}\end{array}\right]$$with reference to $Z_0$. Two lossles...
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GATE ECE 2023 | Question: 42
The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive voltage minima is $30 \mathrm{~cm}$ and the first minimum is located at $10 \mathrm{~cm}$ ... $R_m=100 \; \Omega, l_m=5 \mathrm{~cm}$ $R_m=25 \; \Omega, l_m=5 \mathrm{~cm}$
The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive volta...
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GATE ECE 2023 | Question: 43
The electric field of a plane electromagnetic wave is $\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+\theta) \quad \mathrm{V} / \mathrm{m}$. Which of the following combination(s) will give rise to a left handed ... $C_{1 x}=1, C_{1 y}=2, \theta=3 \pi / 2$ $C_{1 x}=2, C_{1 y}=1, \theta=3 \pi / 4$
The electric field of a plane electromagnetic wave is$\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+...
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GATE ECE 2023 | Question: 44
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
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GATE ECE 2023 | Question: 45
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
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GATE ECE 2023 | Question: 46
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ________ (rounded off to two decimal places).
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-...
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GATE ECE 2023 | Question: 47
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}$, where $k, z, p, a, b$ and $c$ are positive constants. The value of $(a+b+c)$ is ____________ (rounded off to the nearest integer).
The asymptotic magnitude Bode plot of a minimum phase system is shown in thefigure. The transfer function of the system is $(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}$, where ...
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GATE ECE 2023 | Question: 48
Let $\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5)$ and $\mathrm{x}_2(\mathrm{t})$ is shown in the figure below. For $\mathrm{y}(\mathrm{t})=\mathrm{x}_1(\mathrm{t}) * \mathrm{x}_2(\mathrm{t})$, the $\int_{-\infty}^{\infty} \mathrm{y}(\mathrm{t}) \mathrm{dt}$ is ______________ (rounded off to the nearest integer).
Let $\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5)$ and $\mathrm{x}_2(\mathrm{t})$ is shown in the figure below. For $\mathrm{y}(\mathrm{...
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GATE ECE 2023 | Question: 49
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t} u(t)$. The average power of the system output is _____________ $\mathrm{W}$ (rounded off to two decimal places).
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t...
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GATE ECE 2023 | Question: 50
A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm{m}\right)$. The minimum thickness of the dielectric coating, in $\mu \mathrm{m}$, that can be used is_____________(rounded off to two decimal places).
A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm...
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GATE ECE 2023 | Question: 51
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \mathrm{~K}$ is $1 \times 10^{19} \mathrm{~cm}^{-3}$. The thermal equilibrium hole ... $\mathrm{kT}$ at $300 \mathrm{~K}$ is $0.026 \; \mathrm{eV}$.
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \m...
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GATE ECE 2023 | Question: 52
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of $1 \; \mu \mathrm{s}$. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of $1 \mathrm{~V}$ with $12$-bit accuracy is ___________ $\mu \mathrm{s}$ (rounded off to two decimal places).
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of $1 \; \mu \mathrm{s}$. The time for the sampling switch to stay ...
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GATE ECE 2023 | Question: 53
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kHz}$, is __________ (rounded off to the nearest integer).
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kH...
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GATE ECE 2023 | Question: 54
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
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GATE ECE 2023 | Question: 55
The frequency of occurrence of $8$ symbols $(a-h)$ is shown in the table below. A symbol is chosen and it is determined by asking a series of $\text{"yes/no"}$ questions which are assumed to be truthfully answered. The average number of questions when asked in the most ... $\frac{1}{16}$ $\frac{1}{32}$ $\frac{1}{64}$ $\frac{1}{128}$ $\frac{1}{128}$
The frequency of occurrence of $8$ symbols $(a-h)$ is shown in the table below. A symbol is chosen and it is determined by asking a series of $\text{"yes/no"}$ questions ...
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