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82
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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83
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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89
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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92
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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93
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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94
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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96
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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98
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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100
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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102
TIFR ECE 2023 | Question: 3
Let \[ \mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} . \] Compute \[ \min _{(x, y) \in \mathcal{P}} 2 x+3 y \] $2$ $3$ $4$ $6$ None of the above
Let\[\mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} .\]Compute\[\min _{(x, y) \in \mathcal{P}} 2 x+3 y\]$2$$3$$4$$6$N...
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104
TIFR ECE 2023 | Question: 5
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some $x \in \mathrm{B}$ and some $y \in \mathrm{Q}, z=x+y$. The area of $\mathrm{K}$ is $4+\pi$ $6+\pi$ $8+\pi$ $10+\pi$ $12+\pi$
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some...
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105
TIFR ECE 2023 | Question: 6
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the real part of $\ln (x(t)+i y(t))$. $-2$ $1$ $0$ $-1$ $2$
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the rea...
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108
TIFR ECE 2015 | Question: 1
For a time-invariant system, the impulse response completely describes the system if the system is causal and non-linear non-causal and non-linear causal and linear All of the above None of the above
For a time-invariant system, the impulse response completely describes the system if the system iscausal and non-linearnon-causal and non-linearcausal and linearAll of th...
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111
TIFR ECE 2015 | Question: 5
What is the following passive circuit? Low-pass filter High-pass filter Band-pass filter Band-stop filter All-pass filter
What is the following passive circuit?Low-pass filterHigh-pass filterBand-pass filterBand-stop filterAll-pass filter
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112
TIFR ECE 2015 | Question: 12
Consider the following optimization problem \[ \max (2 x+3 y) \] subject to the following three constraints \[ \begin{aligned} x+y & \leq 5, \\ x+2 y & \leq 10, \text { and } \\ x & <3 . \end{aligned} \] Let $z^{*}$ be the ... $(x, y)$ that satisfy the above three constraints such that $2 x+3 y$ equals $z^{*}$.
Consider the following optimization problem\[\max (2 x+3 y)\]subject to the following three constraints\[\begin{aligned}x+y & \leq 5, \\x+2 y & \leq 10, \text { and } \\x...
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113
TIFR ECE 2014 | Question: 4
A system accepts a sequence of real numbers $x[n]$ as input and outputs \[ y[n]=\left\{\begin{array}{ll} 0.5 x[n]-0.25 x[n-1], & n \text { even } \\ 0.75 x[n], & n \text { odd } \end{array}\right. \] The system is non-linear. non-causal. time-invariant. All of the above. None of the above.
A system accepts a sequence of real numbers $x[n]$ as input and outputs\[y[n]=\left\{\begin{array}{ll}0.5 x[n]-0.25 x[n-1], & n \text { even } \\0.75 x[n], & n \text { od...
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115
TIFR ECE 2014 | Question: 10
Consider the two quadrature amplitude modulation $\text{(QAM)}$ constellations below. Suppose that the channel has additive white Gaussian noise channel and no intersymbol interference. The constellation points are picked equally likely. Let $P\text{(QAM)}$ denote the ... .
Consider the two quadrature amplitude modulation $\text{(QAM)}$ constellations below. Suppose that the channel has additive white Gaussian noise channel and no intersymbo...
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