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Recent questions tagged gate2008-ec

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2
GATE ECE 2008 | Question: 2
The system of linear equations \[ \begin{array}{l} 4 x+2 y=7 \\ 2 x+y=6 \end{array} \] has a unique solution no solution an infinite number of solutions exactly two distinct solutions
The system of linear equations\[ \begin{array}{l}4 x+2 y=7 \\2 x+y=6\end{array} \]hasa unique solutionno solutionan infinite number of solutionsexactly two distinct solut...
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3
GATE ECE 2008 | Question: 3
The equation $\sin (z)=10$ has no real or complex solution exactly two distinct complex solutions a unique solution an infinite number of complex solutions
The equation $\sin (z)=10$ hasno real or complex solutionexactly two distinct complex solutionsa unique solutionan infinite number of complex solutions
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4
GATE ECE 2008 | Question: 4
For real values of $x$, the minimum value of the function $f(x)=\exp (x)+\exp (-x)$ is $2$ $1$ $0.5$ $0$
For real values of $x$, the minimum value of the function $f(x)=\exp (x)+\exp (-x)$ is$2$$1$$0.5$$0$
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5
GATE ECE 2008 | Question: 5
Which of the following functions would have only odd powers of $x$ in its Taylor series expansion about the point $x=0?$ $\sin \left(x^{3}\right)$ $\sin \left(x^{2}\right)$ $\cos \left(x^{3}\right)$ $\cos \left(x^{2}\right)$
Which of the following functions would have only odd powers of $x$ in its Taylor series expansion about the point $x=0?$ $\sin \left(x^{3}\right)$$\sin \left(x^{2}\right)...
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6
GATE ECE 2008 | Question: 6
Which of the following is a solution to the differential equation $\dfrac{d x(t)}{d t}+3 x(t)=0?$ $x(t)=3 e^{-t}$ $x(t)=2 e^{-3 t}$ $x(t)=-\frac{3}{2} t^{2}$ $x(t)=3 t^{2}$
Which of the following is a solution to the differential equation $\dfrac{d x(t)}{d t}+3 x(t)=0?$ $x(t)=3 e^{-t}$$x(t)=2 e^{-3 t}$$x(t)=-\frac{3}{2} t^{2}$$x(t)=3 t^{2}$
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7
GATE ECE 2008 | Question: 7
In the following graph, the number of trees $\text{(P)}$ and the number of cut-sets $\text{(Q)}$ are $\mathrm{P}=2, \mathrm{Q}=2$ $\mathrm{P}=2, \mathrm{Q}=6$ $\mathrm{P}=4, \mathrm{Q}=6$ $\mathrm{P}=4, \mathrm{Q}=10$
In the following graph, the number of trees $\text{(P)}$ and the number of cut-sets $\text{(Q)}$ are$\mathrm{P}=2, \mathrm{Q}=2$$\mathrm{P}=2, \mathrm{Q}=6$$\mathrm{P}=4,...
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8
GATE ECE 2008 | Question: 8
In the following circuit, the switch $\mathrm{S}$ is closed at $t=0$. The rate of change of current $\dfrac{d i}{d t}(0+)$ is given by $0$ $\frac{R_{S} I_{S}}{L}$ $\frac{\left(R+R_{s}\right) I_{s}}{L}$ $\infty$
In the following circuit, the switch $\mathrm{S}$ is closed at $t=0$. The rate of change of current $\dfrac{d i}{d t}(0+)$ is given by$0$$\frac{R_{S} I_{S}}{L}$$\frac{\le...
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9
GATE ECE 2008 | Question: 9
The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system? $y(t)=x(t-2)+x(t+4)$ $y(t)=(t-4) x(t+1)$ $y(t)=(t+4) x(t-1)$ $y(t)=(t+5) x(t+5)$
The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system?$y(t)=x...
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11
GATE ECE 2008 | Question: 11
The pole-zero plot given below corresponds to a Low pass filter High pass filter Band pass filter Notch filter
The pole-zero plot given below corresponds to aLow pass filterHigh pass filterBand pass filterNotch filter
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12
GATE ECE 2008 | Question: 12
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the thre...
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13
GATE ECE 2008 | Question: 13
Which of the following is NOT associated with a $\text{p-n}$ junction? Junction Capacitance Charge Storage Capacitance Depletion Capacitance Channel Length Modulation
Which of the following is NOT associated with a $\text{p-n}$ junction?Junction CapacitanceCharge Storage CapacitanceDepletion CapacitanceChannel Length Modulation
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14
GATE ECE 2008 | Question: 14
Which of the following is true? A silicon wafer heavily doped with boron is a $p^{+}$substrate A silicon wafer lightly doped with boron is a $p^{+}$ substrate A silicon wafer heavily doped with arsenic is a $\mathrm{p}^{+}$substrate A silicon wafer lightly doped with arsenic is a $p^{+}$ substrate
Which of the following is true?A silicon wafer heavily doped with boron is a $p^{+}$substrateA silicon wafer lightly doped with boron is a $p^{+}$ substrateA silicon wafe...
1 votes
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15
GATE ECE 2008 | Question: 15
For a Hertz dipole antenna, the half power beam width $\text{(HPBW)}$ in the $\text{E}$-plane is $360^{\circ}$ $180^{\circ}$ $90^{\circ}$ $45^{\circ}$
For a Hertz dipole antenna, the half power beam width $\text{(HPBW)}$ in the $\text{E}$-plane is$360^{\circ}$$180^{\circ}$$90^{\circ}$$45^{\circ}$
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20
GATE ECE 2008 | Question: 20
Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$. For demodulating the signal using envelope detector, the minimum value of $A_{c}$ should be $2$ $1$ $0.5$ $0$
Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$. For demodulating the signal using envelope detector, the min...
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21
GATE ECE 2008 | Question: 21
The Thevenin equivalent impedance $\text{Z}_{\text {th }}$ between the nodes $\text{P}$ and $\text{Q}$ in the following circuit is $1$ $1+s+\frac{1}{s}$ $2+s+\frac{1}{s}$ $\frac{s^{2}+s+1}{s^{2}+2 s+1}$
The Thevenin equivalent impedance $\text{Z}_{\text {th }}$ between the nodes $\text{P}$ and $\text{Q}$ in the following circuit is$1$$1+s+\frac{1}{s}$$2+s+\frac{1}{s}$$\f...
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22
GATE ECE 2008 | Question: 22
The driving point impedance of the following network is given by $Z(s)=\frac{0.2 s}{s^{2}+0.1 s+2}$. The component values are $\begin{array}{lll} \mathrm{L}=5 \mathrm{~H}, & \mathrm{R}=0.5 \; \Omega, & \mathrm{C}=0.1 \mathrm{~F} \end{array}$ ...
The driving point impedance of the following networkis given by $Z(s)=\frac{0.2 s}{s^{2}+0.1 s+2}$. The component values are$\begin{array}{lll} \mathrm{L}=5 \mathrm{~H}, ...
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23
GATE ECE 2008 | Question: 23
The circuit shown in the figure is used to charge the capacitor $\mathrm{C}$ alternately from two current sources as indicated. The switches $\text{S1}$ and $\text{S2}$ ... $\displaystyle{}\sum_{n=0}^{\infty}\left[0.5-e^{-(t-2 n T)}+0.5 e^{-(t-2 n T-T)}\right]$
The circuit shown in the figure is used to charge the capacitor $\mathrm{C}$ alternately from two current sources as indicated. The switches $\text{S1}$ and $\text{S2}$ a...
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24
GATE ECE 2008 | Question: 24
The probability density function (PDF) of a random variable $\mathrm{X}$ is as shown below. The corresponding cumulative distribution function (CDF) has the form
The probability density function (PDF) of a random variable $\mathrm{X}$ is as shown below.The corresponding cumulative distribution function (CDF) has the form
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25
GATE ECE 2008 | Question: 25
The recursion relation to solve $x=e^{-x}$ using Newton-Raphson method is $x_{n+1}=e^{-x_{n}}$ $x_{n+1}=x_{n}-e^{-x_{n}}$ $x_{n+1}=\left(1+x_{n}\right) \frac{e^{-x_{n}}}{1+e^{-x_{n}}}$ $x_{n+1}=\frac{x_{n}^{2}-e^{-x_{n}}\left(1+x_{n}\right)-1}{x_{n}-e^{-x_{n}}}$
The recursion relation to solve $x=e^{-x}$ using Newton-Raphson method is$x_{n+1}=e^{-x_{n}}$$x_{n+1}=x_{n}-e^{-x_{n}}$$x_{n+1}=\left(1+x_{n}\right) \frac{e^{-x_{n}}}{1+e...
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26
GATE ECE 2008 | Question: 26
The residue of the function $f(z)=\dfrac{1}{(z+2)^{2}(z-2)^{2}}$ at $z=2$ is $-\;\frac{1}{32}$ $-\;\frac{1}{16}$ $\frac{1}{16}$ $\frac{1}{32}$
The residue of the function $f(z)=\dfrac{1}{(z+2)^{2}(z-2)^{2}}$ at $z=2$ is$-\;\frac{1}{32}$$-\;\frac{1}{16}$$\frac{1}{16}$$\frac{1}{32}$
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27
GATE ECE 2008 | Question: 27
Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$. The value of $\mathbf{e}^{\mathbf{P}}$ ...
Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$. The value of $\mathbf{e}^{\mathbf{P}}$ is$\left[\begin{array}{cc}2 e^{-2}-3 e^...
1 votes
2 answers
28
GATE ECE 2008 | Question: 28
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is $\exp (\pi)$ $0.5 \exp (\pi)$ $\exp (\pi)+1$ $\exp (\pi)-1$
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is$\exp (\pi)$$0.5 \exp (\pi)$$\exp (\pi)+1$$\exp (\pi)-1$...
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29
GATE ECE 2008 | Question: 29
$P_{X}(x)=M \exp (-2|x|)+N \exp (-3|x|)$ is the probability density function for the real random variable $X$, over the entire $x$ axis. $M$ and $N$ are both positive real numbers. The equation relating $M$ and $N$ is $M+\frac{2}{3} N=1$ $2 M+\frac{1}{3} N=1$ $M+N=1$ $M+N=3$
$P_{X}(x)=M \exp (-2|x|)+N \exp (-3|x|)$ is the probability density function for the real random variable $X$, over the entire $x$ axis. $M$ and $N$ are both positive rea...
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30
GATE ECE 2008 | Question: 30
The value of the integral of the function $g(x, y)=4 x^{3}+10 y^{4}$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $x\text{-}y$ plane is $33$ $35$ $40$ $56$
The value of the integral of the function $g(x, y)=4 x^{3}+10 y^{4}$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $x\text{-}y$ plane...
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32
GATE ECE 2008 | Question: 32
The signal $x(t)$ is described by $x(t)=\left\{\begin{array}{ll} 1 & \text { for }-1 \leq t \leq+1 \\ 0 & \text { otherwise } \end{array}\right.$ Two of the angular frequencies at which its Fourier transform becomes zero are $\pi, 2 \pi$ $0.5 \pi, 1.5 \pi$ $0, \pi$ $2 \pi, 2.5 \pi$
The signal $x(t)$ is described by$x(t)=\left\{\begin{array}{ll}1 & \text { for }-1 \leq t \leq+1 \\0 & \text { otherwise }\end{array}\right.$Two of the angular frequencie...
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35
GATE ECE 2008 | Question: 35
Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system relations $\mathrm{R} 1, \mathrm{R} 2, \mathrm{R} 3, \mathrm{R} 4 .$ ... $\text{(P1, R3), (P2, R1), (P3, R2)}$ $\text{(P1, R1), (P2, R2), (P3, R3)}$
Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system rela...
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GATE ECE 2008 | Question: 36
A memoryless source emits $n$ symbols each with a probability $p$. The entropy of the source as a function of $n$ increases as $\log n$ decreases as $\log (1 / n)$ increases as $n$ increases as $n \log n$
A memoryless source emits $n$ symbols each with a probability $p$. The entropy of the source as a function of $n$increases as $\log n$decreases as $\log (1 / n)$increases...
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40
GATE ECE 2008 | Question: 40
A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is ...
A signal flow graph of a system is given below.The set of equations that correspond to this signal flow graph is$\dfrac{d}{d t}\left(\begin{array}{l}x_{1} \\ x_{2} \\ x_{...
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