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Recent questions tagged gate2009-ec

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1
GATE ECE 2009 | Question: 1
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is $1$ $2$ $3$ $4$
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$
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GATE ECE 2009 | Question: 5
In an n-type silicon crystal at room temperature, which of the following can have a concentration of $4 \times 10^{19} \mathrm{~cm}^{-3}$ ? Silicon atoms Holes Dopant atoms Valence electrons
In an n-type silicon crystal at room temperature, which of the following can have a concentration of $4 \times 10^{19} \mathrm{~cm}^{-3}$ ?Silicon atomsHolesDopant atomsV...
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GATE ECE 2009 | Question: 7
The $\text{ROC}$ of $\text{Z}$-transform of the discrete time sequence $\quad x(n)=\left(\dfrac{1}{3}\right)^{n} u(n)-\left(\dfrac{1}{2}\right)^{n} u(-n-1) \quad$ is $\frac{1}{3}<|z|<\frac{1}{2}$ $|z|>\frac{1}{2}$ $|z|<\frac{1}{3}$ $2<|z|<3$
The $\text{ROC}$ of $\text{Z}$-transform of the discrete time sequence $\quad x(n)=\left(\dfrac{1}{3}\right)^{n} u(n)-\left(\dfrac{1}{2}\right)^{n} u(-n-1) \quad$ is$\fra...
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GATE ECE 2009 | Question: 8
The magnitude plot of a rational transfer function $G(s)$ with real coefficients is shown below. Which of the following compensators hás such a magnitude plot? Lead compensator Lag compensator PID compensator Lead-lag compensator
The magnitude plot of a rational transfer function $G(s)$ with real coefficients is shown below. Which of the following compensators hás such a magnitude plot?Lead compe...
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GATE ECE 2009 | Question: 10
Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown? Only $\text{P}$ has no cutoff-frequency Only $\text{Q}$ has no cutoff-frequency Only $\text{R}$ has no cutoff-frequency All three have cut-off frequencies
Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?Only $\text{P}$ has no cutoff-frequencyOnly $\text{Q}$ has no cu...
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11
GATE ECE 2009 | Question: 11
A fair coin is tossed $10$ times. What is the probability that $\text{ONLY}$ the first two tosses will yield heads? $\left(\frac{1}{2}\right)^{2}$ ${ }^{10} C_{2}\left(\frac{1}{2}\right)^{2}$ $\left(\frac{1}{2}\right)^{10}$ ${ }^{10} C_{2}\left(\frac{1}{2}\right)^{10}$
A fair coin is tossed $10$ times. What is the probability that $\text{ONLY}$ the first two tosses will yield heads?$\left(\frac{1}{2}\right)^{2}$${ }^{10} C_{2}\left(\fra...
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GATE ECE 2009 | Question: 12
If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is
If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is
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13
GATE ECE 2009 | Question: 13
If $f(z) = c_{0} + c_{1} z^{-1},$ then $\displaystyle{} \oint_{\text{unit circle}} \frac{1+f(z)}{z} dz$ is given by $2 \pi c_{1}$ $2 \pi\left(1+c_{0}\right)$ $2 \pi j c_{1}$ $2 \pi j\left(1+c_{0}\right)$
If $f(z) = c_{0} + c_{1} z^{-1},$ then $\displaystyle{} \oint_{\text{unit circle}} \frac{1+f(z)}{z} dz$ is given by$2 \pi c_{1}$$2 \pi\left(1+c_{0}\right)$$2 \pi j c_{1}$...
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GATE ECE 2009 | Question: 14
In the interconnection of ideal sources shown in the figure, it is known that the $60 \mathrm{~V}$ source is absorbing power. Which of the following can be the value of the current source $\text{I}?$ $10 \mathrm{~A}$ $13 \mathrm{~A}$ $15 \mathrm{~A}$ $18 \mathrm{~A}$
In the interconnection of ideal sources shown in the figure, it is known that the $60 \mathrm{~V}$ source is absorbing power.Which of the following can be the value of th...
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15
GATE ECE 2009 | Question: 15
The ratio of the mobility to the diffusion coefficient in a semiconductor has the units $\mathrm{V}^{-1}$ $\mathrm{cm} \cdot \mathrm{V}^{-1}$ $\mathrm{V} \cdot \mathrm{cm}^{-1}$ $\mathrm{V} \cdot \mathrm{s}$
The ratio of the mobility to the diffusion coefficient in a semiconductor has the units$\mathrm{V}^{-1}$$\mathrm{cm} \cdot \mathrm{V}^{-1}$$\mathrm{V} \cdot \mathrm{cm}^{...
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16
GATE ECE 2009 | Question: 16
In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is non-maskable and non-vectored maskable and non-vectored non-maskable and vectored maskable and vectored
In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed o...
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17
GATE ECE 2009 | Question: 17
If the transfer function of the following network is $\dfrac{V_{o}(s)}{V_{i}(s)}=\dfrac{1}{2+s C R}.$ the value of the load resistance $R_{L}$ is $R / 4$ $R / 2$ $R$ $2 R$
If the transfer function of the following network is $\dfrac{V_{o}(s)}{V_{i}(s)}=\dfrac{1}{2+s C R}.$the value of the load resistance $R_{L}$ is$R / 4$$R / 2$$R$$2 R$
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19
GATE ECE 2009 | Question: 19
For a message signal $m(t)=\cos \left(2 \pi f_{m} t\right)$ and carrier of frequency $f_{c}$ which of the following represents a single-side-band (SSB) signal? $\cos \left(2 \pi f_{m} t\right) \cos \left(2 \pi f_{c} t\right)$ ... $\left[1+\cos \left(2 \pi f_{m} t\right] \cos \left(2 \pi f_{c} t\right)\right.$
For a message signal $m(t)=\cos \left(2 \pi f_{m} t\right)$ and carrier of frequency $f_{c}$ which of the following represents a single-side-band (SSB) signal?$\cos \left...
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21
GATE ECE 2009 | Question: 21
Consider two independent random variables $X$ and $Y$ with identical distributions. The variables $X$ and $Y$ take values $0,1$ and $2$ with probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ respectively. What is the conditional probability $P(X+Y=2 \mid X-Y=0) ?$ $0$ $\frac{1}{16}$ $\frac{1}{6}$ $1$
Consider two independent random variables $X$ and $Y$ with identical distributions. The variables $X$ and $Y$ take values $0,1$ and $2$ with probabilities $\frac{1}{2}, \...
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22
GATE ECE 2009 | Question: 22
The Taylor series expansion of $\dfrac{\sin x}{x-\pi}$ at $x=\pi$ is given by $1+\frac{(x-\pi)^{2}}{3 !}+\ldots$ $-1-\frac{(x-\pi)^{2}}{3 !}+\ldots$ $1-\frac{(x-\pi)^{2}}{3 !}+\ldots$ $-1+\frac{(x-\pi)^{2}}{3 !}+\ldots$
The Taylor series expansion of $\dfrac{\sin x}{x-\pi}$ at $x=\pi$ is given by$1+\frac{(x-\pi)^{2}}{3 !}+\ldots$$-1-\frac{(x-\pi)^{2}}{3 !}+\ldots$$1-\frac{(x-\pi)^{2}}{3 ...
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23
GATE ECE 2009 | Question: 23
If a vector field $ \displaystyle{} \vec{V}$ is related to another vector field $ \displaystyle{} \vec{A}$ through $ \displaystyle{} \vec{V}=\nabla \times \vec{A}$, which of the following is true ? Note: $C$ and $S_{C}$ refer to any closed contour and ...
If a vector field $ \displaystyle{} \vec{V}$ is related to another vector field $ \displaystyle{} \vec{A}$ through $ \displaystyle{} \vec{V}=\nabla \times \vec{A}$, which...
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24
GATE ECE 2009 | Question: 24
Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is $s F(s)-f(0)$ $\dfrac{1}{s} F(s)$ $\displaystyle{}\int_{0}^{s} F(\tau) d \tau$ $\dfrac{1}{s}[F(s)-f(0)]$
Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is$s F(s)-f(0)$$\dfrac{1}{s} F(s)$$\...
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25
GATE ECE 2009 | Question: 25
Match each differential equation in $\text{Group I}$ to its family of solution curves from $\text{Group II.}$ ... $\text{P-2, Q-1, R-3, S-3}$ $\text{P-3, Q-2, R-1, S-2}$
Match each differential equation in $\text{Group I}$ to its family of solution curves from $\text{Group II.}$$$\begin{array}{llll} & \textbf{Group I} & & \textbf{Group II...
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26
GATE ECE 2009 | Question: 26
The eigen values of the following matrix are \[ \left[\begin{array}{ccc} -1 & 3 & 5 \\ -3 & -1 & 6 \\ 0 & 0 & 3 \end{array}\right] \] $3,3+5 j, 6-j$ $-6+5 j, 3+j, 3-j$ $3+j, 3-j, 5+j$ $3,-1+3 j,-1-3 j$
The eigen values of the following matrix are\[ \left[\begin{array}{ccc}-1 & 3 & 5 \\-3 & -1 & 6 \\0 & 0 & 3\end{array}\right] \]$3,3+5 j, 6-j$$-6+5 j, 3+j, 3-j$$3+j, 3-j,...
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27
GATE ECE 2009 | Question: 27
An $\text{AC}$ source of $\text{RMS}$ voltage $20 \mathrm{~V}$ with internal impedance $Z_{s}=(1+2 j) \Omega$ feeds a load of impedance $Z_{L}=(7+4 j) \Omega$ in the figure below. The reactive power consumed by the load is $8 \; \mathrm{VAR}$ $16 \; \mathrm{VAR}$ $28 \; \mathrm{VAR}$ $32 \; \mathrm{VAR}$
An $\text{AC}$ source of $\text{RMS}$ voltage $20 \mathrm{~V}$ with internal impedance $Z_{s}=(1+2 j) \Omega$ feeds a load of impedance $Z_{L}=(7+4 j) \Omega$ in the figu...
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28
GATE ECE 2009 | Question: 28
The switch in the circuit shown was on position $a$ for a long time, and is moved to position $b$ at time $t=0$. The current $i(t)$ for $t>0$ is given by $0.2 e^{-125 t} u(t) \; \mathrm{mA}$ $20 e^{-1250 t} u(t) \; \mathrm{mA}$ $0.2 e^{-1250 t} u(t) \; \mathrm{mA}$ $20 e^{-1000 t} u(t) \; \mathrm{mA}$
The switch in the circuit shown was on position $a$ for a long time, and is moved to position $b$ at time $t=0$. The current $i(t)$ for $t>0$ is given by$0.2 e^{-125 t} u...
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GATE ECE 2009 | Question: 29
In the circuit shown, what value of $R_{L}$ maximizes the power delivered to $R_{L}$ ? $2.4 \; \Omega$ $\frac{8}{3} \; \Omega$ $4 \; \Omega$ $6 \; \Omega$
In the circuit shown, what value of $R_{L}$ maximizes the power delivered to $R_{L}$ ?$2.4 \; \Omega$$\frac{8}{3} \; \Omega$$4 \; \Omega$$6 \; \Omega$
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30
GATE ECE 2009 | Question: 30
The time domain behavior of an $R L$ circuit is represented by \[ L \frac{d i}{d t}+R i=V_{o}\left(1+B e^{-R t / L} \sin t\right) u(t). \] For an initial current of $i(0)=\dfrac{V_{o}}{R}$ ... $ i(t) \rightarrow \frac{V_{0}}{R}(1+B)$ $ i(t) \rightarrow \frac{2 V_{0}}{R}(1+B)$
The time domain behavior of an $R L$ circuit is represented by\[ L \frac{d i}{d t}+R i=V_{o}\left(1+B e^{-R t / L} \sin t\right) u(t). \]For an initial current of $i(0)=\...
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GATE ECE 2009 | Question: 31
In the circuit below, the diode is ideal. The voltage $V$ is given by $\min \left(V_{i}, 1\right)$ $\max \left(V_{i}, 1\right)$ $\min \left(-V_{i}, 1\right)$ $\max \left(-V_{i}, 1\right)$
In the circuit below, the diode is ideal. The voltage $V$ is given by$\min \left(V_{i}, 1\right)$$\max \left(V_{i}, 1\right)$$\min \left(-V_{i}, 1\right)$$\max \left(-V_{...
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GATE ECE 2009 | Question: 33
In the following astable multivibrator circuit, which properties of $v_{o}(t)$ depend on $R_{2}$? Only the frequency Only the amplitude Both the amplitude and the frequency Neither the amplitude nor the frequency
In the following astable multivibrator circuit, which properties of $v_{o}(t)$ depend on $R_{2}$?Only the frequencyOnly the amplitudeBoth the amplitude and the frequencyN...
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34
GATE ECE 2009 | Question: 34
In the circuit shown below, the $\text{op-amp}$ is ideal, the transistor has $V_{B E}=0.6 \mathrm{~V}$ and $\beta=150$. Decide whether the feedback in the circuit is positive or negative and determine the voltage $V$ ... $V=0 \mathrm{~V}$ Negative feedback, $V=5 \mathrm{~V}$ Negative feedback, $V=2 \mathrm{~V}$
In the circuit shown below, the $\text{op-amp}$ is ideal, the transistor has $V_{B E}=0.6 \mathrm{~V}$ and $\beta=150$. Decide whether the feedback in the circuit is posi...
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35
GATE ECE 2009 | Question: 35
A small signal source $v_{i}(t)=A \cos 20 t+B \sin 10^{6} t$ is applied to a transistor amplifier as shown below. The transistor has $\beta=150$ and $h_{i e}=3 \; \mathrm{k} \Omega$. Which expression best approximates $v_{o}(t)$ ... $v_{o}(t)=-1500 B \sin 10^{6} t$ $v_{o}(t)=-150 B \sin 10^{6} t$
A small signal source $v_{i}(t)=A \cos 20 t+B \sin 10^{6} t$ is applied to a transistor amplifier as shown below. The transistor has $\beta=150$ and $h_{i e}=3 \; \mathrm...
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36
GATE ECE 2009 | Question: 36
If $X=1$ in the logic equation $[X+Z\{\overline{Y}+(\overline{Z}+X \overline{Y})\}]\{\overline{X}+\overline{Z}(X+Y)\}=1$, then $Y=Z$ $Y=\overline{Z}$ $Z=1$ $Z=0$
If $X=1$ in the logic equation $[X+Z\{\overline{Y}+(\overline{Z}+X \overline{Y})\}]\{\overline{X}+\overline{Z}(X+Y)\}=1$, then$Y=Z$$Y=\overline{Z}$$Z=1$$Z=0$
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37
GATE ECE 2009 | Question: 37
What are the minimum number of $2$-to-$1$ multiplexers required to generate a $2$-input $\text{AND}$ gate and a $2$-input $\text{Ex-OR}$ gate? $1$ and $2$ $1$ and $3$ $1$ and $1$ $2$ and $2$
What are the minimum number of $2$-to-$1$ multiplexers required to generate a $2$-input $\text{AND}$ gate and a $2$-input $\text{Ex-OR}$ gate?$1$ and $2$$1$ and $3$$1$ an...
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GATE ECE 2009 | Question: 39
What are the counting states $\left(Q_{1}, Q_{2}\right)$ for the counter shown in the figure below? $11,10,00,11,10, \ldots$ $01,10,11,00,01, \ldots$ $00,11,01,10,00, \ldots$ $01,10,00,01,10, \ldots$
What are the counting states $\left(Q_{1}, Q_{2}\right)$ for the counter shown in the figure below?$11,10,00,11,10, \ldots$$01,10,11,00,01, \ldots$$00,11,01,10,00, \ldots...
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