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Recent questions tagged gate2007-ec

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1
GATE ECE 2007 | Question: 1
If $E$ denotes expectation, the variance of a random variable $X$ is given by $E\left[X^2\right]-E^2[X]$ $E\left[X^2\right]+E^2[X]$ $E\left[X^2\right]$ $E^2[X]$
If $E$ denotes expectation, the variance of a random variable $X$ is given by$E\left[X^2\right]-E^2[X]$$E\left[X^2\right]+E^2[X]$$E\left[X^2\right]$$E^2[X]$
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2
GATE ECE 2007 | Question: 2
The following plot shows a function $y$ which varies linearly with $x$. The value of the integral $I=\displaystyle{}\int_1^2 y d x$ is $1.0$ $2.5$ $4.0$ $5.0$
The following plot shows a function $y$ which varies linearly with $x$. The value of the integral $I=\displaystyle{}\int_1^2 y d x$ is$1.0$$2.5$$4.0$$5.0$
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3
GATE ECE 2007 | Question: 3
For $|x| \ll 1$, $\operatorname{coth}(x)$ can be approximated as $x$ $x^2$ $\frac{1}{x}$ $\frac{1}{x^2}$
For $|x| \ll 1$, $\operatorname{coth}(x)$ can be approximated as$x$$x^2$$\frac{1}{x}$$\frac{1}{x^2}$
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4
GATE ECE 2007 | Question: 4
$\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}$ is $0.5$ $1$ $2$ not defined
$\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}$ is$0.5$$1$$2$not defined
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5
GATE ECE 2007 | Question: 5
Which one of the following functions is strictly bounded? $\frac{1}{x^2}$ $e^x$ $x^2$ $e^{-x^2}$
Which one of the following functions is strictly bounded?$\frac{1}{x^2}$$e^x$$x^2$$e^{-x^2}$
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6
GATE ECE 2007 | Question: 6
For the function $e^{-x}$, the linear approximation around $x=2$ is $(3-x) e^{-2}$ $1-x$ $[3+2 \sqrt{2}-\left(1+\sqrt{2}\right) x] e^{-2}$ $e^{-2}$
For the function $e^{-x}$, the linear approximation around $x=2$ is$(3-x) e^{-2}$$1-x$$[3+2 \sqrt{2}-\left(1+\sqrt{2}\right) x] e^{-2}$$e^{-2}$
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8
GATE ECE 2007 | Question: 8
The $RC$ circuit shown in the figure is a low-pass filter a high-pass filter a band-pass filter a band-reject filter
The $RC$ circuit shown in the figure isa low-pass filtera high-pass filtera band-pass filtera band-reject filter
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10
GATE ECE 2007 | Question: 10
In a $p^{+} n$ junction diode under reverse bias, the magnitude of electric field is maximum at the edge of the depletion region on the $p$-side the edge of the depletion region on the $n$-side the $p^{+} n$ junction the centre of the depletion region on the $n$-side
In a $p^{+} n$ junction diode under reverse bias, the magnitude of electric field is maximum atthe edge of the depletion region on the $p$-sidethe edge of the depletion r...
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11
GATE ECE 2007 | Question: 11
The correct full wave rectifier circuit is
The correct full wave rectifier circuit is
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12
GATE ECE 2007 | Question: 12
In a transconductance amplifier, it is desirable to have a large input resistance and a large output resistance a large input resistance and a small output resistance a small input resistance and a large output resistance a small input resistance and a small output resistance
In a transconductance amplifier, it is desirable to havea large input resistance and a large output resistancea large input resistance and a small output resistancea smal...
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13
GATE ECE 2007 | Question: 13
$\mathrm{X}=01110$ and $\mathrm{Y}=11001$ are two $5$-bit binary numbers represented in two's complement format. The sum of $\mathrm{X}$ and $\mathrm{Y}$ represented in two's complement format using $6$ bits is $100111$ $001000$ $000111$ $101001$
$\mathrm{X}=01110$ and $\mathrm{Y}=11001$ are two $5$-bit binary numbers represented in two's complement format. The sum of $\mathrm{X}$ and $\mathrm{Y}$ represented in t...
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14
GATE ECE 2007 | Question: 14
The Boolean function $Y=A B+C D$ is to be realized using only $2$ -input NAND gates. The minimum number of gates required is $2$ $3$ $4$ $5$
The Boolean function $Y=A B+C D$ is to be realized using only $2$ -input NAND gates. The minimum number of gates required is$2$$3$$4$$5$
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15
GATE ECE 2007 | Question: 15
If the closed-loop transfer function of a control system is given as $T(s)=\dfrac{s-5}{(s+2)(s+3)},$ then it is an unstable system an uncontrollable system a minimum phase system a non-minimum phase system
If the closed-loop transfer function of a control system is given as $T(s)=\dfrac{s-5}{(s+2)(s+3)},$ then it isan unstable systeman uncontrollable systema minimum phase s...
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16
GATE ECE 2007 | Question: 16
If the Laplace transform of a signal $y(t)$ is $Y(s)=\dfrac{1}{s(s-1)},$ then its final value is $-1$ $0$ $1$ Unbounded
If the Laplace transform of a signal $y(t)$ is $Y(s)=\dfrac{1}{s(s-1)},$ then its final value is$-1$$0$$1$Unbounded
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17
GATE ECE 2007 | Question: 17
If $R(\tau)$ is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is $\text{NOT}$ true? $R(\tau)=R(-\tau)$ $|R(\tau)| \leq R(0)$ $R(\tau)=-R(-\tau)$ The mean square value of the process is $R(0)$
If $R(\tau)$ is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is $\text{NOT}$ true?$R(\tau)=R(-\tau)$$|R(\tau)...
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18
GATE ECE 2007 | Question: 18
If $S(f)$ is the power spectral density of a real, wide-sense stationary random process, then which of the following is $\text{ALWAYS}$ true? $S(0) \geq S(f)$ $S(f) \geq 0$ $S(-f)=-S(f)$ $\displaystyle{}\int_{-\infty}^{\infty} S(f) d f=0$
If $S(f)$ is the power spectral density of a real, wide-sense stationary random process, then which of the following is $\text{ALWAYS}$ true?$S(0) \geq S(f)$$S(f) \geq 0$...
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20
GATE ECE 2007 | Question: 20
If $\mathrm{C}$ is a closed curve enclosing a surface $S$, then the magnetic field intensity $\vec{H}$, the current density $\vec{J}$ and the electric flux density $\vec{D}$ ...
If $\mathrm{C}$ is a closed curve enclosing a surface $S$, then the magnetic field intensity $\vec{H}$, the current density $\vec{J}$ and the electric flux density $\vec{...
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21
GATE ECE 2007 | Question: 21
It is given that $X_{1}, X_{2}, \cdots ,X_{M}$ are $M$ non-zero, orthogonal vectors. The dimension of the vector space spanned by the $2 M$ vectors $X_{1}, X_{2}, \cdots, X_{M},-X_{1},-X_{2}, \cdots,-X_{M}$ is $2 M$ $M+1$ $M$ dependent on the choice of $X_{1}, X_{2}, \cdots, X_{M}$
It is given that $X_{1}, X_{2}, \cdots ,X_{M}$ are $M$ non-zero, orthogonal vectors. The dimension of the vector space spanned by the $2 M$ vectors $X_{1}, X_{2}, \cdots,...
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22
GATE ECE 2007 | Question: 22
Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is $18$ $10$ $-2.25$ indeterminate
Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is$18$$10$$-2.25$indeterminate
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24
GATE ECE 2007 | Question: 24
The solution of the differential equation $k^{2} \dfrac{d^{2} y}{d x^{2}}=y-y_{2}$ under the boundary conditions (i) $y=y_{1}$ at $x=0$ and (ii) $y=y_{2}$ at $x=\infty$, where $k, y_{1}$ and $y_{2}$ ... $y=\left(y_{1}-y_{2}\right) \sinh (x / k)+y_{1}$ $y=\left(y_{1}-y_{2}\right) \exp (-x / k)+y_{2}$
The solution of the differential equation $k^{2} \dfrac{d^{2} y}{d x^{2}}=y-y_{2}$ under the boundary conditions (i) $y=y_{1}$ at $x=0$ and (ii) $y=y_{2}$ at $x=\infty$, ...
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25
GATE ECE 2007 | Question: 25
The equation $x^{3}-x^{2}+4 x-4=0$ is to be solved using the Newton-Raphson method. If $x=2$ is taken as the initial approximation of the solution, then the next approximation using this method will be $\frac{2}{3}$ $\frac{4}{3}$ $1$ $\frac{3}{2}$
The equation $x^{3}-x^{2}+4 x-4=0$ is to be solved using the Newton-Raphson method. If $x=2$ is taken as the initial approximation of the solution, then the next approxim...
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27
GATE ECE 2007 | Question: 27
If the semi-circular contour $D$ of radius $2$ is as shown in the figure, then the value of the integral $\displaystyle{}\oint_{D} \dfrac{1}{\left(s^{2}-1\right)} d s$ is $j \pi$ $-j \pi$ $-\pi$ $\pi$
If the semi-circular contour $D$ of radius $2$ is as shown in the figure, then the value of the integral $\displaystyle{}\oint_{D} \dfrac{1}{\left(s^{2}-1\right)} d s$ is...
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28
GATE ECE 2007 | Question: 28
Two series resonant filters are as shown in the figure. Let the $\text{3-dB}$ bandwidth of Filter $1$ be $B_{1}$ and that of Filter $2$ be $B_{2}$. The value of $\dfrac{B_{1}}{B_{2}}$ is $4$ $1$ $\frac{1}{2}$ $\frac{1}{4}$
Two series resonant filters are as shown in the figure. Let the $\text{3-dB}$ bandwidth of Filter $1$ be $B_{1}$ and that of Filter $2$ be $B_{2}$. The value of $\dfrac{B...
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29
GATE ECE 2007 | Question: 29
For the circuit shown in the figure, the Thevenin voltage and resistance looking into $\mathrm{X}-\mathrm{Y}$ are $4 / 3 \mathrm{~V}, 2 \; \Omega$ $4 \mathrm{~V}, 2 / 3 \; \Omega$ $4 / 3 \mathrm{~V}, 2 / 3 \; \Omega$ $4 \mathrm{~V}, 2 \; \Omega$
For the circuit shown in the figure, the Thevenin voltage and resistance looking into $\mathrm{X}-\mathrm{Y}$ are$4 / 3 \mathrm{~V}, 2 \; \Omega$$4 \mathrm{~V}, 2 / 3 \; ...
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30
GATE ECE 2007 | Question: 30
In the circuit shown, $V_{C}$ is $0$ volts at $t=0 \; \mathrm{sec}$. For $t>0$, the capacitor current $i_{c}(t)$, where $t$ is in seconds, is given by $0.50 \exp (-25 t) \; \mathrm{mA}$ $0.25 \exp (-25 t) \; \mathrm{mA}$ $0.50 \exp (-12.5 t) \; \mathrm{mA}$ $0.25 \exp (-6.25 t) \; \mathrm{mA}$
In the circuit shown, $V_{C}$ is $0$ volts at $t=0 \; \mathrm{sec}$. For $t>0$, the capacitor current $i_{c}(t)$, where $t$ is in seconds, is given by$0.50 \exp (-25 t) \...
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31
GATE ECE 2007 | Question: 31
In the $\text{AC}$ network shown in the figure, the phasor voltage $\text{V}_{\text{AB}}$ (in Volts) is $0$ $5 \angle 30^{\circ}$ $12.5 \angle 30^{\circ}$ $17 \angle 30^{\circ}$
In the $\text{AC}$ network shown in the figure, the phasor voltage $\text{V}_{\text{AB}}$ (in Volts) is$0$$5 \angle 30^{\circ}$$12.5 \angle 30^{\circ}$$17 \angle 30^{\cir...
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33
GATE ECE 2007 | Question: 33
Group I lists four types of $p-n$ ... $\mathrm{P}-2, \mathrm{Q}-1, \mathrm{R}-2, \mathrm{S}-2$
Group I lists four types of $p-n$ junction diodes. Match each device in Group I with one of the options in Group II to indicate the bias condition of that device in its n...
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34
GATE ECE 2007 | Question: 34
The $\text{DC}$ current gain ($\beta$ ) of a $\text{BJT}$ is $50.$ Assuming that the emitter injection efficiency is $0.995$, the base transport factor is $0.980$ $0.985$ $0.990$ $0.995$
The $\text{DC}$ current gain ($\beta$ ) of a $\text{BJT}$ is $50.$ Assuming that the emitter injection efficiency is $0.995$, the base transport factor is$0.980$$0.985$$0...
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35
GATE ECE 2007 | Question: 35
Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II. ... $\text{P-3, Q-4, R-1, S-2}$ $\text{P-3, Q-2, R-1, S-4}$
Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II.$$\begin{array}{ll} \textbf{Group I} & \qqua...
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36
GATE ECE 2007 | Question: 36
For the $\text{Op-Amp}$ circuit shown in the figure, $V_{o}$ is $-2 \mathrm{~V}$ $-1 \mathrm{~V}$ $-0.5 \mathrm{~V}$ $0.5 \mathrm{~V}$
For the $\text{Op-Amp}$ circuit shown in the figure, $V_{o}$ is$-2 \mathrm{~V}$$-1 \mathrm{~V}$$-0.5 \mathrm{~V}$$0.5 \mathrm{~V}$
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37
GATE ECE 2007 | Question: 37
For the $\text{BJT}$ circuit shown, assume that the $\beta$ of the transistor is very large and $V_{B E}=0.7 \mathrm{~V}$. The mode of operation of the $\text{BJT}$ is cut-off saturation normal active reverse active
For the $\text{BJT}$ circuit shown, assume that the $\beta$ of the transistor is very large and $V_{B E}=0.7 \mathrm{~V}$. The mode of operation of the $\text{BJT}$ iscut...
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