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281
GATE ECE 2006 | Question: 18
In the system shown below, $x(t)=(\sin t) u(t)$. In steady-steady-state, the response $y(t)$ will be $\frac{1}{\sqrt{2}} \sin \left(t-\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} \sin \left(t+\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} e^{-t} \sin t$ $\sin t-\cos t$
In the system shown below, $x(t)=(\sin t) u(t)$. In steady-steady-state, the response $y(t)$ will be$\frac{1}{\sqrt{2}} \sin \left(t-\frac{\pi}{4}\right)$$\frac{1}{\sqrt{...
1 votes
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283
GATE ECE 2006 | Question: 20
A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is $10$ Watts $1$ Watt $0.1$ Watt $0.01$ Watt
A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total...
1 votes
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284
GATE ECE 2006 | Question: 21
The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ ... $\left[\begin{array}{ll}4 & 8 \\ 8 & 4\end{array}\right]$
The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ matrix are given by$$\begin{array}{cc} \textbf{Eigenvalue}& \textbf{Eigenvector} \\ \lambda_1=8 & \t...
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285
GATE ECE 2006 | Question: 22
For the function of a complex variable $\text{W}=\ln \text{Z}\; ($where, $\mathrm{W}=u+j \mathrm{v}$ and $\mathrm{Z}=x+j y),$ the $u=$ constant lines get mapped in $\text{Z}$-plane as set of radial straight lines set of concentric circles set of confocal hyperbolas set of confocal ellipses
For the function of a complex variable $\text{W}=\ln \text{Z}\; ($where, $\mathrm{W}=u+j \mathrm{v}$ and $\mathrm{Z}=x+j y),$ the $u=$ constant lines get mapped in $\text...
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286
GATE ECE 2006 | Question: 23
The value of the contour integral $\displaystyle{}\oint_{\mid z-j \mid =2} \;\frac{1}{z^2+4} d z$ in positive sense is $\frac{j \pi}{2}$ $-\frac{\pi}{2}$ $-\frac{j \pi}{2}$ $\frac{\pi}{2}$
The value of the contour integral $\displaystyle{}\oint_{\mid z-j \mid =2} \;\frac{1}{z^2+4} d z$ in positive sense is$\frac{j \pi}{2}$$-\frac{\pi}{2}$$-\frac{j \pi}{2}$$...
1 votes
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287
GATE ECE 2006 | Question: 24
The integral $\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta$ is given by $\frac{1}{2}$ $\frac{2}{3}$ $\frac{4}{3}$ $\frac{8}{3}$
The integral $\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta$ is given by$\frac{1}{2}$$\frac{2}{3}$$\frac{4}{3}$$\frac{8}{3}$
1 votes
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288
GATE ECE 2006 | Question: 25
Three companies $\text{X, Y}$ and $\text{Z}$ ... computer is defective, the probability that it was supplied by $\text{Y}$ is $0.1$ $0.2$ $0.3$ $0.4$
Three companies $\text{X, Y}$ and $\text{Z}$ supply computers to a university. The percentage of computers supplied by them and the probability of those being defective a...
1 votes
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289
GATE ECE 2006 | Question: 26
For the matrix $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right]$, the eigen value corresponding to the eigenvector $\left[\begin{array}{l}101 \\ 101\end{array}\right]$ is $2$ $4$ $6$ $8$
For the matrix $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right]$, the eigen value corresponding to the eigenvector $\left[\begin{array}{l}101 \\ 101\end{array}\ri...
1 votes
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290
GATE ECE 2006 | Question: 27
For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are $y=0$ for $x=0$, and $y=0$ for $x=a$ The form of non-zero solutions of $y$ (where $m$ ... $y=\displaystyle{}\sum_m\;\mathrm{~A}_{m} \;e^{-\frac{m \pi x}{a}}$
For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are$y=0$ for $x=0$, and$y=0$ for $x=a$The form of non-zero solutions of $y$ (where $...
1 votes
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291
GATE ECE 2006 | Question: 28
Consider the function $f(t)$ having Laplace transform $ \text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0 $ The final value of $f(t)$ would be $0$ $1$ $-1 \leq f(\infty) \leq 1$ $\infty$
Consider the function $f(t)$ having Laplace transform $$ \text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0 $$ The final value of $f(t)$ would be$0$$1$$-1...
1 votes
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292
GATE ECE 2006 | Question: 29
As $x$ is increased from $-\infty$ to $\infty$, the function $ f(x)=\frac{e^x}{1+e^x} $ monotonically increases monotonically decreases increases to a maximum value and then decreases decreases to a minimum value and then increases
As $x$ is increased from $-\infty$ to $\infty$, the function $$ f(x)=\frac{e^x}{1+e^x} $$monotonically increasesmonotonically decreasesincreases to a maximum value and th...
1 votes
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293
GATE ECE 2006 | Question: 30
A two-port network is represented by $\text{ABCD}$ ... $\frac{\mathrm{B}+\mathrm{AR}_{\mathrm{L}}}{\mathrm{D}+\mathrm{CR}_{\mathrm{L}}}$
A two-port network is represented by $\text{ABCD}$ parameters given by$$ \left[\begin{array}{c} \mathrm{V}_1 \\ \mathrm{I}_1 \end{array}\right]=\left[\begin{array}{ll} \m...
1 votes
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294
GATE ECE 2006 | Question: 31
In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively $r_e$ and $\beta r_o$ $0$ and $-\beta r_o$ $0,$ and $\beta r_o$ $r_e$ and $-\beta r_o$
In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively$r_e$ and $\beta r_o$$0$ and $-\beta r_o$$0,$ and $\beta r_o$$r_e$ and $-\beta r...
1 votes
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296
GATE ECE 2006 | Question: 33
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is $0.5 \mathrm{~A}$ $2.0 \mathrm{~A}$ $1.0 \mathrm{~A}$ $0.0 \mathrm{~A}$
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is$0...
1 votes
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297
GATE ECE 2006 | Question: 34
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by $8 e^{-0.004 t}$ Volts $8\left(1-e^{-0.004 t}\right)$ Volts $8 u(t)$ Volts $8$ Volts
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by$8 e^{-0.004 t}$ Volts$8\le...
1 votes
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299
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]$$E^2[X]$
1 votes
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300
GATE ECE 2007 | Question: 2
The following plot shows a function $y$ which varies linearly with $x$. The value of the integral $I=\displaystyle{}\int_1^2 y d x$ is $1.0$ $2.5$ $4.0$ $5.0$
The following plot shows a function $y$ which varies linearly with $x$. The value of the integral $I=\displaystyle{}\int_1^2 y d x$ is$1.0$$2.5$$4.0$$5.0$
1 votes
0 answers
301
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}$$\frac{1}{x^2}$
1 votes
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302
GATE ECE 2007 | Question: 4
$\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}$ is $0.5$ $1$ $2$ not defined
$\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}$ is$0.5$$1$$2$not defined
1 votes
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303
GATE ECE 2007 | Question: 5
Which one of the following functions is strictly bounded? $\frac{1}{x^2}$ $e^x$ $x^2$ $e^{-x^2}$
Which one of the following functions is strictly bounded?$\frac{1}{x^2}$$e^x$$x^2$$e^{-x^2}$
1 votes
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304
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}$
1 votes
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306
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
1 votes
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308
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...
1 votes
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309
GATE ECE 2007 | Question: 11
The correct full wave rectifier circuit is
The correct full wave rectifier circuit is
1 votes
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310
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...
1 votes
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311
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...
1 votes
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312
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$
1 votes
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313
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...
1 votes
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314
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
1 votes
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315
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)$$|R(\tau)...
1 votes
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316
GATE ECE 2007 | Question: 18
If $S(f)$ is the power spectral density of a real, wide-sense stationary random process, then which of the following is $\text{ALWAYS}$ true? $S(0) \geq S(f)$ $S(f) \geq 0$ $S(-f)=-S(f)$ $\displaystyle{}\int_{-\infty}^{\infty} S(f) d f=0$
If $S(f)$ is the power spectral density of a real, wide-sense stationary random process, then which of the following is $\text{ALWAYS}$ true?$S(0) \geq S(f)$$S(f) \geq 0$...
1 votes
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318
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,...
1 votes
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319
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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