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1482
GATE ECE 2008 | Question: 61
A rectangular waveguide of internal dimensions ( $\mathrm{a}=4 \mathrm{~cm}$ and $\mathrm{b}=3 \mathrm{~cm}$ ) is to be operated in $\mathrm{TE}_{11}$ mode. The minimum operating frequency is $6.25 \mathrm{~GHz}$ $6.0 \mathrm{~GHz}$ $5.0 \mathrm{~GHz}$ $3.75 \mathrm{~GHz}$
A rectangular waveguide of internal dimensions ( $\mathrm{a}=4 \mathrm{~cm}$ and $\mathrm{b}=3 \mathrm{~cm}$ ) is to be operated in $\mathrm{TE}_{11}$ mode. The minimum o...
1 votes
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1483
GATE ECE 2008 | Question: 62
One end of a loss-less transmission line having the characteristic impedance of $75 \; \Omega$ and length of $1 \mathrm{~cm}$ is short-circuited. At $3 \; \mathrm{GHz}$, the input impedance at the other end of the transmission line is $0$ Resistive Capacitive Inductive
One end of a loss-less transmission line having the characteristic impedance of $75 \; \Omega$ and length of $1 \mathrm{~cm}$ is short-circuited. At $3 \; \mathrm{GHz}$, ...
1 votes
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1484
GATE ECE 2008 | Question: 63
A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $\varepsilon_{r}=9$ ). The magnitude of the reflection coefficient is $0$ $0.3$ $0.5$ $0.8$
A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $\varepsilon_{r}=9$ ). The magnitude of the reflec...
1 votes
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1486
GATE ECE 2008 | Question: 65
At $20 \; \mathrm{GHz}$, the gain of a parabolic dish antenna of $1$ meter diameter and $70 \%$ efficiency is $15 \mathrm{~dB}$ $25 \mathrm{~dB}$ $35 \mathrm{~dB}$ $45 \mathrm{~dB}$
At $20 \; \mathrm{GHz}$, the gain of a parabolic dish antenna of $1$ meter diameter and $70 \%$ efficiency is$15 \mathrm{~dB}$$25 \mathrm{~dB}$$35 \mathrm{~dB}$$45 \mathr...
1 votes
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1487
GATE ECE 2008 | Question: 66
Noise with double-sided power spectral density of $\mathrm{K}$ over all frequencies is passed through a $\text{RC}$ low pass filter with $3 \mathrm{~dB}$ cut-off frequency of $f_{c}$. The noise power at the filter output is $\mathrm{K}$ $\mathrm{K} f_{c}$ $\mathrm{K} \pi f_{c}$ $\infty$
Noise with double-sided power spectral density of $\mathrm{K}$ over all frequencies is passed through a $\text{RC}$ low pass filter with $3 \mathrm{~dB}$ cut-off frequenc...
1 votes
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1489
GATE ECE 2008 | Question: 68
Four messages band limited to $\text{W, W, 2W}$ and $\text{3W}$ respectively are to be multiplexed using $\text{Time Division Multiplexing (TDM)}.$ The minimum bandwidth required for transmission of this $\text{TDM}$ signal is $\mathrm{W}$ $3 \mathrm{W}$ $6 \mathrm{W}$ $7 \mathrm{W}$
Four messages band limited to $\text{W, W, 2W}$ and $\text{3W}$ respectively are to be multiplexed using $\text{Time Division Multiplexing (TDM)}.$ The minimum bandwidth ...
1 votes
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1490
GATE ECE 2008 | Question: 69
Consider the frequency modulated signal $10 \cos \left[2 \pi \times 10^{5} t+5 \sin (2 \pi \times 1500 t)+7.5 \sin (2 \pi \times 1000 t)\right]$ with carrier frequency of $10^{5} \mathrm{~Hz}$. The modulation index is $12.5$ $10$ $7.5$ $5$
Consider the frequency modulated signal $10 \cos \left[2 \pi \times 10^{5} t+5 \sin (2 \pi \times 1500 t)+7.5 \sin (2 \pi \times 1000 t)\right]$ with carrier frequency of...
1 votes
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1491
GATE ECE 2008 | Question: 70
The signal $\cos \omega_{c} t+0.5 \cos \omega_{m} t \sin \omega_{c} t$ is $\mathrm{FM}$ only $\mathrm{AM}$ only both $\mathrm{AM}$ and $\mathrm{FM}$ neither $\mathrm{AM}$ nor $\mathrm{FM}$
The signal $\cos \omega_{c} t+0.5 \cos \omega_{m} t \sin \omega_{c} t$ is$\mathrm{FM}$ only$\mathrm{AM}$ onlyboth $\mathrm{AM}$ and $\mathrm{FM}$neither $\mathrm{AM}$ nor...
1 votes
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1499
GATE ECE 2008 | Question: 78
In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$. The samples $x(n) \quad(n=0,1,2, \cdots \cdots)$ are given by $5\left(1-e^{-0.05 n}\right)$ $5 e^{-0.05 n}$ $5\left(1-e^{-5 n}\right)$ $5 e^{-5 n}$
In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The samples $x(n) \quad(n=0,1,2,...
1 votes
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1501
GATE ECE 2008 | Question: 80
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large. The value of DC current $I_{E}$ is $1 \mathrm{~mA}$ $2 \mathrm{~mA}$ $5 \mathrm{~mA}$ $10 \mathrm{~mA}$
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large.The value of DC curre...
1 votes
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1502
GATE ECE 2008 | Question: 81
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large. The mid-band voltage gain of the amplifier is approximately $-180$ $-120$ $-90$ $-60$
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large.The mid-band voltage ...
1 votes
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1503
GATE ECE 2008 | Question: 82
In the following circuit, the comparator output is logic $\text{ 1 }$ if $\mathrm{V}_{1}>\mathrm{V}_{2}$ and is logic $\text{ 0 }$ ... ) are the counter outputs. The counter starts from the clear state. The stable reading of the LED displays is $06$ $07$ $12$ $13$
In the following circuit, the comparator output is logic $\text{“1”}$ if $\mathrm{V}_{1}>\mathrm{V}_{2}$ and is logic $\text{“0”}$ otherwise. The D/A conversion i...
0 votes
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1507
GATE ECE 1993 | Question 1.1
The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are) $(0,0, \alpha)$ $(\alpha, 0,0)$ $(0,0,1)$ $(0, \alpha, 0)$
The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are)$(0,0, \alpha)$$(\alpha, 0,0)$$(0,0,1)...
0 votes
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1508
GATE ECE 1993 | Question 1.2
The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, is linear non-linear homogeneous of degree two
The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, islinearnon-linearhomogeneousof degree two
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1509
GATE ECE 1993 | Question 1.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$
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1510
GATE ECE 1993 | Question 1.4
Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)? $\mathrm{DO} \; 131=1$ $\mathrm{A}=\mathrm{DIM}^{* * *} 7$ $\text{READ}$ $=15.0$ $\text{GOTO}$ $3=10$
Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)?$\mathrm{DO} \; 131=1$$\mathrm{A}=\mathrm{DIM}^{* * *} 7$$\text{READ}$ $=15.0$$\text{GOTO}$ $3=10$
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1511
GATE ECE 1993 | Question 1.5
Fourier series of the periodic function (period $2 \pi$ ) defined by $f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ ... $\frac{\pi^2}{4}$ $\frac{\pi^2}{6}$ $\frac{\pi^2}{8}$ $\frac{\pi^2}{12}$
Fourier series of the periodic function (period $2 \pi$ ) defined by$f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ is$\frac{\pi}{4}+\sum_1...
0 votes
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1512
GATE ECE 1993 | Question 1.6
Which of the following improper integrals is (are) convergent? $\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$ $\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$ $\int_{0}^{x} \frac{x}{1+x^{2}} d x$ $\int_{0}^{1} \frac{1-\cos x}{x^{5 / 2}} d x$
Which of the following improper integrals is (are) convergent?$\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$$\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$$\int_{0}^...
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1513
GATE ECE 1993 | Question 1.7
The function $f(x, y)=x^{2} y-3 x y+2 y+x$, has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and one local maximum
The function $f(x, y)=x^{2} y-3 x y+2 y+x$, hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum and one loca...
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1514
GATE ECE 1993 | Question 2.1
$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is
$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is
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1515
GATE ECE 1993 | Question 2.2
The radius of convergence of the power series $\sum_{0}^{\infty} \frac{(3 m) !}{(m !)^{3}} x^{3m}$ is ___________.
The radius of convergence of the power series$\sum_{0}^{\infty} \frac{(3 m) !}{(m !)^{3}} x^{3m}$ is ___________.
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1516
GATE ECE 1993 | Question 2.3
If the linear velocity $\overrightarrow{\mathrm{V}}$ is given by $\overrightarrow{\mathrm{V}}=x^{2} y \hat{i}+$ $x y z \hat{j}-y z^{2} k$ the anguarl velocity $\vec{w}$ at the point $(1,1,-1)$ is __________.
If the linear velocity $\overrightarrow{\mathrm{V}}$ is given by $\overrightarrow{\mathrm{V}}=x^{2} y \hat{i}+$ $x y z \hat{j}-y z^{2} k$ the anguarl velocity $\vec{w}$ a...
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1517
GATE ECE 1993 | Question 2.4
Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the second order Runge-Kutta method with step size $h=0.1$ is _________.
Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the sec...
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1518
GATE ECE 1993 | Question 2.5
For $\mathrm{X}=4.0$, the value of $1$ in the $\text{FORTRAN}$ $77$ statement $I=-2^{* *} 2+5.0 ^* X / X ^* 3+\frac{3}{4} \text { is}$___________.
For $\mathrm{X}=4.0$, the value of $1$ in the $\text{FORTRAN}$ $77$ statement$I=-2^{* *} 2+5.0 ^* X / X ^* 3+\frac{3}{4} \text { is}$___________.
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1519
GATE ECE 1993 | Question 2.6
The value of the double integral $\int_{0}^{1} \int_{x}^{1 / x} \frac{x}{1+y^{2}}$ $d x d y$ is
The value of the double integral $\int_{0}^{1} \int_{x}^{1 / x} \frac{x}{1+y^{2}}$ $d x d y$ is
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1520
GATE ECE 1993 | Question 2.7
If $\mathrm{A}=\left(\begin{array}{cccc}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i\end{array}\right)$ the matrix $\mathrm{A}^{4}$, calculated by the use of Cayley - Hamilton theorem or otherwise, is
If $\mathrm{A}=\left(\begin{array}{cccc}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i\end{array}\right)$the matrix $\mathrm{A}^{4}$, calculated by t...
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