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1641
GATE ECE 2006 | Question: 59
A linear system is described by the following state equation $X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc} 0 & 1 \\ -1 & 0\end{array}\right]$ ... $\left[\begin{array}{cc}\cos t & -\sin t \\ \cos t & \sin t\end{array}\right]$
A linear system is described by the following state equation$$X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$$The...
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1642
GATE ECE 2007 | Question: 55
A unity feedback control system has an open-loop transfer function $G(s)=\dfrac{K}{s\left(s^{2}+7 s+12\right)}$. The gain $K$ for which $s=-1+j 1$ will lie on the root locus of this system is $4$ $5.5$ $6.5$ $10$
A unity feedback control system has an open-loop transfer function $G(s)=\dfrac{K}{s\left(s^{2}+7 s+12\right)}$. The gain $K$ for which $s=-1+j 1$ will lie on the root lo...
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1644
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}$$45 \mathr...
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1645
GATE ECE 2008 | Question: 70
The signal $\cos \omega_{c} t+0.5 \cos \omega_{m} t \sin \omega_{c} t$ is $\mathrm{FM}$ only $\mathrm{AM}$ only both $\mathrm{AM}$ and $\mathrm{FM}$ neither $\mathrm{AM}$ nor $\mathrm{FM}$
The signal $\cos \omega_{c} t+0.5 \cos \omega_{m} t \sin \omega_{c} t$ is$\mathrm{FM}$ only$\mathrm{AM}$ onlyboth $\mathrm{AM}$ and $\mathrm{FM}$neither $\mathrm{AM}$ nor...
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1647
GATE ECE 2008 | Question: 80
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large. The value of DC current $I_{E}$ is $1 \mathrm{~mA}$ $2 \mathrm{~mA}$ $5 \mathrm{~mA}$ $10 \mathrm{~mA}$
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large.The value of DC curre...
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1648
GATE ECE 1993 | Question 6.10
The bandwidth of an $n$-stage tuned amplifier, with each stage having a band width of $B$, is given by $\mathrm{B} / n$ $\mathrm{B} / \sqrt{n}$ $\mathrm{B} \sqrt{2^{1 / n}-1}$ $\mathrm{B} / \sqrt{2^{1 / n}-1}$
The bandwidth of an $n$-stage tuned amplifier, with each stage having a band width of $B$, is given by$\mathrm{B} / n$$\mathrm{B} / \sqrt{n}$$\mathrm{B} \sqrt{2^{1 / n}-1...
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1649
GATE ECE 2010 | Question: 4
For the two-port network shown below, the short-circuit admittance parameter matrix is $\left[\begin{array}{cc}4 & -2 \\ -2 & 4\end{array}\right] \mathrm{S}$ $\left[\begin{array}{cc}1 & -0.5 \\ -0.5 & 1\end{array}\right] \text{S}$ ... $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right] \text{S}$
For the two-port network shown below, the short-circuit admittance parameter matrix is$\left[\begin{array}{cc}4 & -2 \\ -2 & 4\end{array}\right] \mathrm{S}$$\left[\begin{...
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1651
GATE ECE 2011 | Question: 48
The channel resistance of an $\text{N}$-channel $\text{JFET}$ shown in the figure below is $600 \; \Omega$ when the full channel thickness $\left(\mathrm{t}_{\mathrm{ch}}\right)$ of $10 \; \mu \mathrm{m}$ ... $480 \; \Omega$ $600 \; \Omega$ $750 \; \Omega$ $1000 \; \Omega$
The channel resistance of an $\text{N}$-channel $\text{JFET}$ shown in the figure below is $600 \; \Omega$ when the full channel thickness $\left(\mathrm{t}_{\mathrm{ch}}...
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1653
GATE ECE 1999 | Question 2.20
The input to a matched filter is given by $s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} \mathrm{sec} \\ & \text{otherwise} \end{array}$ The peak amplitude of the filter output is $10$ volts $5$ volts $10$ millivolts $5$ millivolts
The input to a matched filter is given by$s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} ...
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1654
GATE ECE 1999 | Question 14
The loop transfer function of a feedback control system is given by \[\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(s+1)}{s\left(1+\mathrm{T}_{S}\right)(1+2 s)}, \mathrm{K}>0\] Using Routh - Hurwitz criterion, determine the region of $\mathrm{K}-\mathrm{T}$ plane in which the closed - loop system is stable.
The loop transfer function of a feedback control system is given by\[\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(s+1)}{s\left(1+\mathrm{T}_{S}\right)(1+2 s)}, \mathrm{K}...
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1655
GATE ECE 2001 | Question: 20
A system of three electric charges lying in a straight line is in equilibrium. Two of the charges are positive with magnitudes $Q$ and $2 Q$, and are $50 \mathrm{~cm}$ apart. Determine the sign, magnitude and position of the third charge.
A system of three electric charges lying in a straight line is in equilibrium. Two of the charges are positive with magnitudes $Q$ and $2 Q$, and are $50 \mathrm{~cm}$ ap...
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1656
GATE ECE 1998 | Question 2.30
All transmission line sections shown in the figure is have a characteristic impedance $\text{R}_{0}+\text{j}_{0}$. The input impedance $\text{Z}_{\text {in}}$ equals $\frac{2}{3} \text{R}_{0}$ $\mathrm{R}_{0}$ $\frac{3}{2} \text{R}_{0}$ $2 \mathrm{R}_{\mathrm{0}}$
All transmission line sections shown in the figure is have a characteristic impedance $\text{R}_{0}+\text{j}_{0}$. The input impedance $\text{Z}_{\text {in}}$ equals$\fra...
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1657
GATE ECE 1998 | Question 2.40
The far field of an antenna varies with distance $\mathrm{r}$ as $\frac{1}{r}$ $\frac{1}{r^{2}}$ $\frac{1}{r^{3}}$ $\frac{1}{\sqrt{r}}$
The far field of an antenna varies with distance $\mathrm{r}$ as$\frac{1}{r}$$\frac{1}{r^{2}}$$\frac{1}{r^{3}}$$\frac{1}{\sqrt{r}}$
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1658
GATE ECE 2003 | Question: 50
If the $\text{op-amp}$ in the figure is idea, the output voltage Voult will be equal to $1 \mathrm{~V}$ $6 \mathrm{~V}$ $14 \mathrm{~V}$ $17 \mathrm{~V}$
If the $\text{op-amp}$ in the figure is idea, the output voltage Voult will be equal to$1 \mathrm{~V}$$6 \mathrm{~V}$$14 \mathrm{~V}$$17 \mathrm{~V}$
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1660
GATE ECE 2003 | Question: 77
Choose the correct one from among the alternative $\text{A, B, C. D}$ after matching an item in Group $1$ with the most appropriate item in Group $2.$ ... $\text{P - 6 Q - 1 R - 3 S - 2}$ $\text{P - 5 Q - 6 R - 1 S - 3}$
Choose the correct one from among the alternative $\text{A, B, C. D}$ after matching an item in Group $1$ with the most appropriate item in Group $2.$$\begin{array}{ll}\q...
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1663
GATE ECE 2006 | Question: 49
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be $\overline{\mathrm{AB} \overline{\mathrm{C}}}$ $\overline{\mathrm{A}}$ $\mathrm{AB} \overline{\mathrm{C}}$ $\mathrm{A}$
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be$\overline{\mathrm{AB} \overline{\mathrm{C}}}$$\overline{\mathrm{A}}$$\mathrm{AB} \ove...
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1665
GATE ECE 2007 | Question: 71
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of $1 \times 10^{-4} \mathrm{~cm}^{2}$ ... is $50 \; \mathrm{~nm}$ $143 \; \mathrm{~nm}$ $350 \; \mathrm{~nm}$ $1 \; \mu \mathrm{m}$
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of ...
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1666
GATE ECE 2008 | Question: 54
The logic function implemented by the following circuit at the terminal $\text{OUT}$ is $\text{P NOR Q}$ $\text{P NAND Q}$ $\text{P OR Q}$ $\text{P AND Q}$
The logic function implemented by the following circuit at the terminal $\text{OUT}$ is$\text{P NOR Q}$$\text{P NAND Q}$$\text{P OR Q}$$\text{P AND Q}$
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1668
GATE ECE 2008 | Question: 57
Which of the following Boolean Expressions correctly represents the relation between $\text{P, Q, R}$ and $\mathrm{M}_{1}?$ $\text{M}_{1} = \text{(P OR Q) XOR R}$ $\text{M}_{1} = \text{(P AND Q) XOR R}$ $\text{M}_{1} = \text{(P NOR Q) XOR R}$ $\text{M}_{1} = \text{(P XOR Q) XOR R}$
Which of the following Boolean Expressions correctly represents the relation between $\text{P, Q, R}$ and $\mathrm{M}_{1}?$ $\text{M}_{1} = \text{(P OR Q) XOR R}$$\text{M...
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1671
GATE ECE 2009 | Question: 42
The $4$-point Discrete Fourier Transform (DFT) of a discrete time sequence $\{1,0,2,3\}$ is $[0,-2+2 j, 2,-2-2 j]$ $[2,2+2 \mathrm{j}, 6,2-2 \mathrm{j}]$ $[6,1-3 \mathrm{j}, 2,1+3 \mathrm{j}]$ $[6,-1+3 \mathrm{j}, 0,-1-3 \mathrm{j}]$
The $4$-point Discrete Fourier Transform (DFT) of a discrete time sequence $\{1,0,2,3\}$ is$[0,-2+2 j, 2,-2-2 j]$$[2,2+2 \mathrm{j}, 6,2-2 \mathrm{j}]$$[6,1-3 \mathrm{j},...
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1674
GATE ECE 1997 | Question 5.4
(1) Wave tilt Under-water propagation (2) Faraday Rotation Ground wave propagation Space wave propagation Ionospheric propagation
(1) Wave tiltUnder-water propagation(2) Faraday RotationGround wave propagationSpace wave propagationIonospheric propagation
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1675
GATE ECE 1997 | Question 26
Find the mean of a function $X(T)=\sin ^{2}(\alpha T)$, where $\alpha$ is a constant, and $T$ is a random variable. The $p d f$ of $\mathrm{T}$ is given by, \[ \begin{aligned} f(T) &=e^{-T} \text { for } T \geq 0 \\ &=0 \text { for } T<0 \end{aligned} \]
Find the mean of a function $X(T)=\sin ^{2}(\alpha T)$, where $\alpha$ is a constant, and $T$ is a random variable. The $p d f$ of $\mathrm{T}$ is given by,\[\begin{align...
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1677
GATE ECE 1999 | Question 2.24
In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operated at $25 \; \mathrm{MHz}$. Its electrical path length is $0.5$ meters $\lambda$ meters $\pi / 2$ radians $180$ degrees
In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operate...
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1678
GATE ECE 1998 | Question 2.7
Two $2^{\prime}$ 's complement number having sign bits $x$ and $y$ are added and the sign bit of the result is $z$. Then, the occurrence of overflow is indicated by the Boolean function $x y z$ $\bar{x} \bar{y} \bar{z}$ $\bar{x} \bar{y} z+x y \bar{z}$ $x y+y z+z x$
Two $2^{\prime}$ 's complement number having sign bits $x$ and $y$ are added and the sign bit of the result is $z$. Then, the occurrence of overflow is indicated by the B...
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1680
GATE ECE 1998 | Question 16
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}}=0.2 \mathrm{~V}, \beta=100$ and $V_{BE(\text {sat})}=0.7 \mathrm{~V}$. The $\alpha$ of $Q_{1}$ in its inverse active mode is $0.01$.
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}...
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