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GATE ECE 1999 | Question 1.10
The logical expresion $y=\mathrm{A}+\overline{\mathrm{A}} \mathrm{B} $ is equivalent to$y=\mathrm{AB}$$y=\overline{\mathrm{A}} \mathrm{B}$$y=\bar{A}+\mathrm{B}$$y=\mathr...
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GATE ECE 1999 | Question 1.11
A Darlington emitter - follower circuit is sometimes used in the output stage of a $\text{TTL}$ gate in order toincrease its $\mathrm{I}_{\mathrm{OL}}$reduce its $\mathrm...
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GATE ECE 1999 | Question 1.12
Commercially available $\text{ECL}$ gears use two ground lines and one negative supply in order toreduce power dissipationincrease fan-outreduce loading effecteliminate t...
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GATE ECE 1999 | Question 1.13
The resolution of a $4$ - bit counting $\text{ADC}$ is $0.5$ volts. For an analog input of $6.6$ volts, the digital output of the $\text{ADC}$ will be$1011$$1101$$1100$$1...
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GATE ECE 1999 | Question 1.14
For a second-order system with the closed-loop transfer function\[T(s)=\frac{9}{s^{2}+4 s+9}\]the settling time for $2$ - percent band, in seconds, is$1.5$$2.0$$3.0$$4.0$...
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GATE ECE 1999 | Question 1.15
The gain margin (in $d \mathrm{B}$ ) of a system a having the loop transfer function\[\mathrm{G}(s) \mathrm{H}(s)=\frac{\sqrt{2}}{s(s+1)} \text { is }\]$0$$3$$6$$\infty$
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GATE ECE 1999 | Question 1.16
The system moded described by the state equations is\[\begin{array}{l}\mathrm{X}=\left[\begin{array}{cc}0 & 1 \\2 & -3\end{array}\right] x+\left[\begin{array}{l}0 \\1\end...
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GATE ECE 1999 | Question 1.17
The phase margin (in degrees) of a system having the loop transfer function\[\mathrm{G}(s) \mathrm{H}(s)=\frac{2 \sqrt{3}}{s(s+1)} \text { is }\]$45^{\circ}$$-30^{\circ}$...
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GATE ECE 1999 | Question 1.18
A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ isa real and even function of $\omega$a imaginary and o...
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GATE ECE 1999 | Question 1.19
The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this i...
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GATE ECE 1999 | Question 1.20
A modulated signal is given by,\[s(t)=m_{1}(t) \cos \left(2 \pi f_{c} t\right)+m_{2}(t) \sin \left(2 \pi f_{c} t\right)\]where the baseband signal $m_{1}(t)$ and $m_{2}(t...
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GATE ECE 1999 | Question 1.21
A modulated signal is given by\[s(t)=e^{-a t} \cos \left[\left(\omega_{c}+\Delta \omega\right) t\right] u(t),\]where $a, \omega_{c}$ and $\Delta \omega$ are positive cons...
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GATE ECE 1999 | Question 1.22
An electric field on a plane is described by its potential\[\mathrm{V}=20\left(r^{-1}+r^{-2}\right)\]where $r$ is the distance from the source. The field is due toa monop...
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GATE ECE 1999 | Question 1.23
Assuming perfect conductors of a transmission line, pure $\text{TEM}$ propagation is $\text{NOT}$ possible incoaxial cableair-filled cylindrical waveguideparallel twin-wi...
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GATE ECE 1999 | Question 1.24
Indicate which one of the following will $\text{NOT}$ exist in a rectangular resonant cavity.$\mathrm{TE}_{110}$$\mathrm{TE}_{011}$$\mathrm{TM}_{110}$$\mathrm{TM}_{111}$
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GATE ECE 1999 | Question 1.25
Identify which one of the following will $\text{NOT}$ satisfy the wave equation.$50 \; e^{f(\omega t-3 z)}$$\sin [\omega(10 z+5 t)]$$\cos \left(y^{2}+5 t\right)$$\sin (x)...
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GATE ECE 1999 | Question 2.1
The Fourier series representation of an impules train denoted by\[s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text { is given by }\]$\frac{1}{\mathrm{~T}...
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GATE ECE 1999 | Question 2.2
The Thevenin equivalent voltage $\mathrm{V}_{\mathrm{TH}}$ appearing between the terminals $A$ and $B$ of the network shown in the given figure is given by$j 16(3-j 4)$$j...
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GATE ECE 1999 | Question 2.3
The value of $R$ (in ohms) required for maximum power transfer in the network shown in the given figure$2$$4$$8$$16$
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GATE ECE 1999 | Question 2.4
A Delta-connected network with its Wye-equivalent is shown in the given figure is. The resistances $R_{1}, R_{2}$ and $R_{3}$ (in ohms) are respectively$1.5,3$ and $9$$3,...
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GATE ECE 1999 | Question 2.5
An $n$-channel $\text{JEFT}$ has $\mathrm{I}_{\mathrm{DSS}}=2 \mathrm{~mA}$ and $\mathrm{V}_{p}=-4 \mathrm{~V}$. Its transconductance $\mathrm{gm}$ (in milliohm) for an a...
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GATE ECE 1999 | Question 2.6
An $\text{npn}$ transistor (with $\mathrm{C}=0.3 \; \mathrm{pF}$ ) has a unity gain cutoff frequency $f_{\mathrm{T}}$ of $400 \; \mathrm{MHz}$ at a $\text{dc}$ bias curre...
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GATE ECE 1999 | Question 2.7
An amplifier has an open-loop gain of $100$, an input impedance of $1 \; \mathrm{k \Omega}$, and an output impedance of $100 \; \Omega$. A feedback network with a feedbac...
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GATE ECE 1999 | Question 2.8
A $\text{dc}$ power supply has a no-load voltage if $30 \mathrm{~V}$, and a full-load voltage of $25 \mathrm{~V}$ at a full - load current of $1 \mathrm{~A}$. Its output ...
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GATE ECE 1999 | Question 2.9
An amplifier is assumed to have a single-pole high-frequency transfer function. The rise time of its output response to a step function input is $35\;\text{nsec}$. The up...
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GATE ECE 1999 | Question 2.10
The minimized form of the logical expression $(\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+\bar{A} B C+A B \bar{C})$ is$\overline{\mathrm{A}} \overline{\mathrm{C}}+\mathrm{...
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GATE ECE 1999 | Question 2.11
For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical expressions for the outputs $\text{D}$ ( = $\text{A}$ minus $\text{B}...
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GATE ECE 1999 | Question 2.12
The ripple counter shown in the given figure is works as a$\bmod -3$ up counter$\bmod -5$ up counter$\bmod - 3$ down counter$\bmod - 5$ down counter
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GATE ECE 1999 | Question 2.13
If $\text{CS}=\text{A}_{15} \; \text{ A}_{14} \; \text{A}_{13}$ is used as the chip select logic of a $4 \; \text{K RAM}$ in an $8085$ system, then its memory range will ...
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GATE ECE 1999 | Question 2.14
If the closed-loop transfer function $T(s)$ of a unity negative feedback system is given by\[\mathrm{T}(\mathrm{s})=\frac{a_{n -1} \mathrm{~s}+a_{n}}{\mathrm{~s}^{n}+n_{1...
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GATE ECE 1999 | Question 2.15
Consider the points $s_{1}=-3+j 4$ and $s_{2}=-3-j 2$ in the $s$-plane. Then, for a system with the open-loop Transfer function\[G(s) H(s)=\frac{K}{(s+1)^{4}}\]$s_{1}$ is...
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GATE ECE 1999 | Question 2.16
For the system described by the state equation\[x=\left[\begin{array}{ccc}0 & 1 & 0 \\0 & 0 & 1 \\0.5 & 1 & 2\end{array}\right] x+\left[\begin{array}{l}0 \\0 \\1\end{arra...
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GATE ECE 1999 | Question 2.17
The $z$-transform of a signal is given by\[C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}}\]Its final value is$1 / 4$zero$1.0$infinity
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GATE ECE 1999 | Question 2.18
The Nyquist sampling frequency (in $\mathrm{Hz}$ ) of a signal given by$6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)$ is$200$$300$$500$$1000$
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GATE ECE 1999 | Question 2.19
The peak-to-peak input to an $8$-bit $\text{PCM}$ coder is $2$ volts. The signal power-to-quantization noise power ratio (in $d\text{B}$) for an input of $0.5 \cos \left(...
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GATE ECE 1999 | Question 2.20
The input to a matched filter is given by$s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} ...
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GATE ECE 1999 | Question 2.21
Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samp...
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GATE ECE 1999 | Question 2.22
In a twin-wire transmission line in air, the adjacent voltage maxima are at $12.5 \mathrm{~cm}$ and $27.5 \mathrm{~cm}$. The operating frequency is$300 \; \mathrm{MHz}$$1...
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GATE ECE 1999 | Question 2.23
A trasmitting antenna radiates $251 \mathrm{~W}$ isotropically. A receiving antenna, located $100 \mathrm{~m}$ away from the transmitting antenna, has an effective apertu...
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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 operate...
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