Recent questions tagged gate1991-ec

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1

GATE ECE 1991 | Question 1.1
An excitation is applied to a system at $\mathrm{t}=\mathrm{T}$ and its response is zero for $-\infty<t<T$. Such a system is non-causal system stable system causal system unstable system

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GATE ECE 1991 | Question 1.2
In a series RLC high $Q$ circuit, the current peaks at a frequency equal to the resonant frequency greater than the resonant frequency less than the resonant frequency none of the above

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GATE ECE 1991 | Question 1.3
The voltage across an impedance in a network is $V(s)=z(s) I(s)$, where $V(s)$, $Z(s)$ are the Laplace transforms of the corresponding time function $v(t), z(t)$ and $i(t)$. The voltage $v(t)$ is: $v(t)=z(t) \cdot v(t)$ $v(t)=\int_0^1 i(t) \cdot z(t-\tau) d \tau$ $v(t)=\int_0^1 i(t) \cdot z(t+\tau) d \tau$ $v(t)=z(t)+i(t)$

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GATE ECE 1991 | Question 1.4
Two two-port networks are connected in cascade. The combination is to be represented as a single two-port network. The parameters of the network are obtained by multiplying the individual $z$-parameter matrix $h$-parameter matrix $y$-parameter matrix $\text{ABCD}$ parameter matrix

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GATE ECE 1991 | Question 1.5
The pole-zero pattern of a certain filter is shown in the figure below. The filter must be of the following type. low pass high pass all pass band pass

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GATE ECE 1991 | Question 1.6
The necessary and sufficient condition for a rational function of $\mathrm{s}$. $\mathrm{T}(\mathrm{s})$ to be driving point impedance of an $\text{RC}$ network is that all poles and zeros should be simple and lie on the negative axis in the $s$-plane ... $s$-plane simple and lie on the positive real axis of the $s$-plane

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7

GATE ECE 1991 | Question 1.7
In the signal flow graph of Figure, the gain $c / r$ will be $\frac{11}{9}$ $\frac{22}{15}$ $\frac{24}{23}$ $\frac{44}{23}$

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GATE ECE 1991 | Question 1.8
A second order system has a transfer function given by $ G(s)=\frac{25}{s^2+8 s+25} $ If the system, initially at rest is subjected to a unit step input at $\mathrm{t}=0$, the second peak in response will occur at $\pi \mathrm{sec}$ $\frac{\pi}{3}$ sec $\frac{2 \pi}{3} \sec$ $\frac{\pi}{2}$ sec

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GATE ECE 1991 | Question 1.9
The open loop transfer function of a feedback control system is: $ G(s) H(s)=\frac{1}{(s+1)^3} $ The gain margin of the system is: $2$ $4$ $8$ $16$

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GATE ECE 1991 | Question 1.10
A unity feedback control system has the open loop transfer function $ G(s)=\frac{4(1+2 s)}{s^2(s+2)} $ If the input to the system is a unit ramp, the steady state error will be $0$ $0.5$ $2$ $\textsf{infinity}$

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GATE ECE 1991 | Question 1.11
The characteristic equation of a feedback control system is given by $ s^3+5 s^2+(K+6) s+K=0 $ Where $K>0$ is a scalar variable parameter. In the root loci diagram of the system the asymptotes of the root locus for large values of $\mathrm{K}$ meet at a point in the $s$-plane whose coordinates are $(-3,0)$ $(-2,0)$ $(-1,0)$ $(2,0)$

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12

GATE ECE 1991 | Question 1.12
A linear second order single input continuous time system is described by the following set of differential equations ... and $u(t)$ is the control variable. The system is: controllable and stable controllable but unstable uncontrollable and unstable uncontrollable and stable

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GATE ECE 1991 | Question 1.13
A linear time-invariant discrete-time system is described by the vector matrix difference equation $ x(k+1)=F \underline{X}(k)+G \underline{u}(k) $ Where $\underline{X}(k)$ is the state vector, $F$ is an $n \times n$ constant matrix, $G$ is a $(n \times r)$ ... by inverse $Z$-transform of $ZI - F$ $(Z I-F) Z$ $(Z I-F)^{-1} G$ $(Z I-F)^{-1} Z$

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GATE ECE 1991 | Question 1.14
A silicon sample is uniformly doped with $10^{16}$ phosphorous atoms $/ \mathrm{cm}^3$ and $2 \times 10^{16}$ boron atoms $/ \mathrm{cm}^3$. If all the dopants are fully ionized, the material is $\mathrm{n}$ ... $2 \times 10^{16} / \mathrm{cm}^3$ $T_2$ will get damaged and $T_1$ will be safe

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GATE ECE 1991 | Question 1.15
An $n$-type silicon sample, having electron mobility $\mu_n=$ twice the hole mobility $\mu_p$, is subjected to a steady illumination such that the electron concentration doubles from its thermal equilibrium value. As a result, the conductivity of the sample increases by a factor of ...

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16

GATE ECE 1991 | Question 1.16
The small signal capacitances of an abrupt $P_1-n$ junction is $1 \mathrm{nF} / \mathrm{Cm}^2$ at zero bias. If the built in voltage is $1$ volt, the capacitance at a reverse bias voltage of $99$ volts is equal to $\ldots$

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17

GATE ECE 1991 | Question 1.17
Referring to the figure. The switch $S$ is in position $1$ initially and steady state conditions exist from time $\mathrm{t}=0$ to $t=t_0$. The switch is suddenly thrown into position $2$. The current $1$ through the $10 \mathrm{~K}$ resistor as a function of ... $0$ , is .... (Give the sketch showing the magnitudes of the current at $t=0$, $t=t_0$ and $t=\infty$ )

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GATE ECE 1991 | Question 1.18
Discrete transistors $T_1$ and $T_2$ having maximum collector current rating of $0.75$ amps are connected in parallel as shown in the figure. This combination is treated as a single transistor to carry a total current of $1$ ampere, when biased with self bias ... will be safe $T_1$ will get damaged and $T_2$ will be safe $T_2$ will get damaged and $T_1$ will be safe

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19

GATE ECE 1991 | Question 1.19
The built-in potential of the gate junction of a $n$-channel $\text{JFET}$ is $0.5$ volts. The drain current saturates at $V_{D S}=4.0$ volts when $V_{G S}=0$. The pinch off voltage is _________.

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20

GATE ECE 1991 | Question 1.20
In figure, all transistors are identical and have a high value of beta. The voltage $V_{D C}$ is equal to _________.

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21

GATE ECE 1991 | Question 1.21
In figure, both transistors are identical and have a high value of beta. Take the $dc$ base-emitter voltage drop as $0.7$ volt and $\mathrm{KT} / \mathrm{q}=25 \; \mathrm{mV}$. The small signal low frequency voltage gain $\left(V_o / V_i\right)$ is equal to__________.

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22

GATE ECE 1991 | Question 1.22
In figure the input $V_1$ is a $100 \mathrm{~Hz}$ triangular wave having a peak to peak amplitude of 2 volts and an average value of zero volts. Given that the diode is ideal, the average value of the output $V_0$ is ___________.

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23

GATE ECE 1991 | Question 1.23
In figure, the $n$-channel $\text{MOSFETs}$ are identical and their current voltage characteristics are given by the following expressions: For $V_{D S}, I_D=\left[\left(V_{G S}-1\right) V_{D S}-\frac{V^2 D S}{2}\right] m A$ For ... respectively and $I_0$ is the drain current. The current $I_{D C}$ flowing through the transistor ' $\mathrm{M}$ ' is equal to__________.

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24

GATE ECE 1991 | Question 1.24
In order that the circuit of Figure works properly as differentiator, it should be modified to ________ (draw the modified circuit)

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25

GATE ECE 1991 | Question 1.25
Two non-inverting amplifiers, one having a unity gain and the other having a gain of twenty are made using identical operational amplifiers. As a compared to the unity gain amplifier, the amplifier with gain twenty has less negative feedback greater input impedance less bandwidth none of the above

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26

GATE ECE 1991 | Question 1.26
Two dimensional addressing of $256 \times 8$ bit $\text{ROM}$ using to $1$ selectors requires ________ (how many?) $\text{NAND}$ gates.

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27

GATE ECE 1991 | Question 1.27
The $\textsf{CMOS}$ equivalent of the following $\textsf{nMOS}$ gate (in figure) is___________ (draw the circuit).

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28

GATE ECE 1991 | Question 1.28
In figure, the Boolean expression for the output in terms of inputs $A, B$ and $C$ when the clock $\textsf{'CK'}$ is high, is given by __________.

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29

GATE ECE 1991 | Question 1.29
An $\text{S-R FLIP-FLOP}$ can be converted into a $\textsf{T FLIP FLOP}$ by connecting __________ to $\mathrm{Q}$ and ___________ to $\mathrm{Q}$.

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30

GATE ECE 1991 | Question 1.30
A bit stored in a $\text{FAMOS}$ device can be erased by _____________.

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31

GATE ECE 1991 | Question 1.31
A signal has frequency components from $300 \mathrm{~Hz}$ to $1.8 \; \mathrm{KHz}$. The minimum possible rate at which the signal has to be sampled is ___________.

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32

GATE ECE 1991 | Question 1.32
A sequential multiplexer is connected as shown in figure. Each time the multiplexer receives the clock, it switches to the next channel (From $6$ it goes to $1$). If the input signals are $A=5 \cos 2 \pi\left(4 \times 10^3 t\right)$ ... $D=4 \cos 2 \pi\left(1.7 \times 10^3 t\right)$ he minimum clock frequency should be _________ $\mathrm{KHz}$.

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33

GATE ECE 1991 | Question 1.33
For the signal constellation shown in figure below, the type of modulation is ___________.

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34

GATE ECE 1991 | Question 1.34
Two resistors $R_1$ and $R_2$ (in ohms) at temperatures $T_1$ and $T_2 K$ respectively, are connected in series. Their equivalent noise temperatures is ___________ $K$.

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35

GATE ECE 1991 | Question 1.35
A binary source has symbol probabilities $0.8$ and $0.2$. If extension coding (blocks of $4$ symbols) is used. The lower and upper bounds on the average code word length are (a) lower _________. (b) higher ________.

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36

GATE ECE 1991 | Question 1.36
In a reflex Klystron oscillator the maximum possible efficiency is $58 \%$ the frequency of oscillation varies linearly with the reflector voltage the power output varies continuously with reflector voltage the power output is maximum at fixed frequency.

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37

GATE ECE 1991 | Question 1.37
The input impedance of a short-circuited lossless transmission line quarter wave length is purely reactive purely resistive infinite dependent on the characteristic impedance of the line.

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38

GATE ECE 1991 | Question 1.38
The electric field component of a uniform plane electromagnetic wave propagating in the $Y$-direction in a lossless medium will satisfy the equation. $\frac{\partial^2 E_y}{\partial y^2}=\mu \in \frac{\partial^2 E_y}{\partial t^2}$ ... $\frac{\sqrt{E_x^2+E_z^2}}{\sqrt{H_x^2+H_z^2}}=\sqrt{\frac{\mu}{\epsilon}}$

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39

GATE ECE 1991 | Question 6
In figure, the operational amplifier is ideal and its output can swing between $-15$ and $+15$ volts. The input $v_\rho$ which is zero for $t<0$, is switched to $5$ volts at the instant $\mathrm{t}=0$. Given that the output $v_0$ is ... $v_0$ and $v_i$. You must give the values of important parameters of this sketch.

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40

GATE ECE 1991 | Question 7
In figure, the operational amplifiers are ideal and their output can swing between $-15$ and $+15$ volts. Sketch on same diagram, the waveform of voltages $V_1$ and $V_2$ as a function of time. You must give the values of important parameters of this sketch.

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