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Recent questions tagged gate1998-ec

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GATE ECE 1998 | Question 1.7
The parallel RLC circuit shown in the figure is in resonance. In this circuit $\left|\mathrm{I}_{\mathrm{R}}\right|<1 \mathrm{~mA}$ $\left|\mathrm{I}_{\mathrm{R}}+\mathrm{I}_{\mathrm{L}}\right|>1 \mathrm{~mA}$ ... $\left|\mathrm{I}_{\mathrm{R}}+\mathrm{I}_{\mathrm{C}}\right|>1 \mathrm{~mA}$
The parallel RLC circuit shown in the figure is in resonance. In this circuit$\left|\mathrm{I}_{\mathrm{R}}\right|<1 \mathrm{~mA}$$\left|\mathrm{I}_{\mathrm{R}}+\mathrm{I...
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GATE ECE 1998 | Question 1.1
A network has $7$ nodes and $5$ independent loops. The number of branches in the network is $13$ $12$ $11$ $10$
A network has $7$ nodes and $5$ independent loops. The number of branches in the network is$13$$12$$11$$10$
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GATE ECE 1998 | Question 1.2
The eigen values of the matrix $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$ are $1,1$ $-1,-1$ $j,-j$ $1,-1$
The eigen values of the matrix $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$ are$1,1$$-1,-1$$j,-j$$1,-1$
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GATE ECE 1998 | Question 1.3
If $f(t)=\frac{\omega}{s^2+\omega^2}$, then the value of $\lim _{t \rightarrow \infty} f(t)$ cannot be determined is zero is unity is infinite
If $f(t)=\frac{\omega}{s^2+\omega^2}$, then the value of $\lim _{t \rightarrow \infty} f(t)$cannot be determinedis zerois unityis infinite
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GATE ECE 1998 | Question 1.4
The trigonometric Fourier series of a periodic time function can have only cosine terms sine terms cosine and sine terms $d.c$. and cosine terms
The trigonometric Fourier series of a periodic time function can have onlycosine termssine termscosine and sine terms$d.c$. and cosine terms
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GATE ECE 1998 | Question 1.5
The nodal method of circuit analysis is based on $\text{KVL}$ and Ohm's law $\mathrm{KCL}$ and Ohm's law $\text{KCL}$ and $\text{KVL}$ $\text{KCL, KVL}$ and Ohm's law
The nodal method of circuit analysis is based on$\text{KVL}$ and Ohm's law$\mathrm{KCL}$ and Ohm's law$\text{KCL}$ and $\text{KVL}$$\text{KCL, KVL}$ and Ohm's law
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GATE ECE 1998 | Question 1.6
Superposition theorem is $\text{NOT}$ applicable to networks containing nonlinear elements dependent voltage sources dependent current sources transformers
Superposition theorem is $\text{NOT}$ applicable to networks containingnonlinear elementsdependent voltage sourcesdependent current sourcestransformers
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GATE ECE 1998 | Question 1.8
A periodic signal $x(t)$ of period $T_0$ is given by $ x(t)= \begin{cases}1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2}\end{cases} $ The $\text{d.c}$. component of $x(t)$ is $\frac{\mathrm{T}_1}{\mathrm{T}_0}$ $\frac{\mathrm{T}_1}{2 \mathrm{T}_0}$ $\frac{2 \mathrm{T}_1}{\mathrm{T}_0}$ $\frac{\text{T}_0}{\text{T}_1}$
A periodic signal $x(t)$ of period $T_0$ is given by$$ x(t)= \begin{cases}1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2}\end{cases} $$The $\text{d.c}$. component of $x(t)$ is...
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GATE ECE 1998 | Question 1.9
The unit impulse response of a linear time-invariant system is the unit step function $u(t)$. For $t>0$, the response of the system to an excitation $e^{-a t} u(t), a>0$ will be $a e^{-a t}$ $(1 / a)\left(1-e^{-a t}\right)$ $a\left(1-e^{-a t}\right)$ $1-e^{-a t}$
The unit impulse response of a linear time-invariant system is the unit step function $u(t)$. For $t>0$, the response of the system to an excitation $e^{-a t} u(t), a>0$ ...
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GATE ECE 1998 | Question 1.10
The short-circuit admittance matrix o a two-port network is $ \left[\begin{array}{cc} 0 & -1 / 2 \\ 1 / 2 & 0 \end{array}\right] $ The two-port network is non-reciprocal and passive non-reciprocal and active reciprocal and passive reciprocal and active
The short-circuit admittance matrix o a two-port network is$$ \left[\begin{array}{cc} 0 & -1 / 2 \\ 1 / 2 & 0 \end{array}\right] $$The two-port network isnon-reciprocal a...
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GATE ECE 1998 | Question 1.11
The voltage across the terminals $a$ and $b$ in the figure is $0.5 \mathrm{~V}$ $3.0 \mathrm{~V}$ $3.5 \mathrm{~V}$ $4.0 \mathrm{~V}$
The voltage across the terminals $a$ and $b$ in the figure is$0.5 \mathrm{~V}$$3.0 \mathrm{~V}$$3.5 \mathrm{~V}$$4.0 \mathrm{~V}$
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GATE ECE 1998 | Question 1.12
The electron and hole concentrations in a intrinsic semiconductor are $n_i$ and $p_i$ respectively. When doped with a $p$-type material, these change to $n$ and $p$, respectively. Then $n+p=n_i+p_i$ $n+n i=p+p_i$ $n p_i=n_i p$ $n p=n_i p_i$
The electron and hole concentrations in a intrinsic semiconductor are $n_i$ and $p_i$ respectively. When doped with a $p$-type material, these change to $n$ and $p$, resp...
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GATE ECE 1998 | Question 1.13
The $f_{\mathrm{T}}$ of a $\text{BJT}$ is related to its $g m, \mathrm{C}_\pi$ and $\mathrm{C}_\mu$ as follows $f_{\mathrm{T}}=\frac{\mathrm{C}_\pi+\mathrm{C}_{\mu}}{g_\text{m}}$ ... $f_{\mathrm{T}}=\frac{g_\text{m}}{2 \pi\left(\mathrm{C}_\pi+\mathrm{C}_{\mu}\right)}$
The $f_{\mathrm{T}}$ of a $\text{BJT}$ is related to its $g m, \mathrm{C}_\pi$ and $\mathrm{C}_\mu$ as follows$f_{\mathrm{T}}=\frac{\mathrm{C}_\pi+\mathrm{C}_{\mu}}{g_\te...
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GATE ECE 1998 | Question 1.14
The static characteristic of an adequately forward biased $p-n$ junction is a straight line, if the plot is of $\log I $ vs. $\log V$ $\log I$ vs. $V$ $I$ vs. $\log V$ $I$ vs. $V$
The static characteristic of an adequately forward biased $p-n$ junction is a straight line, if the plot is of$\log I $ vs. $\log V$$\log I$ vs. $V$$I$ vs. $\log V$$I$ vs...
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GATE ECE 1998 | Question 1.15
A long specimen of $p$-type semiconductor material is positively charged is electrically neutral has an electric field directed along its length acts as a dipole
A long specimen of $p$-type semiconductor materialis positively chargedis electrically neutralhas an electric field directed along its lengthacts as a dipole
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GATE ECE 1998 | Question 1.16
The $Z$-transform of the time function $\sum_{k=0}^{\infty} \delta(n-k)$ is $\frac{Z-1}{Z}$ $\frac{Z}{Z-1}$ $\frac{Z}{(Z-1)^2}$ $\frac{(Z-1)^2}{Z}$
The $Z$-transform of the time function $\sum_{k=0}^{\infty} \delta(n-k)$ is$\frac{Z-1}{Z}$$\frac{Z}{Z-1}$$\frac{Z}{(Z-1)^2}$$\frac{(Z-1)^2}{Z}$
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GATE ECE 1998 | Question 1.17
The number of roots of $s^3+5 s^2+7 s+3=0$ in the left half of the $s$-plane is zero one two three
The number of roots of $s^3+5 s^2+7 s+3=0$ in the left half of the $s$-plane iszeroonetwothree
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GATE ECE 1998 | Question 1.18
The transfer function of a tachometer is of the form $\mathrm{Ks}$ $\frac{\mathrm{K}}{\mathrm{s}}$ $\frac{\mathrm{K}}{(s+1)}$ $\frac{\mathrm{K}}{s(s+1)}$
The transfer function of a tachometer is of the form$\mathrm{Ks}$$\frac{\mathrm{K}}{\mathrm{s}}$$\frac{\mathrm{K}}{(s+1)}$$\frac{\mathrm{K}}{s(s+1)}$
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GATE ECE 1998 | Question 1.19
Consider a unity feedback control system with open-loop transfer function $\mathrm{G} (s)=\frac{\mathrm{K}}{s(s+1)}$. The steady state error of the system due to a unit step input is zero $\mathrm{K}$ $1 / \mathrm{K}$ infinite
Consider a unity feedback control system with open-loop transfer function $\mathrm{G} (s)=\frac{\mathrm{K}}{s(s+1)}$.The steady state error of the system due to a unit st...
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GATE ECE 1998 | Question 1.20
The transfer function of a zero-order-hold system is $(1 / s)\left(1+e^{-sT}\right)$ $(1 / s)\left(1-e^{-sT}\right)$ $1-(1 / s) e^{-sT}$ $1+(1 / s) e^{-s T}$
The transfer function of a zero-order-hold system is$(1 / s)\left(1+e^{-sT}\right)$$(1 / s)\left(1-e^{-sT}\right)$$1-(1 / s) e^{-sT}$$1+(1 / s) e^{-s T}$
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GATE ECE 1998 | Question 1.21
In the Bode-plot of a unity feedback control system, the value of phase of $G(j \omega)$ at the gain cross over frequency is $-125^{\circ}$. The phase margin of the system is $-125^{\circ}$ $-55^{\circ}$ $55^{\circ}$ $125^{\circ}$
In the Bode-plot of a unity feedback control system, the value of phase of $G(j \omega)$ at the gain cross over frequency is $-125^{\circ}$. The phase margin of the syste...
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GATE ECE 1998 | Question 1.22
Consider a feedback control system with loop transfer function $ \mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(1+0.5 s)}{s(1+s)(1+2 s)} $ The type of the closed loop system is zero one two three
Consider a feedback control system with loop transfer function$$ \mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(1+0.5 s)}{s(1+s)(1+2 s)} $$The type of the closed loop syste...
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GATE ECE 1998 | Question 1.23
The transfer function of a phase lead controller is $\frac{1+3 \mathrm{Ts}}{1+\mathrm{Ts}}$. The maximum value of phase provided by this controller is $90^{\circ}$ $60^{\circ}$ $45^{\circ}$ $30^{\circ}$
The transfer function of a phase lead controller is $\frac{1+3 \mathrm{Ts}}{1+\mathrm{Ts}}$. The maximum value of phase provided by this controller is$90^{\circ}$$60^{\ci...
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GATE ECE 1998 | Question 1.24
The Nyquist plot of a phase transfer function $g(j \omega) H(j \omega)$ of a system encloses the $(-1,0)$ point. The gain margin of the system is less than zero zero greater than zero infinity
The Nyquist plot of a phase transfer function $g(j \omega) H(j \omega)$ of a system encloses the $(-1,0)$ point. The gain margin of the system isless than zerozerogreater...
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GATE ECE 1998 | Question 1.25
The transfer function of a system is $\frac{2 s^2+6 s+5}{(s+1)^2(s+2)} $ The characteristic equation of the system is $2 s^2+6 s+5=0$ $(s+1)^2(s+2)=0$ $2 s^2+6 s+5+(s+1)^2(s+2)=0$ $2 s^2+6 s+5-(s+1)^2(s+2)=0$
The transfer function of a system is$$\frac{2 s^2+6 s+5}{(s+1)^2(s+2)} $$The characteristic equation of the system is$2 s^2+6 s+5=0$$(s+1)^2(s+2)=0$$2 s^2+6 s+5+(s+1)^2(s...
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GATE ECE 1998 | Question 1.26
In a synchro error detector, the output voltage is proportional to $[\omega(t)]^n$, where $\omega(t)$ is the rotor velocity and $n$ equals $-2$ $-1$ $1$ $2$
In a synchro error detector, the output voltage is proportional to $[\omega(t)]^n$, where $\omega(t)$ is the rotor velocity and $n$ equals$-2$$-1$$1$$2$
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GATE ECE 1998 | Question 1.27
Two identical $\text{FETs}$, each characterised by the parameters $g_m$ and $r_d$ are connected in parallel. The composite $\text{FET}$ is then characterised by the parameters $\frac{g_m}{2}$ and $2 r_d$ $\frac{g_m}{2}$ and $\frac{r_d}{2}$ $2 g_m$ and $\frac{r_d}{2}$ $2 g_m$ and $2 r_d$
Two identical $\text{FETs}$, each characterised by the parameters $g_m$ and $r_d$ are connected in parallel. The composite $\text{FET}$ is then characterised by the param...
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GATE ECE 1998 | Question 1.28
The circuit of the figure is an example of feedback of the following type current series current shunt voltage series voltage shunt
The circuit of the figure is an example of feedback of the following typecurrent seriescurrent shuntvoltage seriesvoltage shunt
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GATE ECE 1998 | Question 1.29
In a differential amplifier, $\text{CMRR}$ can be improved by using an increased emitter resistance collector resistance power supply voltages source resistance
In a differential amplifier, $\text{CMRR}$ can be improved by using an increasedemitter resistancecollector resistancepower supply voltagessource resistance
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GATE ECE 1998 | Question 1.30
From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier gain-bandwidth product slow rate upper $3-\mathrm{dB}$ frequency lower $3-d \mathrm{B}$ frequency
From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the ampl...
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GATE ECE 1998 | Question 1.32
The emitter coupled pair of $\text{BJT's}$ gives a linear transfer relation between the differential output voltage and the differenital input voltage $\mathrm{V}_{i d }$ only when the magnitude of $V_{i d}$ is less $\alpha$ times the thermal voltage, where $\alpha$ is $4$ $3$ $2$ $1$
The emitter coupled pair of $\text{BJT's}$ gives a linear transfer relation between the differential output voltage and the differenital input voltage $\mathrm{V}_{i d }$...
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GATE ECE 1998 | Question 1.33
In a shunt-shunt negative feedback amplifier, as compared to the basic amplifier both, input and output impedances, decrease input impedance decreases but output impedance increases input impedance increases but output impedance decreases both input and output impedances increases.
In a shunt-shunt negative feedback amplifier, as compared to the basic amplifierboth, input and output impedances, decreaseinput impedance decreases but output impedance ...
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GATE ECE 1998 | Question 1.34
A multistage amplifier has a low-pass response with three real poles at $s=-\omega_{1}-\omega_{2}$ and $\omega_{3}$. The approximate overall bandwidth $\mathrm{B}$ of the amplifier will be given by $\mathrm{B}=\omega_{1}+\omega_{2}+\omega_{3}$ ... $\mathrm{B}=\sqrt{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}}$
A multistage amplifier has a low-pass response with three real poles at $s=-\omega_{1}-\omega_{2}$ and $\omega_{3}$. The approximate overall bandwidth $\mathrm{B}$ of the...
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GATE ECE 1998 | Question 1.35
A high-Q quartz crystal exhibits series resonance at the frequency $\omega_{s}$ and parallel resonance at the frequency $\omega_{p}$. Then $\omega_{s}$ is very close to, but less than $\omega_{p}$ $\omega_{s} \ll \omega_{p}$ $\omega_{s}$ is very close to, but greater than $\omega_{p}$ $\omega_{s} \gg \omega_{p}$
A high-Q quartz crystal exhibits series resonance at the frequency $\omega_{s}$ and parallel resonance at the frequency $\omega_{p}$. Then$\omega_{s}$ is very close to, b...
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GATE ECE 1998 | Question 1.36
One input terminal of high gain comparator circuit is connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will be a sinusoid a full rectified sinusoid a half rectified sinusoid a square wave
One input terminal of high gain comparator circuit is connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will bea sinuso...
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GATE ECE 1998 | Question 1.37
In a series regulated power supply circuit, the voitage gain $A_{v}$ of the 'pass' transistor satisfies the condition $\mathrm{A}_{v} \rightarrow \infty$ $1<<\mathrm{A}_{v}<\infty$ $\mathrm{A}_{v} \approx 1$ $\mathrm{A}_{v}<<1$
In a series regulated power supply circuit, the voitage gain $A_{v}$ of the 'pass' transistor satisfies the condition$\mathrm{A}_{v} \rightarrow \infty$$1<<\mathrm{A}_{v}...
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GATE ECE 1998 | Question 1.39
In the $\text{MOSFET}$ amplifier of the figure is the signal outputs $V_{1}$ and $V_{2}$ obey the relationship $\mathrm{V}_{1}=\frac{\mathrm{V}_{2}}{2}$ $\mathrm{V}_{1}=-\frac{\mathrm{V}_{2}}{2}$ $\mathrm{V}_{1}=2 \mathrm{V}_{2}$ $\mathrm{V}_{1}=-2 \mathrm{V}_{2}$
In the $\text{MOSFET}$ amplifier of the figure is the signal outputs $V_{1}$ and $V_{2}$ obey the relationship$\mathrm{V}_{1}=\frac{\mathrm{V}_{2}}{2}$$\mathrm{V}_{1}=-\f...
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GATE ECE 1998 | Question 2.1
The minimum number of $2$-input $\text{NAND}$ gates required to implement the Boolean function $Z=A \bar{B} C$, assiming that $A, B$ and $C$ are available, is two three five six
The minimum number of $2$-input $\text{NAND}$ gates required to implement the Boolean function $Z=A \bar{B} C$, assiming that $A, B$ and $C$ are available, istwothreefive...
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