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Recent questions tagged gate2004-ec

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42
GATE ECE 2004 | Question: 42
The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain current $\left(\mathrm{I}_{\mathrm{D}}\right)$ is $1 \mathrm{~mA}$ ... $2 \mathrm{~mA}$ $3 \mathrm{~mA}$ $9 \mathrm{~mA}$ $4 \mathrm{~mA}$
The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain...
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45
GATE ECE 2004 | Question: 45
Assuming that the $\beta$ of the transistor is extremely large and $\text{V}_{\text{B E}}=0.7 \mathrm{~V}, \text{I}_{\text{C}}$ and $\text{V}_{\text{CE}}$ ... $\mathrm{I}_{\mathrm{C}}=0.5 \mathrm{~mA}, \mathrm{~V}_{\mathrm{CE}}=3.9 \mathrm{~V}$
Assuming that the $\beta$ of the transistor is extremely large and $\text{V}_{\text{B E}}=0.7 \mathrm{~V}, \text{I}_{\text{C}}$ and $\text{V}_{\text{CE}}$ in the circuit ...
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46
GATE ECE 2004 | Question: 46
A bipolar transistor is operating in the active region with a collector current of $1 \mathrm{~mA}$. Assuming that the $\beta$ of the transistor is $100$ and the thermal voltage $\left(\mathrm{V}_{\mathrm{T}}\right)$ is $25 \; \mathrm{mV}$ ... $g_{m}=40 \mathrm{~mA} / \mathrm{V}$ and $r_{n}=2.5 \; \mathrm{k} \Omega$
A bipolar transistor is operating in the active region with a collector current of $1 \mathrm{~mA}$. Assuming that the $\beta$ of the transistor is $100$ and the thermal ...
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47
GATE ECE 2004 | Question: 47
The value of $\mathrm{C}$ required for sinusoidal oscillations of frequency $1 \; \mathrm{kHz}$ in the circuit of given figure is $\frac{1}{2 \pi} \; \mu \text{F}$ $2 \pi \; \mu \text{F}$ $\frac{1}{2 \pi \sqrt{6}} \; \mu \text{F}$ $2 \pi \sqrt{6} \; \mu \text{F}$
The value of $\mathrm{C}$ required for sinusoidal oscillations of frequency $1 \; \mathrm{kHz}$ in the circuit of given figure is$\frac{1}{2 \pi} \; \mu \text{F}$$2 \pi \...
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48
GATE ECE 2004 | Question: 48
In the $\text{op-amp}$ circuit given in the figure, the load current $i_{\text{L}}$ is $-\frac{v_{s}}{R_{2}}$ $\frac{v_{s}}{R_{2}}$ $-\frac{v_{s}}{R_{\text{L}}}$ $\frac{v_{s}}{R_{1}}$
In the $\text{op-amp}$ circuit given in the figure, the load current $i_{\text{L}}$ is$-\frac{v_{s}}{R_{2}}$$\frac{v_{s}}{R_{2}}$$-\frac{v_{s}}{R_{\text{L}}}$$\frac{v_{s}...
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50
GATE ECE 2004 | Question: 50
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ ...
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ and peak values of the voltage respectively across a resistive load. If PIV is the ...
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51
GATE ECE 2004 | Question: 51
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is $1$ $2$ $3$ $4$
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is$1$$2$$3$$4$
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52
GATE ECE 2004 | Question: 52
The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to $\overline{\mathrm{A}} \mathrm{C}+\mathrm{B} \overline{\mathrm{C}}+\mathrm{AC}$ ...
The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to$\overline{\mathrm{A}} \mathrm{C}+\mathrm{B} \overline{\mathrm{C}}+\mathrm{AC}$$\overline{\math...
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53
GATE ECE 2004 | Question: 53
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ? $25, 9$ and $57$ respectively $-6,-6$ and $-6$ respectively $-7,-7$ and $-7$ respectively $-25, -9$ and $-57$ respectively
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ?$25, 9$ and $57$ respectively$-6,-6$ and $-6$ r...
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55
GATE ECE 2004 | Question: 55
The number of memory cycles required to execute the following $8085$ instructions $\text{LDA 3000 H}$ $\text{LXI D, FOF 1 H}$ would be $2$ for (I) and $2$ for (II) $4$ for (I) and $3$ for (II) $3$ for (I) and $3$ for (II) $3$ for (I) and $4$ for (II)
The number of memory cycles required to execute the following $8085$ instructions$\text{LDA 3000 H}$$\text{LXI D, FOF 1 H}$would be$2$ for (I) and $2$ for (II)$4$ for (I)...
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56
GATE ECE 2004 | Question: 56
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops. The $2$-input gate is a NAND gate a NOR gate an OR gate an AND gate
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops.The $2$-input gate isa NAND gatea NOR gat...
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59
GATE ECE 2004 | Question: 59
It is desired to multiply the numbers $0 \mathrm{AH}$ by $0 \mathrm{BH}$ and store the result in the accumulator. The numbers are available in registers $B$ and $C$ respectively. A Part of the $8085$ ... $\text{ADD B, JNZ LOOP, DCR C}$ $\text{DCR C, JNZ LOOP, ADD B}$ $\text{ADD B, DCR C, JNZ LOOP}$
It is desired to multiply the numbers $0 \mathrm{AH}$ by $0 \mathrm{BH}$ and store the result in the accumulator. The numbers are available in registers $B$ and $C$ respe...
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60
GATE ECE 2004 | Question: 60
A $1 \; \mathrm{kHz}$ sinusoidal signal is ideally sampled at $1500$ samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey $800 \mathrm{~Hz}$. The output signal has the frequency zero $\text{Hz}$ $0.75 \; \mathrm{kHz}$ $0.5 \; \mathrm{kHz}$ $0.25 \; \mathrm{kHz}$
A $1 \; \mathrm{kHz}$ sinusoidal signal is ideally sampled at $1500$ samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey...
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61
GATE ECE 2004 | Question: 61
A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a $\text{DC}$ $12 \; \mathrm{kHz}$ sinusoid $8 \; \mathrm{kHz}$ sinusoid $14 \; \mathrm{kHz}$ sinusoid
A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a$\text{DC}...
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62
GATE ECE 2004 | Question: 62
Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$ The conjugate anti-symmetric part of the sequence is $[-4-j 2.5 \quad j 2 \quad 4-j 2.5]$ $[-j 2.5 \quad 1 \quad j 2.5]$ $[-j 5 \quad j 2 \quad 0]$ $\left[\begin{array}{lll}-4 & 1 & 4\end{array}\right]$
Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$The conjugate anti-symmetric part of the sequence is$[-4-j 2.5 \quad j...
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63
GATE ECE 2004 | Question: 63
A causal $\text{LTI}$ system is described by the difference equation \[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\] The system is stable only if $|\alpha|=2, \quad|\beta|<2$ $|\alpha|>2, \quad|\beta|>2$ $|\alpha|<2$, any value of $\beta$ $|\beta \mid<2,$ any value of $\alpha$
A causal $\text{LTI}$ system is described by the difference equation\[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\]The system is stable only if$|\alpha|=2, \quad|\beta|<2$$|...
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64
GATE ECE 2004 | Question: 64
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state value is $2.7 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.1 \; \mathrm{sec}$
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state val...
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65
GATE ECE 2004 | Question: 65
The impulse response $h|n|$ ... $4 \sqrt{2} e^{j \pi n / 4}$ $4 e^{j \pi n / 4}$ $-4 e^{j \pi n / 4}$
The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...
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66
GATE ECE 2004 | Question: 66
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure. Then $Y(f)$ is $-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}$ $-\frac{1}{2} X(f / 2) e^{j 2 \pi f}$ $-X(f / 2) e^{j 2 \pi f}$ $-\mathrm{X}(f / 2) e^{-j2 \pi f}$
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...
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67
GATE ECE 2004 | Question: 67
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase of the system response at $20 \mathrm{~Hz}$ is $-90^{\circ}$ $0^{\circ}$ $90^{\circ}$ $-180^{\circ}$
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase...
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68
GATE ECE 2004 | Question: 68
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is $\frac{1-\left(b e+c f+d g\right)}{a b c}$ $\frac{b e d g}{1-(b e+c f+d g)}$ $\frac{a b c d}{1-\left(b e+c f+d g\right)+bedg}$ $\frac{1-\left(b e+cf+d g\right)+b ed g}{a b c d}$
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is$\frac{1-\left(b e+c f+d g\right)}{a b c}$$\frac{b e d g}{1-(b e+c f+d g)}$$\fr...
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69
GATE ECE 2004 | Question: 69
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ ...
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ is$\frac{1}{3}\left[\begin{array}{cc}\sin (-4 t)+2 \sin (-t) & -2 \sin (-4 t)+2 \sin (-t...
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70
GATE ECE 2004 | Question: 70
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$ The range of $\mathrm{K}$ for which the system is stable is $\frac{21}{44}>\mathrm{K}>0$ $13>\mathrm{K}>0$ $\frac{21}{4}<\mathrm{K}<\infty$ $-6<\mathrm{K}<\infty$
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$The range of $\mathrm{K}$ for which the system is stable is$\fr...
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71
GATE ECE 2004 | Question: 71
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is $4$ $2$ $3$ $1$
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is$4$$2$$3$$1$
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72
GATE ECE 2004 | Question: 72
The state variable equations of a system are: $\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$ The system is controllable but not observable observable but not controllable neither controllable nor observable controllable and observable
The state variable equations of a system are:$\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$The system iscontrollabl...
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73
GATE ECE 2004 | Question: 73
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by $\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{array}\right]$ ... $\left[\begin{array}{cc}0 & e^{t} \\ e^{t} & 0\end{array}\right]$
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by$\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{a...
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76
GATE ECE 2004 | Question: 76
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ ... $\sqrt{5 / 4+\cos \left(2 \pi \times 10^{6} t\right)}$
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ amplitude are fed to a balanced modulator. The...
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77
GATE ECE 2004 | Question: 77
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal frequency detector. The output of the detector is $0.1 \; \mathrm{kHz}$ sinusoid $20.1 \; \mathrm{kHz}$ sinusoid a linear function of time a constant
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal freq...
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79
GATE ECE 2004 | Question: 79
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ ... $\text{X}$. The root-mean square value of the quantization noise is $0.573$ $0.198$ $2.205$ $0.266$
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ is quantized as follows:$\begin{array}{ll} \qquad \text{If 0 < X < 0.3,} & \text{x}_{4} = 0...
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80
GATE ECE 2004 | Question: 80
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ ... $\text{1-S, 2-P, 3-U, 4-Q}$ $\text{1-U, 2-R, 3-S, 4-Q}$
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item i...
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