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1041
GATE ECE 2005 | Question: 33
Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right]$ Then $(a+b)=$ $\frac{7}{20}$ $\frac{3}{20}$ $\frac{19}{60}$ $\frac{11}{20}$
Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{a...
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1042
GATE ECE 2005 | Question: 34
The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is $1$ $\pi$ $2$ $2 \pi$
The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is$1$$\pi$$2$$2 \pi$
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1043
GATE ECE 2005 | Question: 35
The derivative of the symmetric function drawn in given figure will look like
The derivative of the symmetric function drawn in given figure will look like
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1044
GATE ECE 2005 | Question: 36
Match the following and choose the correct combination: ... $\text{E-1, F-3, G-4, H-2}$ $\text{E-5, F-3, G-4, H-1}$
Match the following and choose the correct combination:$\begin{array}{ll} \textbf{Group 1} & \textbf{Group 2} \\ \text { E. Newton-Raphson method} & \text { 1. Solving no...
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1045
GATE ECE 2005 | Question: 37
Given an orthogonal matrix $A=\left[\begin{array}{cccc}1 & 1 & 1 & 1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{array}\right]$ $\left[\mathrm{AA}^{\mathrm{T}}\right]^{-1}$ ...
Given an orthogonal matrix $A=\left[\begin{array}{cccc}1 & 1 & 1 & 1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{array}\right]$ $\left[\mathrm{AA}^{\mathrm...
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1046
GATE ECE 2005 | Question: 38
For the circuit show in the figure, the instantaneous current $i_{i}(t)$ is $\frac{10 \sqrt{3}}{2} \angle 90^{\circ} \mathrm{Amps}$. $\frac{10 \sqrt{3}}{2} \angle-90^{\circ}$ Amps. $5 \angle 60^{\circ}$ Amps. $5 \angle-60^{\circ}$ Amps.
For the circuit show in the figure, the instantaneous current $i_{i}(t)$ is$\frac{10 \sqrt{3}}{2} \angle 90^{\circ} \mathrm{Amps}$.$\frac{10 \sqrt{3}}{2} \angle-90^{\circ...
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1047
GATE ECE 2005 | Question: 39
Impedance $\mathrm{Z}$ as shown in the given figure is $j 29 \Omega$ $j9 \Omega$ $j 19 \Omega$ $j 39 \Omega$
Impedance $\mathrm{Z}$ as shown in the given figure is$j 29 \Omega$$j9 \Omega$$j 19 \Omega$$j 39 \Omega$
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1048
GATE ECE 2005 | Question: 40
For the circuit shown in the figure, Thevenin's voltage and Thevenin's equivalent resistance atterminals $a-b$ is $5 \mathrm{~V}$ and $2 \; \Omega$. $7.5 \mathrm{~V}$ and $2.5 \; \Omega$. $4 \mathrm{~V}$ and $2 \; \Omega$. $3 \mathrm{~V}$ and $2.5 \; \Omega$.
For the circuit shown in the figure, Thevenin's voltage and Thevenin's equivalent resistance atterminals $a-b$ is$5 \mathrm{~V}$ and $2 \; \Omega$.$7.5 \mathrm{~V}$ and $...
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1049
GATE ECE 2005 | Question: 41
If $R_{1}=R_{2}=R_{4}=R$ and $R_{3}=1.1 R$ in the bridge circuit shown in the figure, then the reading in the ideal voltmeter connected between $a$ and $b$ is $0.238 \mathrm{~V}$. $0.138 \mathrm{~V}$. $-0.238 \mathrm{~V}$ $1 \mathrm{~V}$.
If $R_{1}=R_{2}=R_{4}=R$ and $R_{3}=1.1 R$ in the bridge circuit shown in the figure, then the reading in the ideal voltmeter connected between $a$ and $b$ is$0.238 \math...
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1050
GATE ECE 2005 | Question: 42
The $h$ parameters of the circuit shown in the figure are $\left[\begin{array}{cc}0.1 & 0.1 \\ -0.1 & 0.3\end{array}\right]$ $\left[\begin{array}{cc}10 & -1 \\ 1 & 0.05\end{array}\right]$ $\left[\begin{array}{ll}30 & 20 \\ 20 & 20\end{array}\right]$ $\left[\begin{array}{cc}10 & 1 \\ -1 & 0.05\end{array}\right]$
The $h$ parameters of the circuit shown in the figure are$\left[\begin{array}{cc}0.1 & 0.1 \\ -0.1 & 0.3\end{array}\right]$$\left[\begin{array}{cc}10 & -1 \\ 1 & 0.05\end...
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1051
GATE ECE 2005 | Question: 43
A square pulse of $3$ volts amplitude is applied to $C-R$ circuit shown in the figure. The capacitor is initially uncharged. The output voltage $\mathrm{V}_{0}$ at time $t=2 \mathrm{sec}$ is $3 \mathrm{~V}$ $-3 \mathrm{~V}$ $4 \mathrm{~V}$ $-4 \mathrm{~V}$
A square pulse of $3$ volts amplitude is applied to $C-R$ circuit shown in the figure. The capacitor is initially uncharged. The output voltage $\mathrm{V}_{0}$ at time $...
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1054
GATE ECE 2005 | Question: 46
For an $\text{npn}$ transistor connected as shown in the figure, $V_{B E}=0.7$ volts. Given that reverse saturation current of the junction at room temperature $300^{\circ} \mathrm{K}$ is $10^{-13} \mathrm{~A}$, the emitter current is $30 \mathrm{~mA}$. $39 \mathrm{~mA}$. $49 \mathrm{~mA}$. $20 \mathrm{~mA}$.
For an $\text{npn}$ transistor connected as shown in the figure, $V_{B E}=0.7$ volts. Given that reverse saturation current of the junction at room temperature $300^{\cir...
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1055
GATE ECE 2005 | Question: 47
The voltage $e_{0}$ indicated in the figure has been measured by an ideal voltmeter. Which of the following can be calculated? Bias current of the inverting input only Bias current of the inverting and non-inverting inputs only Input offset current only Both the bias currents and the input offset current.
The voltage $e_{0}$ indicated in the figure has been measured by an ideal voltmeter. Which of the following can be calculated?Bias current of the inverting input onlyBias...
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1056
GATE ECE 2005 | Question: 48
The $\text{OP-amp}$ circuit shown in the figure is a filter. The type of filter and its cut-off frequency are respectively high pass, $1000 \; \mathrm{rad/sec}$. low pass, $1000 \; \mathrm{rad/sec}$. high pass, $10000 \; \mathrm{rad/sec}$. low pass, $10000 \; \mathrm{rad/sec}$.
The $\text{OP-amp}$ circuit shown in the figure is a filter. The type of filter and its cut-off frequency are respectivelyhigh pass, $1000 \; \mathrm{rad/sec}$.low pass, ...
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1057
GATE ECE 2005 | Question: 49
In an ideal differential amplifier shown in the figure, a large value of $\left(R_{E}\right)$. increases both the differential and common-mode gains. increases the common-mode gain only. decreases the differential-mode gain only decreases the common-mode gain only.
In an ideal differential amplifier shown in the figure, a large value of $\left(R_{E}\right)$.increases both the differential and common-mode gains.increases the common-m...
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1062
GATE ECE 2005 | Question: 54
The Boolean expression for the truth table shown is ... $\overline{\mathrm{B}}(\mathrm{A}+\mathrm{C})(\overline{\mathrm{A}}+\overline{\mathrm{C}})$
The Boolean expression for the truth table shown is$$\begin{array}{|c|c|c|c|}\hline \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{F} \\\hline 0 & 0 & 0 & 0 \\\hline 0 & ...
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1064
GATE ECE 2005 | Question: 56
The present output $Q_{n}$ of an edge triggered JK flip-flop is logic $0.$ If $\mathrm{J}=1$, then $\mathrm{Q}_{n+1}$ cannot be determined will be logic $0$ will be logic $1$ will race around
The present output $Q_{n}$ of an edge triggered JK flip-flop is logic $0.$ If $\mathrm{J}=1$, then $\mathrm{Q}_{n+1}$cannot be determinedwill be logic $0$will be logic $1...
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1065
GATE ECE 2005 | Question: 57
The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is $Q_{2} \; Q_{1} \; Q_{0}=011$, then its next state $\left(Q_{2} \; Q_{1} \; Q_{n}\right)$ will be $010$ $100$ $111$ $101$
The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is $Q_{2} \; Q_{1} \; Q_{0}=011$, then its next stat...
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1066
GATE ECE 2005 | Question: 58
What memory address range is $\text{NOT}$ represented by chip $\# \; 1$ and chip $\# \; 2$ in the figure $\text{A}_{0}$ to $\text{A}_{15}$ in this figure are the address lines and $\text{CS}$ means Chip Select. 0100-02FF 1500-16FF F900-FAFF F800-F9FF
What memory address range is $\text{NOT}$ represented by chip $\# \; 1$ and chip $\# \; 2$ in the figure $\text{A}_{0}$ to $\text{A}_{15}$ in this figure are the address ...
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1067
GATE ECE 2005 | Question: 59
The output $y(t)$ of a linear time invariant system is related to its input $x(t)$ by the following equation: $y(t)=0.5 x\left(t-t_{d}+\mathrm{T}\right)+x\left(t-t_{d}\right)+0.5 x\left(t-t_{d}-\mathrm{T}\right)$ ... $(1+\cos \omega \mathrm{T}) e^{-j \omega t_d}$ $(1-0.5 \cos \omega \mathrm{T}) e^{-j \omega t_d}$
The output $y(t)$ of a linear time invariant system is related to its input $x(t)$ by the following equation:$y(t)=0.5 x\left(t-t_{d}+\mathrm{T}\right)+x\left(t-t_{d}\rig...
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1068
GATE ECE 2005 | Question: 60
Match the following and choose the correct combination. ... $\mathrm{E}-2, \mathrm{~F}-1, \mathrm{G}-4, \mathrm{H}-3$
Match the following and choose the correct combination.$$\begin{array}{ll} \qquad \qquad \quad \textbf{Group 1} & \quad \qquad \qquad \qquad \qquad \textbf{Group 2} \\ \t...
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1070
GATE ECE 2005 | Question: 62
For a signal $x(f)$ the fourier transform is $X(f)$. Then the inverse Fourier transform of $X(3 f+2)$ is given by $\frac{1}{2 x}\left(\frac{t}{2}\right) e^{j 3 \pi t}$ $\frac{1}{3 x}\left(\frac{t}{3}\right) e^{-14 \pi t / 3}$ $3 x(3 t) e^{-j 4 \pi t}$ $x(3 t+2)$
For a signal $x(f)$ the fourier transform is $X(f)$. Then the inverse Fourier transform of $X(3 f+2)$ is given by$\frac{1}{2 x}\left(\frac{t}{2}\right) e^{j 3 \pi t}$$\fr...
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1071
GATE ECE 2005 | Question: 63
The polar diagram of a conditionally stable system for open loop gain $\text{K}=1$ is shown in the figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for $\mathrm{K}<5$ ... $5<\mathrm{K}$. $\text{K}>\frac{1}{8}$ and $\text{K}<5$.
The polar diagram of a conditionally stable system for open loop gain $\text{K}=1$ is shown in the figure. The open loop transfer function of the system is known to be st...
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1073
GATE ECE 2005 | Question: 65
Given the ideal operational amplifier circuit shown in the figure indicate the correct transfer characteristics assuming ideal diodes with zero cut-in voltage.
Given the ideal operational amplifier circuit shown in the figure indicate the correct transfer characteristics assuming ideal diodes with zero cut-in voltage.
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1074
GATE ECE 2005 | Question: 66
A ramp input applied to an unity feedback system results in $5 \%$ steady state error. The type number and zero frequency gain of the system are respectively $1$ and $20$ $0$ and $20$ $0$ and $\frac{1}{20}$ $1$ and $\frac{1}{20}$
A ramp input applied to an unity feedback system results in $5 \%$ steady state error. The type number and zero frequency gain of the system are respectively$1$ and $20$$...
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1075
GATE ECE 2005 | Question: 67
A double integrator plant, $\mathrm{G}(s)=\frac{\mathrm{K}}{s^{2}}, \mathrm{H}(\mathrm{s})=1$ is to be compensated to achieve the damping ratio $\zeta=0.5$, and an undamped natural frequency, $\omega_{n}=5 \; \mathrm{rad/s}$ ... $\frac{\mathrm{s}-6}{\mathrm{~s}+8.33}$ $\frac{\text{s}-6}{\text{s}}$
A double integrator plant, $\mathrm{G}(s)=\frac{\mathrm{K}}{s^{2}}, \mathrm{H}(\mathrm{s})=1$ is to be compensated to achieve the damping ratio $\zeta=0.5$, and an undamp...
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1076
GATE ECE 2005 | Question: 68
An unity feedback system is given as, $\mathrm{G}(s)=\frac{\mathrm{K}(1-s)}{s(s+3)}$ Indicate the correct root locus diagram.
An unity feedback system is given as,$\mathrm{G}(s)=\frac{\mathrm{K}(1-s)}{s(s+3)}$Indicate the correct root locus diagram.
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1077
GATE ECE 2005 | Question: 69
A $\text{MOS}$ capacitor made using $p$ type substrate is in the accumulation mode. The dominant charge in the channel is due to the presence of holes electrons positively charged ions negatively charged ions
A $\text{MOS}$ capacitor made using $p$ type substrate is in the accumulation mode. The dominant charge in the channel is due to the presence ofholeselectronspositively c...
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1079
GATE ECE 2005 | Question: 71
A signal as shown in the figure is applied to a matched filter. Which of the following does represent the output of this matched filter?
A signal as shown in the figure is applied to a matched filter. Which of the following does represent the output of this matched filter?
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