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Recent questions tagged numerical-answers

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122
GATE2020: 17
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
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123
GATE2020: 18
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The rms value of the line current $\text{(in amperes, rounded off to one decimal place)}$ is __________.
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The ...
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124
GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
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125
GATE2020: 20
A second order system has closed loop poles located at $s=-3\pm j4$. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places) is ________
A second order system has closed loop poles located at $s=-3\pm j4$. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two dec...
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126
GATE2017: 31
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ at upper half-power frequency will be _________.
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ a...
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127
GATE2017: 32
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across the capacitor, in volt, at $t=5\mu s$ is _________.
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across th...
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128
GATE2017: 35
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
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129
GATE2017: 36
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undamped natural frequency $\omega_n$ of $\text{4 rad/s}$ respectively. The value of $K_p$ will be__________________.
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undampe...
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130
GATE2017: 37
The loop transfer function of a closed-loop system is given by $G(s)H(s)=\frac{K(s+6)}{s(s+2)}$. The breakaway point of the root-loci will be ___________.
The loop transfer function of a closed-loop system is given by $G(s)H(s)=\frac{K(s+6)}{s(s+2)}$. The breakaway point of the root-loci will be ___________.
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131
GATE2017: 40
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
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132
GATE2017: 41
In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by $I_D=\frac{1}{2}(V_{GS}-1)^2$ $mA$, where $V_{GS}$ is in $V$. If $V_s=+5V$, then the value of $R_s$ in $K\Omega$ is _______________.
In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by $I_D=\frac{1}{2}(V_{GS}-1)^2$ $mA$, whe...
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133
GATE2017: 42
The two-input voltage multiplier, shown in the figure, has a scaling factor of $1$ and produces voltage output. If $V_1=+15\;V$ and $V_2=+3\;V$, the value of $V_\circ$ in $\text{volt}$ is _______________.
The two-input voltage multiplier, shown in the figure, has a scaling factor of $1$ and produces voltage output. If $V_1=+15\;V$ and $V_2=+3\;V$, the value of $V_\circ$ in...
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134
GATE2017: 44
The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between $\pm7\;V$. The width of the hysteresis band is ______________$V$.
The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between $\pm7\;V$. The width of the hysteresis band is _________...
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138
GATE2017: 48
In the a.c. bridge, shown in the figure, $R=10^3$ $\Omega$ and $C=10^{-7}$ $F$. If the bridge is balanced at a frequency $\omega_\circ$, the value of $\omega_\circ$ in $\text{rad/s}$ is ____________.
In the a.c. bridge, shown in the figure, $R=10^3$ $\Omega$ and $C=10^{-7}$ $F$. If the bridge is balanced at a frequency $\omega_\circ$, the value of $\omega_\circ$ in ...
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140
GATE2017: 50
A resistance temperature detector $(RTD)$ is connected to a circuit, as shown in the figure. Assume the opamp to be ideal. If $V_\circ=+2.0$ $V$, then the value of $x$ is _______________.
A resistance temperature detector $(RTD)$ is connected to a circuit, as shown in the figure. Assume the opamp to be ideal. If $V_\circ=+2.0$ $V$, then the value of $x$ is...
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145
GATE2017: 55
An angle modulated signal with carrier frequency $\omega_c=2\pi\times10^6\;rad/s$ is given by $\varphi_m(t)=\cos(\omega_ct+5\sin(1000\pi t)+10\sin(2000\pi t))$. The maximum deviation of the frequency in the angle modulated signal from that of the carrier is _______________$kHz$.
An angle modulated signal with carrier frequency $\omega_c=2\pi\times10^6\;rad/s$ is given by $\varphi_m(t)=\cos(\omega_ct+5\sin(1000\pi t)+10\sin(2000\pi t))$. The maxim...
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146
GATE2017: 27
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
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147
GATE2017: 30
For the circuit, shown in the figure, the total real power delivered by the source to the loads is _____________$\text{kW}$.
For the circuit, shown in the figure, the total real power delivered by the source to the loads is _____________$\text{kW}$.
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148
GATE2017: 1
If $\text{v}$ is a non-zero vector of dimensions $3\times1$, then the matrix $A=VV^T$ has a rank = ____________.
If $\text{v}$ is a non-zero vector of dimensions $3\times1$, then the matrix $A=VV^T$ has a rank = ____________.
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149
GATE2017: 6
A series $\text {R-L-C}$ circuit is excited with a $50\;\text{V}$, $50\;\text{Hz}$ sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor $\text(V_L)$ is ___________$\text{V}$.
A series $\text {R-L-C}$ circuit is excited with a $50\;\text{V}$, $50\;\text{Hz}$ sinusoidal source. The voltages across the resistance and the capacitance are shown in ...
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150
GATE2017: 8
A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at $\text{Node-1}$ is $-1\;\text{V}$, then the voltage at $\text{Node-2}$ is _____________ $\text{V}$.
A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at $\text{Node-1}$ is $-1\;\text{V}$, then the voltage at $\text{Node-2}$...
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151
GATE2017: 9
A periodic signal $\text{x(t)}$ is shown in the figure. The fundamental frequency of the signal $\text{x(t)}$ in $\text Hz$ is ____________.
A periodic signal $\text{x(t)}$ is shown in the figure. The fundamental frequency of the signal $\text{x(t)}$ in $\text Hz$ is ____________.
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152
GATE2017: 14
The differential amplifier, shown in the figure, has a differential gain of $A_d=100$ and common mode gain of $A_c=0.1$. If $V_1=5.01\;\text{V}$ and $V_2=5.00\;\text{V}$, then $\text{Vo}$, in $\text{volt}$ (up to one decimal place) is ______________.
The differential amplifier, shown in the figure, has a differential gain of $A_d=100$ and common mode gain of $A_c=0.1$. If $V_1=5.01\;\text{V}$ and $V_2=5.00\;\text{V}$,...
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153
GATE2017: 16
The figure shows a phase locked loop. The output frequency is locked at $f_0=5\;\text{kHz}$. The value of $f_i$ in $\text{kHz}$ is _______________.
The figure shows a phase locked loop. The output frequency is locked at $f_0=5\;\text{kHz}$. The value of $f_i$ in $\text{kHz}$ is _______________.
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154
GATE2019 IN: 16
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
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155
GATE2019 IN: 18
Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, and all source voltages are scaled up by a factor 10, the power dissipated in the circuit scles up by a factor of $\_\_\_\_\_\_$.
Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, an...
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156
GATE2019 IN: 19
In the circuit shown below, initially the switch S${_1}$ is open, then capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After s${_1}$ is closed, the charge on C2 in steady state is $\_\_\_\_\_$ coulomb.
In the circuit shown below, initially the switch S${_1}$ is open, then capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After s${_1}$ is closed...
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157
GATE2019 IN: 20
An 8-bit weighted resistor digital-to-analog converter(DAC) has the smallest resistance of 500 $\Omega$. The largest resistance has a value $\_\_\_\_$ k$\Omega$.
An 8-bit weighted resistor digital-to-analog converter(DAC) has the smallest resistance of 500 $\Omega$. The largest resistance has a value $\_\_\_\_$ k$\Omega$.
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158
GATE2019 IN: 21
The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is $\_\_\_\_$.
The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is $\_\_\_\_$.
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