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Recent questions tagged gate2015-in

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41
GATE2015-40
The linear $I-V$ characteristics of 2-terminal non-ideal dc sources $X$ and $Y$ are shown in the figure. If the sources are connected to a $1\Omega$ resistor as shown, the current through the resistor in amperes is ______________ A.
The linear $I-V$ characteristics of 2-terminal non-ideal dc sources $X$ and $Y$ are shown in the figure. If the sources are connected to a $1\Omega$ resistor as shown, th...
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42
GATE2015-41
Consider the circuits shown in the figure. The magnitude of the ratio of the currents, i.e., $|I_1/I_2|$, is ___________.
Consider the circuits shown in the figure. The magnitude of the ratio of the currents, i.e., $|I_1/I_2|$, is ___________.
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43
GATE2015-42
The circuit shown in the figure is in series resonance at frequency $f_c\;Hz$. The value of $V_c$ in volts is _____________ $V$.
The circuit shown in the figure is in series resonance at frequency $f_c\;Hz$. The value of $V_c$ in volts is _____________ $V$.
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44
GATE2015-43
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $10\% $, the output frequency in kilohertz becomes ____________ $kHz.$
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $1...
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46
GATE2015-46
In the circuit shown in the figure, it is found that $V_{BE}=0.7\:V$ and $V_E=0\:V$. If $\beta_{dc}=99$ for the transistor, then the value of $R_B$ in kilo ohms is _______________ $k\Omega$.
In the circuit shown in the figure, it is found that $V_{BE}=0.7\:V$ and $V_E=0\:V$. If $\beta_{dc}=99$ for the transistor, then the value of $R_B$ in kilo ohms is ______...
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47
GATE2015-47
An opamp has ideal characteristics except that its open loop gain is given by the expression $Av(S)=10^4/(1+10^{-3}\;s).$ This op-amp is used in the circuit shown in the figure. The 3-dB bandwidth of the circuit, in $\text{rad/s}$, is $10^2$ $10^3$ $10^4$ $10^6$
An opamp has ideal characteristics except that its open loop gain is given by the expression $Av(S)=10^4/(1+10^{-3}\;s).$ This op-amp is used in the circuit shown in the ...
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51
GATE2015-51
For the circuit shown in the figure, the rising edge triggered D-flip flop with asynchronous reset has a clock frequency of $\text{1 Hz}$. The $\text{NMOS}$ transistor has an $ON$ resistance of $1000\:\Omega$ and an $OFF$ resistance of infinity. The nature of the output waveform is
For the circuit shown in the figure, the rising edge triggered D-flip flop with asynchronous reset has a clock frequency of $\text{1 Hz}$. The $\text{NMOS}$ transistor ha...
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52
GATE2015-52
A transfer function $G(s)$ with the degree of its numerator polynomial zero and the degree of its denominator polynomial two has a Nyquist plot shown in the figure. The transfer function represents a stable, type-0 system a stable, type-1 system an unstable, type-0 system an unstable, type-1 system
A transfer function $G(s)$ with the degree of its numerator polynomial zero and the degree of its denominator polynomial two has a Nyquist plot shown in the figure. The t...
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53
GATE2015-53
In the circuit shown in the figure, both the $\text{NMOS}$ transistors are identical with their threshold voltages being $\text{5 V}$. Ignoring channel length modulation, the output voltage $V_{out}$ in volt is ______________ $V$.
In the circuit shown in the figure, both the $\text{NMOS}$ transistors are identical with their threshold voltages being $\text{5 V}$. Ignoring channel length modulation,...
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54
GATE2015-54
The signal $x[n]=\sin(\pi n/6)/(\pi n)$ is processed through a linear filter with the impulse response $h[n]=\sin(\omega_cn)/(\pi n)$ where $\omega_c>\pi/6$. The output of the filter is $sin(2\omega_cn)/(\pi n)$ $sin(\pi n/3)/(\pi n)$ $[sin(\pi n/6)/(\pi n)]^2$ $sin(\pi n/6)/(\pi n)$
The signal $x[n]=\sin(\pi n/6)/(\pi n)$ is processed through a linear filter with the impulse response $h[n]=\sin(\omega_cn)/(\pi n)$ where $\omega_c>\pi/6$. The output o...
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56
GATE2015-56
Consider a low-pass filter module with a pass-band ripple of $\delta$ in the gain magnitude. If $M$ such identical modules are cascaded, ignoring the loading effects, the pass-band ripple of the cascade is $1-(1-\delta)^M$ $\delta^M$ $(1-\delta^M)$ $(1-\delta)^M$
Consider a low-pass filter module with a pass-band ripple of $\delta$ in the gain magnitude. If $M$ such identical modules are cascaded, ignoring the loading effects, the...
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57
GATE2015-57
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
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58
GATE2015-58
If the deflection of the galvanometer in the bridge circuit shown in the figure is zero, then the value of $R_X$ in ohms is _______________ $\Omega.$
If the deflection of the galvanometer in the bridge circuit shown in the figure is zero, then the value of $R_X$ in ohms is _______________ $\Omega.$
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59
GATE2015-59
In the potentiometer circuit shown in the figure, the expression for $V_X$ is ____________. $(1-2\alpha)V$ $(1-\alpha)V$ $(\alpha-1)V$ $\alpha V$
In the potentiometer circuit shown in the figure, the expression for $V_X$ is ____________.$(1-2\alpha)V$$(1-\alpha)V$$(\alpha-1)V$$\alpha V$
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60
GATE2015-60
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are $\pm \frac{\pi}{4}$ $\pm \frac{\pi}{3}$ $\pm \frac{\pi}{2}$ $\pm \frac{5\pi}{6}$
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are$\pm \frac{\pi}{4}$$\pm \frac{\pi}{3}$$\pm \fr...
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61
GATE2015-61
A system is represented in state-space as $\dot{X}=AX+BU,$ where $A=\begin{bmatrix} 1 & 2 \\ \alpha & 6\end{bmatrix}$ and $B=\begin{bmatrix} 1 \\ 1\end{bmatrix}$. The value of $\alpha$ for which the system is not controllable is _____________.
A system is represented in state-space as $\dot{X}=AX+BU,$ where $A=\begin{bmatrix} 1 & 2 \\ \alpha & 6\end{bmatrix}$ and $B=\begin{bmatrix} 1 \\ 1\end{bmatrix}$. The val...
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65
GATE2015-65
The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased by increasing the angular magnification of the telescope increasing the period of the grating decreasing the period of the grating decreasing the slit-width of the collimator
The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased byincreasing the angular magnification of the telescopeincrea...
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