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561
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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562
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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563
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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564
GATE2015-44
The Seebeck coefficients, in $\mu V/^\circ C,$ for copper, constant an and iron, with respect to platinum, are $1.9, \:-38.3$ and $13.3$, respectively. The magnitude of the thermo emf $E$ developed in the circuit shown in the figure, in millivolts is _____________ $mV$.
The Seebeck coefficients, in $\mu V/^\circ C,$ for copper, constant an and iron, with respect to platinum, are $1.9, \:-38.3$ and $13.3$, respectively. The magnitude of t...
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566
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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567
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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571
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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572
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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573
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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574
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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576
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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577
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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578
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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579
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$$\alpha V$
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580
GATE2015-60
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are $\pm \frac{\pi}{4}$ $\pm \frac{\pi}{3}$ $\pm \frac{\pi}{2}$ $\pm \frac{5\pi}{6}$
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are$\pm \frac{\pi}{4}$$\pm \frac{\pi}{3}$$\pm \fr...
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581
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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585
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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586
GATE2014-GA-1
Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease ___________ short-term memory loss. experienced has experienced is experiencing experiences
Choose the most appropriate word from the options given below to complete the following sentence.A person suffering from Alzheimer’s disease ___________ short-term memo...
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587
GATE2014-GA-2
Choose the most appropriate word from the options given below to complete the following sentence. ____________is the key to their happiness; they are satisfied with what they have. Contentment Ambition Perseverance Hunger
Choose the most appropriate word from the options given below to complete the following sentence.____________is the key to their happiness; they are satisfied with what t...
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589
GATE2014-GA-4
In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$.The average time between successive occurrences of such earthquakes is ______years.
In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$.The average time between successive occurrence...
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590
GATE2014-GA-5
The population of a new city is $5$ million and is growing at $20\%$ annually. How many years would it take to double at its growth rate? $3-4$ years $4-5$ years $5-6$ years $6-7$ years
The population of a new city is $5$ million and is growing at $20\%$ annually. How many years would it take to double at its growth rate?$3-4$ years$4-5$ years$5-6$ years...
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594
GATE2014-GA-9
$X$ is $1$ km northeast of $Y$. $Y$ is $1$ km southeast of $Z$. $W$ is $1$ km west of $Z$. $P$ is $1$ km south of $W$. $Q$ is $1$ km east of $P$. What is the distance between $X$ and $Q$ in km? $1$ $\sqrt 2$ $\sqrt 3$ $2$
$X$ is $1$ km northeast of $Y$. $Y$ is $1$ km southeast of $Z$. $W$ is $1$ km west of $Z$. $P$ is $1$ km south of $W$. $Q$ is $1$ km east of $P$. What is the distance bet...
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596
GATE2014-1
Given $x(t)=3\sin (1000\; \pi t)\; and\;y(t)=5\cos (1000\;\pi t+\frac{\pi}{4})$ The $x-y$ plot will be a circle a multi-loop closed curve a hyperbola an ellipse
Given $x(t)=3\sin (1000\; \pi t)\; and\;y(t)=5\cos (1000\;\pi t+\frac{\pi}{4})$The $x-y$ plot will bea circlea multi-loop closed curvea hyperbolaan ellipse
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597
GATE2014-2
Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.
Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________....
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598
GATE2014-3
The figure shows the plot of $y$ as a function of $x$ The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is : $\frac{d^2y}{dx^2}=1$ $\frac{dy}{dx}=x$ $\frac{dy}{dx}=-x$ $\frac{dy}{dx}=|x|$
The figure shows the plot of $y$ as a function of $x$The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is :$\fr...
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