GATE EC question library

If the transistor in the figure is in saturation, then

The number of comparators required in a $3$-bit comparator type ADC is

If the input to the digital circuit the figure, consisting of a cascade of $20 \; \mathrm{XOR}$-gates is $\mathrm{X}$, then the output $Y$ is equal to

$4$-bit $2$'s complement representation of a decimal number is $1000.$ The number is

A $741$-type opamp has a gain-bandwidth product of $1 \; \mathrm{MHz}$. A non-inverting amplifier using this opamp and having a voltage gain of $20 \mathrm{~dB}$ will exhibit a $-3-\mathrm{dB}$ bandwidth of

In a negative feedback amplifier using voltage-series (i.e. voltage-sampling, series mixing) feedback. ($R_i$ and $R_o$ denote the input and output resistances respectively)

In given figure a silicon diode is carrying a constant current of $1 \mathrm{~mA}$. When the temperature of the diode is $20^{\circ} \mathrm{C}, \mathrm{V}_{\mathrm{D}}$ is found to be $700 \; \mathrm{mV}$. If the temperature rises to $40^{\circ} \mathrm{C}, \mathrm{V}_{\mathrm{D}}$ becomes approximately equal to

Which of the following cannot be the Fourier series expansion of a periodic signal ?

Convolution of $x(t+5)$ with impulse function $\delta(t-7)$ is equal to

In given figure $1.2,$ the switch was closed for a long time before opening at $t=0$. The voltage $V x$ at $t=0^{+}$ is

The dependent current source shown in given figure.

A person with a receiver is $5 \; \mathrm{Km}$ away from the transmitter. What is the distance that this person must move further to detect a $3-d B$ decrease in signal strength?

The electric field on the surface of a perfect conductor is $2 \mathrm{~Vm}$. The conductor is immersed in water with $\epsilon=80 \epsilon_{0}$. The surface charge density on the conductor is $\left(\epsilon_{0}=10^{-4} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

Distilled water at $25^{\circ} \mathrm{C}$ is characterized by $\sigma=1.7 \times 10^{-1} \mathrm{mho} / \mathrm{m}$ and $\epsilon=78 \; \epsilon_{0}$ at a frequency of $3 \; \mathrm{GHz}.$ Its loss tangent $\tan\delta$ is $\left(\epsilon=10^{-9} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

A plane wave is characterized by $\overline{\mathrm{E}}=\left(0.5 \hat{x}+\hat{y} e^{jz} / 2 \right)e^{jzet – jkz}.$ This wave is

If the variance $\sigma_{x}^{2}$ of $d(n)=x(n)-x(n-1)$ is one-tenth the variance $\sigma_{x}^{2}$ of a stationary zero-mean discrete-time signal $x(n)$, then the normalized autocorrelation function $R_{x x}(k) / \sigma_{x}^{2}$ at $k=1$ is

A signal $x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t$ is ideally sampled with a sampling period of $50 \; \mu \mathrm{sec}$ and then passed through an ideal lowpass filter with cut-off frequency of $15 \; \mathrm{kHz}$. Which of the following frequencies is/are present at the filter output?

In the figure $m(t)=\frac{2 \sin 2 \pi t}{t}, s(t)=\cos 200 \pi t$ and $n(t)$ $=\frac{\sin 199 \pi t}{t}$. The output $y(t)$ will be

An angle-modulated signal is given by $s(t)=\cos 2 \pi\left(2 \times 10^{6} t+30 \sin 150 t+40 \cos 150 t\right)$.The maximum frequency and phase deviations of $s(t)$ are

The system with the open loop transfer function $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)=\frac{1}{s\left(s^{2}+s+1\right)}$ has a gain margin of