GATE EC question library

The voltage $(ܸV_{C})$ across the capacitor (in Volts) in the network shown is ______.

In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.

The $2$-port admittance matrix of the circuit shown is given by

An $n$-type silicon sample is uniformly illuminated with light which generates $10^{20}$ electron-hole pairs per $cm^{3}$ per second. The minority carrier lifetime in the sample is $1\mu s$. In the steady state, the hole concentration in the sample is approximately $10^{x}$, where $x$ is an integer. The value of $x$ is _______.

A piece of silicon is doped uniformly with phosphorous with a doping concentration of $10^{16}/cm^{3}.$ The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is $1.6 \times 10^{-19} \:C.$ The conductivity $\text{(in S } cm^{-1})$ of the silicon sample at …

If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period $T?$

In the circuit shown, $V_{0} = V_{0A}$ for switch $SW$ in position $A$ and $V_{0} = V_{0B}$ for $SW$ in position $B$. Assume that the opamp is ideal. The value of $\dfrac{V_{0B}}{V_{0A}}$ is ___________.

In the bistable circuit shown, the ideal opamp has saturation levels of $\pm\: 5\: V.$ The value of $R_{1} \text{(in}\: k\Omega)$ that gives a hysteresis width of $500\: mV$ is ________.

In the figure shown, the output ܻ$Y = AB + \overline{C}\:\:\overline{D}$ is required to be ܻ The gates $G1$ and $G2$ must be, respectively,

In an $8085$ microprocessor, which one of the following instructions changes the content of the accumulator?

A mod-$n$ counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of $n$ is _______.

Let the signal ݂$f(t) = 0$ outside the interval $[T_{1},T_{2}]$, where ܶ$T_{1}$ and ܶ$T_{2}$ are finite. Furthermore, $\mid f(t) \mid < \infty$. The region of convergence (RoC) of the signal’s bilateral Laplace transform $F(s)$ is

Two causal discrete-time signals $x[n]$ and $y[n]$ are related as $y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]$. If the $z$-transform of $y[n]$ is $\dfrac{2}{z(z-1)^{2}},$ the value of $x[2]$ is _______.

By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the form

For the signal flow graph shown in the figure, the value of $\dfrac{C(s)}{R(s)}$ is

A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.

A sinusoidal signal of amplitude $A$ is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is $31.8\: dB,$ the number of levels in the quantizer is __________.

The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ The sampled signal is passed through a filter with impulse response $\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t – \dfrac{\pi}{2}\right)$ The filter output is

In a source free region in vacuum, if the electrostatic potential $\varphi = 2x^{2} + y^{2} + cz^{2},$ the value of constant ܿ$c$ must be _______.

The electric field of a uniform plane electromagnetic wave is $$\overrightarrow{E} = \left(\overrightarrow{a}_{x} + j 4 \overrightarrow{a}_{y}\right) \text{exp }[j(2\pi \times 10^{7}t – 0.2z)].$$ The polarization of the wave is