GATE EC question library

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

Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is

The value of the integral $\int_{-\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.

If $C$ denotes the counterclockwise unit circle, the value of the contour integral $$\dfrac{1}{2\pi j}\oint_{C} Re\{z\}dz$$ is __________.

Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.

An $LC$ tank circuit consists of an ideal capacitor $C$ connected in parallel with a coil of inductance $L$ having an internal resistance $R.$ The resonant frequency of the tank circuit is

In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.

In the circuit shown, the initial voltages across the capacitors $C_{1}$ and $C_{2}$ are $1\: V$ and $3\: V,$ respectively. The switch is closed at time $t = 0$. The total energy dissipated (in Joules) in the resistor $R$ until steady state is reached, is __________.

A dc voltage of $10\: V$ is applied across an $n$-type silicon bar having a rectangular cross-section and a length of $1\:cm$ as shown in figure. The donor doping concentration $N_{D}$ and the mobility of electrons $\mu_{n}$ are $10^{16} cm^{-3}$ and $1000\: cm^{2} V^{-1} s^{-1},$ respectively. The average time $(\text{in}\: \mu s)$ taken by …

In a MOS capacitor with an oxide layer thickness of $10\: nm,$ the maximum depletion layer thickness is $100\: nm.$ The permittivities of the semiconductor and the oxide layer are $\varepsilon_{s}$ and $\varepsilon_{ox}$ respectively. Assuming $\varepsilon_{s}/\varepsilon_{ox} = 3,$ the ratio of the maximum capacitance to the minimum capacitance of …

The energy band diagram and the electron density profile $n(x)$ in a semiconductor are shown in the figures. Assume that $n(x) = 10^{15}e^{\left(\dfrac{q\alpha x}{kT}\right)}\:cm^{-3} ,$ with $\alpha = 0.1\:V/cm$ and $x$ expressed in cm. Given $\dfrac{kT}{q} = 0.026\;V,D_{n} = 36\:cm^{2}s^{-1},$ and $\dfrac{D}{\mu} = \dfrac{kT}{q}.$ The electron …