GATE EC question library

For a $\text{MOS}$ capacitor, $\text{V}_{\mathrm{fb}}$ and $\text{V}_{\mathrm{t}}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width $\left(\mathrm{W}_{\mathrm{dep}}\right)$ for varying gate voltage $\left(\text{V}_g\right)$ is best represented by

Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_{g}$. Which of the following statement is true? ($c$ is the velocity of light in vacuum.)

In the circuit shown below, $\text{V}_1$ and $\text{V}_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a

A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

In the circuit shown below, $\mathrm{P}$ and $\mathrm{Q}$ are the inputs. The logical function realized by the circuit shown below is

The synchronous sequential circuit shown below works at a clock frequency $1 \; \mathrm{GHz}$. The throughput, in $\text{Mbits/s,}$ and the latency, in $\text{ns,}$ respectively, are

The open loop transfer function of a unity negative feedback system is $G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}$, where $k, T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in $\text{rad/s,}$ is

Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$. The system is

Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$. Assuming $\omega_{0}=10 B$, the energy in the $m(t) \cos \omega_{0} t$ is

The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ is Note: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, periodic (iii) Discrete, aperiodic (c) Discrete, aperiodic (iv) Discrete, periodic (d) Discrete, periodic

For a real signal, which of the following is/are valid power spectral density/densities?

In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).

For the two port network shown below, the $[\mathrm{Y}] –$parameters is given as $$[Y]=\frac{1}{100}\left[\begin{array}{cc}2 & -1 \\ -1 & 4 / 3\end{array}\right] S$$ The value of load impedance $\mathrm{Z}_{\mathrm{L},}$ in $\Omega$, for maximum power transfer will be ____________ (rounded off to the nearest integer).

For the circuit shown below, the propagation delay of each $\mathrm{NAND}$ gate is $1 \mathrm{~ns}$. The critical path delay, in $\text{ns,}$ is______________(rounded off to the nearest integer).

In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch is opened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}, \text{in volts,}$ is_____________ (rounded off to the nearest integer).

A random variable $\mathrm{X}$, distributed normally as $\mathrm{N(0,1)}$ undergoes the transformation $\mathrm{Y}=\mathrm{h}(\mathrm{X})$, given in the figure. The form of the probability density function of $\mathrm{Y}$ is (In the options given below, $a, b, c$ are non-zero constants and $g(y)$ is piece-wise continuous function).

The value of the line integral $\int_{P}^{Q}\left(z^{2} d x+3 y^{2} d y+2 x z \; d z\right)$ along the straight line joining the points $P(1,1,2)$ and $Q(2,3,1)$ is

Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\boldsymbol{x}^{T} \boldsymbol{x}}$ The trace of the matrix $P=\boldsymbol{x} \boldsymbol{x}^{T}$ is

The $\frac{V_{\text{OUT }}}{V_{\text{IN }}}$ of the circuit shown below is