GATE EC question library

Identify which of the following is $\text{NOT}$ a true of the graph shown in the given figure is

Identify which one of the following will $\text{NOT}$ satisfy the wave equation.

Indicate which one of the following will $\text{NOT}$ exist in a rectangular resonant cavity.

Assuming perfect conductors of a transmission line, pure $\text{TEM}$ propagation is $\text{NOT}$ possible in

An electric field on a plane is described by its potential $$\mathrm{V}=20\left(r^{-1}+r^{-2}\right)$$ where $r$ is the distance from the source. The field is due to

A modulated signal is given by $$s(t)=e^{-a t} \cos \left[\left(\omega_{c}+\Delta \omega\right) t\right] u(t),$$ where $a, \omega_{c}$ and $\Delta \omega$ are positive constants, and $\omega_{c} \gg \Delta \omega$. The complex envelope of $s(t)$ is given by

A modulated signal is given by, $$s(t)=m_{1}(t) \cos \left(2 \pi f_{c} t\right)+m_{2}(t) \sin \left(2 \pi f_{c} t\right)$$ where the baseband signal $m_{1}(t)$ and $m_{2}(t)$ have bandwidths of $10 \; \mathrm{kHz}$ and $15 \; \mathrm{kHz}$, respectively. The bandwidth of the modulated signal, in $\mathrm{kHz}$, is

The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by $$y(t)=(1 / 100) \cos \left(100 t-10^{-6}\right) \cos \left(10^{6} t-1.56\right)$$ The group delay $\left(t_{g}\right)$ and the phase delay $\left(t_{p}\right)$ in …

A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ is

The phase margin (in degrees) of a system having the loop transfer function $$\mathrm{G}(s) \mathrm{H}(s)=\frac{2 \sqrt{3}}{s(s+1)} \text{ is }$$

The system moded described by the state equations is $$\begin{array}{l} \mathrm{X}=\left[\begin{array}{cc} 0 & 1 \\ 2 & -3 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 1 \end{array}\right] u \\ \mathrm{Y}=\left[\begin{array}{ll} 1 & 1 \end{array}\right] x \end{array}$$

The gain margin (in $d \mathrm{B}$ ) of a system a having the loop transfer function $$\mathrm{G}(s) \mathrm{H}(s)=\frac{\sqrt{2}}{s(s+1)} \text{ is }$$

For a second-order system with the closed-loop transfer function $$T(s)=\frac{9}{s^{2}+4 s+9}$$ the settling time for $2$ - percent band, in seconds, is

The resolution of a $4$ - bit counting $\text{ADC}$ is $0.5$ volts. For an analog input of $6.6$ volts, the digital output of the $\text{ADC}$ will be

Commercially available $\text{ECL}$ gears use two ground lines and one negative supply in order to

A Darlington emitter - follower circuit is sometimes used in the output stage of a $\text{TTL}$ gate in order to

The logical expresion $y=\mathrm{A}+\overline{\mathrm{A}} \mathrm{B}$ is equivalent to

Crossover distortion behaviour is characteristic of

In the cascade amplifier shown in the given figure, if the common - emitter stage $\left(Q_{1}\right)$ has a transconductance $\mathrm{gm}_{1}$, and the common base stage $\left(Q_{2}\right)$ has a transconductance $\mathrm{gm}_{2^{\prime}}$, then the overall transconductance $g\left(=i_{0} / v_{1}\right)$ of the cascade amplifier is

Negative feedback in an amplifier