GATE EC question library

Medium $1$ has the electrical permittivity $\varepsilon_{1}=1.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the left of $x=0$ plane. Medium $2$ has the electrical permittivity $\varepsilon_{2}=2.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the right of $x=0$ plane. If $\mathrm{E}_{1}$ in medium …

If the electric field intensity is given by $$\mathrm{E}=\left(x u_{x}+y u_{y}+z u_{z}\right) \text{ volt } / \mathrm{m} \text{, }$$ the potential difference between $X(2,0,0)$ and $Y(1,2,3)$ is

A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with $\varepsilon_{r}=4$. The reflection coefficient for the normal incidence, is

If the electric field intensity associated with a uniform plane electromagnetic wave travelling in a perfect dielectric medium is given by $E(z, t)=10 \cos \left(2 \pi \times 10^{7} t=0.1 \pi z\right)$ volt $/ \mathrm{m}$, then the velocity of the travelling wave is

A short-circuited stub is shunt connected to a transmission line as shown in the figure is. If $Z_{0}=50 \mathrm{ohm}$, the admittance $Y$ seen at the junction of the stub and the transmission line is

A rectangular metal wave guide filled with a dielectric material of relative permittivity $\varepsilon_{r}=4$ has the inside dimensions $3.0 \mathrm{~cm} \times 1.2 \mathrm{~cm}$. The cut-off frequency for the dominant mode is

Two identical antennas are placed in the $\theta=\pi / 2$ plane as shown in the figure. The elements have equal amplitude excitation with $180^{\circ}$ polarity difference, operating at wavelength $\lambda$. The correct value of the magnitude of the far-zone resultant electric field strength normalized with that of a single element, both computed for …

The phase velocity for the $\mathrm{TE}_{10}$ – mode in an air-filled rectangular waveguide is ( $c$ is the velocity of plane waves in free space)

In an impedance Smith chart, a clockwise movement along a constant resistance circle gives rise to

The $\text{VSWR}$ can have any value between

The line-of-sight communication requires the transmit and receive antennas to face each other. If the transmit antenna is vertically polarized, for best reception the receive antenna should be

For a bit-rate of $8 \; \mathrm{kbps}$, the best possible values of the transmitted frequencies in a coherent binary FSK system are

Consider a sampled signal $y(t)=5 \times 10^{\circ}$ ${ }^6 x(t) \sum_{(n-\infty}^{+\infty} \delta \left(t-n \mathrm{T}_x\right)$ where $x(t)=10 \cos \left(8 \pi \times 10^3\right) t$ and $T_s=100 \; \mu \mathrm{sec}$. When $y(t)$ is passed through an ideal lowpass filter with a cut-off frequency of 5 $\mathrm{kHz}$, the output of the filter is

A $1 \; \mathrm{MHz}$ sinusoidal carrier is amplitude modulated by a symmetrical square wave of period $100 \; \mu \mathrm{sec}$. Which of the following frequencies will NOT be present in the modulated signal?

A linear phase channel with phase delay $T_p$ and group delay $T_g$ must have ($f$ denotes frequency)

The Fourier transform $\mathrm{F}\left\{e^{-t} u(t)\right\}$ is equal to $\frac{1}{1+j 2 \pi f}$. Therefore, $\mathrm{F}\left\{\frac{1}{1+j 2 \pi t}\right\}$ is

The transfer function $\mathrm{Y}(s) / \mathrm{U}(\mathrm{s})$ of a system described by the state equations $x(t)=-2 x(t)+2 u(t)$ and $y(t)=0.5 x(t)$ is

The phase margin of a system with the open-loop transfer function $\mathrm{G}(s) \mathrm{H}(s)=\frac{(1-s)}{(1+s)(2+s)}$ is

Which of the following points is NOT on the root locus of a system with the open-loop transfer function $\mathrm{G}(s) \mathrm{H}(s)=\frac{k}{s(s+1)(s+3)}$

Consider a system with the transfer function $G(s)=\frac{s+6}{k s^2+s+6}$. Its damping ratio will be $0.5$ when the value of $k$ is