GATE EC question library

The magnetic field intensity vector of a plane wave is given by $\overline{\mathrm{H}}(x, y, z, t)=10 \sin \left(50000 t+0.004 x+30 \; \hat{a}_{y}\right)$, where $\hat{a}_{y}$ denotes the unit vector in $y$ direction. The wave is propagating with a phase velocity

Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure represent

Refractive index of glass is $1.5.$ Find the wavelength of a beam of light with a frequency of $10^{14} \mathrm{~Hz}$ in glass. Assume velocity of light is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ in vacuum.

In what range should $\operatorname{Re}(s)$ remain so that the Laplace transform of the function $e^{(n+2)t+5}$ exits?

Given the matrix $\left[\begin{array}{cc}-4 & 2 \\ 4 & 3\end{array}\right]$, the eigenvector is

Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right]$ Then $(a+b)=$

The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is

Match the following and choose the correct combination: …

Given an orthogonal matrix $A=\left[\begin{array}{cccc}1 & 1 & 1 & 1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{array}\right]$ $\left[\mathrm{AA}^{\mathrm{T}}\right]^{-1}$ is

For the circuit show in the figure, the instantaneous current $i_{i}(t)$ is

Impedance $\mathrm{Z}$ as shown in the given figure is

For the circuit shown in the figure, Thevenin's voltage and Thevenin's equivalent resistance atterminals $a-b$ is

If $R_{1}=R_{2}=R_{4}=R$ and $R_{3}=1.1 R$ in the bridge circuit shown in the figure, then the reading in the ideal voltmeter connected between $a$ and $b$ is

The $h$ parameters of the circuit shown in the figure are

A square pulse of $3$ volts amplitude is applied to $C-R$ circuit shown in the figure. The capacitor is initially uncharged. The output voltage $\mathrm{V}_{0}$ at time $t=2 \mathrm{sec}$ is

A Silicon sample $\mathrm{A}$ is doped with $10^{18}$ atoms $/ \mathrm{cm}^{3}$ of Boron. Another sample $\mathrm{B}$ of identical dimensions is doped with $10^{18}$ atoms $/ \mathrm{cm}^{3}$ of Phosphorus. The ratio of electron to hole mobility is $3.$ The ratio of conductivity of the sample $\mathrm{A}$ to $\mathrm{B}$ is

A Silicon PN junction diode under reverse bias has depletion region of width $10 \; \mu \mathrm{m}$. The relative permittivity of Silicon,$\varepsilon_{r}=11.7$ and the permittiveity of free space $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{~F/m}$. The depletion capacitance of the diode per square meter is

For an $\text{npn}$ transistor connected as shown in the figure, $V_{B E}=0.7$ volts. Given that reverse saturation current of the junction at room temperature $300^{\circ} \mathrm{K}$ is $10^{-13} \mathrm{~A}$, the emitter current is

The voltage $e_{0}$ indicated in the figure has been measured by an ideal voltmeter. Which of the following can be calculated?

The $\text{OP-amp}$ circuit shown in the figure is a filter. The type of filter and its cut-off frequency are respectively