The value of x  for which all the Eigen–values of the matrix given below are real is

The magnitude and phase of the complex Fourier series coefficients ${\mathrm{a}}_{\mathrm{K}}$ of a periodic signal $\mathrm{x}\left(\mathrm{t}\right)$ are shown in the figure. Choose the correct statement form the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set purely imaginary numbers.

The voltage (V_C) across the capacitor (in Volts) in the network shown is ______

In the circuit shown the average value of the voltage ${\mathrm{V}}_{\mathrm{a}\mathrm{b}}$ (in volts) in steady state condition is _____________.

The 2-port admittance matrix of the circuit shown is given by

A piece of silicon is doped uniformly with phosphorus with a doping concentration of ${10}^{16}/\mathrm{c}{\mathrm{m}}^3.$ The expected value of mobility versus doping concentration for silicon full dopant ionization is shown below. The Charge of an electron is $1.6\times {10}^{-19}\mathrm{C}$. The conductivity $\left(\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{c}{\mathrm{m}}^{-1}\right)$ of the silicon sample at $300\mathrm{K}$ is_________

If the circuit shown has to function as a clamping circuit, which one of the following conditions should be satisfied for sinusoidal signal of period T?

In the circuit shown, V₀ = V_0A for switch SW in position A and V₀ = V_0B for SW in position B. Assume that the Op-Amp is ideal. The value of $\frac{{\mathrm{V}}_{0\mathrm{B}}}{{\mathrm{V}}_{0\mathrm{A}}}$ is ______.

In the bistable circuit shown, the ideal Op-Amp has a saturation level of ± 5V. The value of R₁(in k Ω) that gives a hysteresis width of 500 mV is __________.

In the figure shown, the output Y is required to be Y = A.B + C̅.D̅. The gates G₁ and G₂ must be respectively.

A mod–n counter using a synchronous binary up–counter with synchronous clear input is shown in the figure. The value of n is_________.

For the signal flow Graph shown in the figure, the value of $\frac{\mathrm{C}\left(\mathrm{s}\right)}{\mathrm{R}\left(\mathrm{s}\right)}$  is

A unity negative feedback system has an open loop transfer function,

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}}{\mathrm{s}\left(\mathrm{s}+10\right)}$

The gain K for which the system to have damping ratio of $0.25$ is_________.

The signal $\cos \left(10\pi \mathrm{t}+\frac{\pi }{4}\right)$ is ideally sampled at a sampling frequency of $15\mathrm{H}\mathrm{z}$. the sampled signal is passed through a filter with impulse response

The electric field of a uniform plane electromagnetic wave is

$\overrightarrow{\mathrm{E}}=\left({\overrightarrow{\mathrm{a}}}_{\mathrm{x}}+\mathrm{j}4{\overrightarrow{\mathrm{a}}}_{\mathrm{y}}\right)\exp \left[\mathrm{j}\left(2\pi \times {10}^7\mathrm{t}-0.2\mathrm{z}\right)\right]$

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a–b is ______________.

In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1V and 3V, 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 $10\mathrm{V}$ is applied across an n – type silicon bar having a rectangular cross - section and a length of $1\mathrm{c}\mathrm{m}$ as shown in figure. The donor doping concentration ${\mathrm{N}}_{\mathrm{D}}$ and the mobility of electrons ${\mu }_{\mathrm{n}}$ are ${10}^{-16}\mathrm{c}{\mathrm{m}}^{-3}$ and $1000\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1},$ respectively. The average time (in μsec) taken by the electrons to move from one end of the bar to other end is____________

The energy band diagram and the electron density profile n(x) in a semiconductor are shown in the figures. Assume that $\mathrm{n}\left(\mathrm{x}\right)={10}_{\mathrm{e}}^{15}\left(\frac{\mathrm{q}\mathrm{a}\mathrm{x}}{\mathrm{k}\mathrm{T}}\right)\mathrm{c}{\mathrm{m}}^{-3}$, with $\alpha =0.1\mathrm{V}/\mathrm{c}\mathrm{m}$ and x expressed in cm. Given $\frac{\mathrm{k}\mathrm{T}}{\mathrm{q}}=0.026\mathrm{V},{\mathrm{D}}_{\mathrm{n}}=36\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1},\mathrm{a}\mathrm{n}\mathrm{d}\frac{\mathrm{D}}{\mu }=\frac{\mathrm{k}\mathrm{T}}{\mathrm{q}}$. The electron current density (in A/cm²) at x = 0 is

The figure shows a binary counter with synchronous clear input with the decoding logic shown, the counter works as a

A 1 to 8 demultiplexer with data input ${\mathrm{D}}_{\mathrm{i}\mathrm{n}}$, address inputs ${\mathrm{S}}_0,{\mathrm{S}}_1\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{S}}_2$, (with ${\mathrm{S}}_0$ as the LSB) and ${\overline{\mathrm{Y}}}_0\mathrm{t}\mathrm{o}{\overline{\mathrm{Y}}}_7$ as the eight de-multiplexed output, is to be designed using two 2 to 4 decoders (with enable input $\overline{\mathrm{E}}$ and address input ${\mathrm{A}}_0\mathrm{a}\mathrm{n}\mathrm{d}{A}_1$) as shown in the figure. ${\mathrm{D}}_{\mathrm{i}\mathrm{n}},{\mathrm{S}}_0,{\mathrm{S}}_1,\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{S}}_2$ are to be connected to $\mathrm{P},\mathrm{Q},\mathrm{R},\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{S}$, but not necessarily in this order. The respective input connections to $\mathrm{P},\mathrm{Q},\mathrm{R}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{S}$ terminals should be

The diode in the circuit given below has V_ON = 0.7V but is ideal otherwise. The current (in mA) in the 4k Ω resistor is __________.

Assuming that the Op-Amp in the circuit shown below is ideal, the output voltage V₀ (in volts) is ___________________

For the voltage regulator circuit shown, the input voltage (V_in) is 20 V ± 20% and the regulated output voltage (V_out) is 10 V. Assume the opamp to be ideal. For a load R_L drawing 200 mA, the maximum power dissipation in Q₁ (in Watts) is _________.

In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical parameters with β ≫ 1 . The open circuit small signal voltage gain is approximately ________________________

The state variable representation of a system is given as

$\begin{array}{l}\dot{\mathrm{x}}=\left[\begin{array}{cc}0& 1\\ 0& -1\end{array}\right]\mathrm{x};\mathrm{x}\left(0\right)=\left[\begin{array}{c}1\\ 0\end{array}\right]\\ \mathrm{y}=\left[\begin{array}{cc}0& 1\end{array}\right]\mathrm{x}\end{array}$

The output of a standard second – order systems for a unit step input is given as

$\mathrm{y}\left(\mathrm{t}\right)=1-\frac{2}{\sqrt{3}}{\mathrm{e}}^{-\mathrm{t}}\cos \left(\sqrt{3\mathrm{t}}-\frac{\pi }{6}\right)$

The transfer function of a mass – spring – damper system is given by

$\mathrm{G}\left(\mathrm{s}\right)=\frac{1}{\mathrm{M}{\mathrm{s}}^2+\mathrm{B}\mathrm{s}+\mathrm{K}}$

The frequency response data for the system are given in the following table.

A zero mean white Gaussian noise having power spectral density $\frac{{\mathrm{N}}_0}{2}$ is passed through an LTI filter whose impulse response $\mathrm{h}\left(\mathrm{t}\right)$ is shown in the figure. The variance of the filtered noise at $\mathrm{t}=4$ is

Two half – wave dipole antennas placed as shown in the figure are excited with sinusoidal varying current of frequency $3\mathrm{M}\mathrm{H}\mathrm{z}$ and phase shift of π/2 between them (the element at the origin leads in phase.) If the maximum radiated E – field at the point P in the x-y plane occurs at an azimuthal angle of 60°, the distance $\mathrm{d}$ (in meters) between the antennas is__________

The electric field of a plane wave propagation in a lossless non – magnetic medium is given by the following expression

$\mathrm{E}\left(\mathrm{z},\mathrm{t}\right)={\hat{\mathrm{a}}}_{\mathrm{x}}5\cos \left(2\pi \times {10}^9\mathrm{t}+\beta \mathrm{z}\right)+{\hat{\mathrm{a}}}_{\mathrm{y}}3\cos \left(2\pi \times {10}^9\mathrm{t}+\beta \mathrm{z}-\frac{\pi }{2}\right)$

The type of the polarization is