GATE EC question library

In the given circuit, $V_{0}$ is

In the differential amplifer of the figure, if the source resistance of the current source $I_{E E}$ is infinite, then the common-mode gain is

Given that $\mathcal{L}[f(t)]=\frac{s+2}{s^2+1}, \mathcal{L}[f(t)]=\frac{s^2+1}{(s+3)(s+2)},$ $h(t)=\int_0^1 f(\tau) g(t-\tau) d \tau, \mathcal{L}[h(t)]$ is

In the given circuit, the value of the voltage source $\mathrm{E}$ is

In the given circuit, the voltage $\text{v(t)}$ is

Two coaxial cables $1$ and $2$ are filled with different dielectric constants $\varepsilon_{r 1}$ and $\varepsilon_{r 2}$ respectively. The ratio of the wavelengths in the two cables, $\left(\lambda_{1} / \lambda_{2}\right)$ is

A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is

A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is

For an $8$ feet $(2.4 \mathrm{~m})$ parabolic dish antenna operating at $4 \; \mathrm{GHz}$, the minimum distance required for far field measurement is closest to

A uniform plane wave in air impinges at $45^{\circ}$ angle on a lossless dielectric material with dielectric constant $\varepsilon_{r}$. The transmitted wave propagates in a $30^{\circ}$ direction with respect to the normal. The value of $\varepsilon_{r}$ is

In an $\text{FM}$ system, a carrier of $100\; \mathrm{MHz}$ is modulated by a sinusoidal signal of $5 \; \mathrm{kHz}$. The bandwidth by Carson's approximation is $1 \; \mathrm{MHz}$. If $y(t)=(\text{modulated waveform})^{3}$, then by using Carson's approximation, the bandwidth of $y(t)$ around $300 \; \mathrm{MHz}$ and the spacing of spectral …

A system described by the transfer function $\mathrm{H}(s)=\frac{1}{s^{3}+\alpha s^{2}+k s+3}$ is stable. The constraints on $\alpha$ and $k$ are

A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ are respectively given by

The Hilbert transform of $\cos \omega_{1} t+\sin \omega_{2} t$ is

A message $m(t)$ bandlimited to the frequency $f_{m}$ has a power of $P_{m}$. The power of the output signal in given figure is

In a digital communication system employing Frequency Shift Keying $\text{(FSK)}$, the $0$ and $1$ bit are represented by sine waves of $10 \; \mathrm{kHz}$ and $25 \; \mathrm{kHz}$ respectively. These waveforms will be orthogonal for a bit interval of

In given figure, the steady state output voltage corresponding to the input voltage $3+4 \sin 100 t \mathrm{~V}$ is

One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$. for $n \geq 1, n$ odd, are respectively proportional to

In given figure, the $J$ and $K$ inputs of all the four Flip-Flips are made high. The frequency of the signal at output $Y$ is

The contents of Register $\text{(B)}$ and Accumulator $\text{(A)}$ of $8085$ microprocessor are $49 \mathrm{H}$ and $3 \mathrm{AH}$ respectively. The contents of $\mathrm{A}$ and the slatus of carry flag $(C Y)$ and sign flag $(S)$ after executing $\text{SUB B}$ instructions are