GATE EC question library

The first dominant pole encountered in the frequency response of a compensated $\text{op - amp}$ is approximately at

The early effect in a bipolar junction transistor is caused by

A $2$-port network is shown in the given figure. The parameter $h_{21}$ for this network can be given by

If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to

The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{T})=a^{\prime \prime T}$ is

A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ has its electric field given by $\overrightarrow{\mathrm{E}}=0.5 \hat{\mathrm{X}} \mathrm{e}^{-(z / 3)} \sin \left(10^{8} t-\beta z\right) \mathrm{V} / \mathrm{m}$. The wave impedance, in ohms is

In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operated at $25 \; \mathrm{MHz}$. Its electrical path length is

A trasmitting antenna radiates $251 \mathrm{~W}$ isotropically. A receiving antenna, located $100 \mathrm{~m}$ away from the transmitting antenna, has an effective aperture of $500 \mathrm{~cm}^{2}$. The total received by the antenna is

In a twin-wire transmission line in air, the adjacent voltage maxima are at $12.5 \mathrm{~cm}$ and $27.5 \mathrm{~cm}$. The operating frequency is

Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed ($\text{TDM}$) and transmitted. The transmitted sample rate (in $\mathrm{Hz}$ ) is

The input to a matched filter is given by $s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} \mathrm{sec} \\ & \text{otherwise} \end{array}$ The peak amplitude of the filter output is

The peak-to-peak input to an $8$-bit $\text{PCM}$ coder is $2$ volts. The signal power-to-quantization noise power ratio (in $d\text{B}$) for an input of $0.5 \cos \left(\omega_{m} t\right)$ is

The Nyquist sampling frequency (in $\mathrm{Hz}$ ) of a signal given by $6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)$ is

The $z$-transform of a signal is given by $$C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}}$$ Its final value is

For the system described by the state equation $$x=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0.5 & 1 & 2 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right] u$$ If the control signal $u$ is given by $u=[-0.5-3-5]$ $x+v$, then the eigenvalues of the closed-loop system will be

Consider the points $s_{1}=-3+j 4$ and $s_{2}=-3-j 2$ in the $s$-plane. Then, for a system with the open-loop Transfer function $$G(s) H(s)=\frac{K}{(s+1)^{4}}$$

If the closed-loop transfer function $T(s)$ of a unity negative feedback system is given by $$\mathrm{T}(\mathrm{s})=\frac{a_{n -1} \mathrm{~s}+a_{n}}{\mathrm{~s}^{n}+n_{1} s^{n-1}+\ldots+a_{n-1} s+a_{n}}$$ then the steady state error for a unit ramp input is

If $\text{CS}=\text{A}_{15} \; \text{ A}_{14} \; \text{A}_{13}$ is used as the chip select logic of a $4 \; \text{K RAM}$ in an $8085$ system, then its memory range will be

The ripple counter shown in the given figure is works as a

For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical expressions for the outputs $\text{D}$ ( = $\text{A}$ minus $\text{B}$ ) and $\text{X}(=$ borrow) are