GATE EC question library

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

The minimized form of the logical expression $(\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+\bar{A} B C+A B \bar{C})$ is

An amplifier is assumed to have a single-pole high-frequency transfer function. The rise time of its output response to a step function input is $35\;\text{nsec}$. The upper $-3 \; d B$ frequency (in $\text{MHz}$) for the amplifier to a sinusoidal input is approximately at

A $\text{dc}$ power supply has a no-load voltage if $30 \mathrm{~V}$, and a full-load voltage of $25 \mathrm{~V}$ at a full - load current of $1 \mathrm{~A}$. Its output resistance and load regulation, respectively, are

An amplifier has an open-loop gain of $100$, an input impedance of $1 \; \mathrm{k \Omega}$, and an output impedance of $100 \; \Omega$. A feedback network with a feedback factor of $0.99$ is connected to the amplifier in a voltage series feedback mode. The new input and output impedances, respectively, are

An $\text{npn}$ transistor (with $\mathrm{C}=0.3 \; \mathrm{pF}$ ) has a unity gain cutoff frequency $f_{\mathrm{T}}$ of $400 \; \mathrm{MHz}$ at a $\text{dc}$ bias current $I_{c}=1 \mathrm{~mA}$. The value of its $C_{\mu}$ (in $\mathrm{~pF}$ ) is approximately $\left(\mathrm{V}_{\mathrm{T}}=26 \; \mathrm{mV}\right)$

An $n$-channel $\text{JEFT}$ has $\mathrm{I}_{\mathrm{DSS}}=2 \mathrm{~mA}$ and $\mathrm{V}_{p}=-4 \mathrm{~V}$. Its transconductance $\mathrm{gm}$ (in milliohm) for an applied gate-to-source voltage $\mathrm{V}_{\mathrm{GS}}$ of $-2 \mathrm{~V}$ is

A Delta-connected network with its Wye-equivalent is shown in the given figure is. The resistances $R_{1}, R_{2}$ and $R_{3}$ (in ohms) are respectively

The Thevenin equivalent voltage $\mathrm{V}_{\mathrm{TH}}$ appearing between the terminals $A$ and $B$ of the network shown in the given figure is given by

The Fourier series representation of an impules train denoted by $$s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text{ is given by }$$

The units of $\frac{q}{k T}$ are