GATE EC question library

As $x$ is increased from $-\infty$ to $\infty$, the function $$f(x)=\frac{e^x}{1+e^x}$$

A two-port network is represented by $\text{ABCD}$ parameters given by $$\left[\begin{array}{c} \mathrm{V}_1 \\ \mathrm{I}_1 \end{array}\right]=\left[\begin{array}{ll} \mathrm{A} & \mathrm{B} \\ \mathrm{C} & \mathrm{D} \end{array}\right]\left[\begin{array}{c} \mathrm{V}_2 \\ -\mathrm{I}_2 \end{array}\right]$$ if port-$2$ is terminated by …

In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively

The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is

In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by

Consider two transfer functions $$\mathrm{G}_1(s)=\frac{1}{s^2+a s+b} \text{ and } \mathrm{G}_2(s)=\frac{s}{s^2+a s+b}$$ The $3\text{-dB}$ bandwidths of their frequency responses are, respectively

A negative resistance $R_{\text{neg }}$ is connected to a passive network $N$ having driving point impedance $Z_{1}$ (s) as shown below. For $Z_{2}(s)$ to be positive real,

In the circuit shown below, the switch wa connected to position $1$ at $t<0$ and at $t=0$, it is changed to position $2$. Assume that $y$ the diode has zero voltage drop and a storage time $t_{s}$. For $0 < t \leq t_{s}, \text{V}_{\text{R}}$ is given by (all in volts)

The majority carriers in an $n$-type semiconductor have an average drift velocity $\mathrm{V}$ in a direction perpendicular to a uniform magnetic field $\text{B}.$ The electric field $\mathrm{E}$ induced due to Hall effect acts in the direction

Find the correct match between Group $1$ and Group $2$ …

A heavily doped $n$-type semiconductor has the following data Hole-electron mobility ratio : $0.4$ Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$ Intrinsic concentration : $1.5 \times 10^{4} \; \mathrm{atoms/m}^{3}$ The ratio of conductance of the $n$-type semiconductor to that of the intrinsic semiconductor of same material and …

For the circuit shown in the following figure, the capacitor $C$ is initially uncharged. At $t=0$, the switch $S$ is closed. The voltage $V_{C}$ across the capacitor at $t=1$ millisecond is In the figure shown above, the $\text{OP AMP}$ is supplied with $\pm 15 \mathrm{~V}$ and the ground has been shown by the symbol $\nabla$.

A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-$5$ number is represented by tis corresponding $3$-bit binary code. For example, the base-$5$ number $24$ will be represented by its BCP code $010100.$ In this numbering system, the BCP code $100010011001$ corresponds to the following number in base-$5$ …

An $\frac{\mathrm{I}}{\mathrm{O}}$ peripheral device shown in Figure $(b)$ below is to be interfaced to an $8085$ microprocessor. To select the $\frac{\mathrm{I}}{\mathrm{O}}$ device in the $\frac{\mathrm{I}}{\mathrm{O}}$ address range $\mathrm{D} 4 \mathrm{H}-\mathrm{D} 7 \mathrm{H}$, its chip-select $(\overline{C S})$ should be connected to …

For the circuit shown in figure below, two $4$-bit parallel-in serial-out shift registers loaded with the data shown are used to feed the data to a full adder. Initially, all the flip-flops are in clear state. After applying two clock pulses, the outputs of the fulladder should be

Two $\text{D}$-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following $\mathrm{Q}_{1} \mathrm{Q}_{0}$ sequence $00 \longrightarrow 01 \longrightarrow 11 \longrightarrow 10 \longrightarrow 00 \longrightarrow \dots$ The inputs $D_{0}$ and $D_{1}$ respectively should be connected as

Following is the segment of a $8085$ assembly language program $\text{LXISP,EFFFH}$ $\text{CALL 3000 H}$ $3000 \mathrm{H}: \mathrm{LXIH}, 3 \mathrm{CF} 4 \mathrm{H}$ $\text{PUSH PSW}$ $\text{SPIH}$ $\text{POP PSW}$ $\text{RET}$ On completion of $\text{RET}$ execution, the contents of $\mathrm{SP}$ is

The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be

A signal $m(t)$ with bandwidth $500 \mathrm{~Hz}$ is first multiplied by a signal $g(t)$ where $$g(t)=\sum_{\mathrm{R}=-\infty}^{\infty}(-1)^{k} \delta\left(t-0.5 \times 10^{-4} k\right)$$ The resulting signal is then passed through an ideal lowpass filter with bandwidth $1 \; \mathrm{kHz}$. The output of the lowpass filter would be