GATE EC question library

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_{1}$ of the first section to the input impedance $Z_{2}$ of the second section is

Consider the configuration shown in the figure which is a portion of a larger electrical network For $R = 1\: \Omega$ and currents $i_{1} = 2A,i_{4} = -1A,i_{5} = -4A,$ which one of the following is $\textbf{TRUE}?$

When the optical power incident on a photodiode is $10\:\mu W$ and the responsivity is $0.8\: A/ W,$ the photocurrent generated $(\text{in} \:\mu A)$ is_______.

In the figure, assume that the forward voltage drops of the $PN$ diode $D_{1}$ and Schottky diode $D_{2}$ are $0.7\: V$ and $0.3\: V,$ respectively. If ON denotes conducting state of the diode and OFF denotes non-conducting state of the diode, then in the circuit,

If fixed positive charges are present in the gate oxide of an $n$-channel enhancement type MOSFET, it will lead to

A good current buffer has

In the ac equivalent circuit shown in the figure, if $i_{in}$ is the input current and $R_{F}$ is very large, the type of feedback is

In the low-pass filter shown in the figure, for a cut-off frequency of $5\:kHz,$ the value of $R_{2}\:(\text{in}\:k\Omega)$ is ______.

In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of $1\: V.$ Ignoring the body-effect, the output voltage at $P,Q$ and $R$ are,

The Boolean expression $(X+Y)(X+\overline{Y}) + \overline{(X\;\overline{Y}) + \overline{X}}$ simplifies to

Five JK flip-flops are cascaded to form the circuit shown in Figure. Clock pulses at a frequency of $1\: MHz$ are applied as shown. The frequency $(\text{in}\:kHz)$ of the waveform at $Q3$ is ________.

A discrete-time signal $x[n] = \sin(\pi^{2}n),n$ being an integer, is

Consider two real valued signals, $x(t)$ band-limited to $[-500\:Hz,500\:Hz]$ and $y(t)$ band-limited to $[-1\:kHz,1\:kHz].$ For $z(t) = x(t)\cdot y(t),$ the Nyquist sampling frequency (in $kHz$) is _______.

A continuous, linear time-invariant filter has an impulse response $h(t)$ described by $$h(t) = \begin{cases}3 & \text{for } 0 \leq t \leq 3 \\ 0 & \text{otherwise} \end{cases}$$ When a constant input of value $5$ is applied to this filter, the steady state output is ________.

The forward path transfer function of a unity negative feedback system is given by $$G(s) = \frac{K}{(s+2)(s-1)}$$. The value of $K$ which will place both the poles of the closed-loop system at the same location, is _______.

Consider the feedback system shown in the figure. The Nyquist plot of $G(s)$ is also shown. Which one of the following conclusions is correct?

In a code-division multiple access $(\text{CDMA})$ system with $N = 8$ chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is ________.

The capacity of a Binary Symmetric Channel $\text{(BSC)}$ with cross-over probability $0.5$ is ________.

A two-port network has scattering parameters given by $[S] = \begin{bmatrix}s_{11} &s_{12} \\s_{21} &s_{22} \end{bmatrix}.$ If the port-2 of the two-port is short circuited, the $s_{11}$ parameter for the resultant one-port network is

The force on a point charge $+q$ kept at a distance $d$ from the surface of an infinite grounded metal plate in a medium of permittivity $\epsilon\:$ is