GATE EC question library

The characteristic polynomial of a system is $q(s)=2 s^{5}+s^{4}+4 s^{3}+2 s^{2}+2 s+1$. The system is

The transfer function of a system is $\mathrm{G}(s)=\frac{100}{(s+1)(s+100)}$. For a unit-step input to the system the approximate settling time for $2 \%$ criterion is

The system shown in the figure is remains stable when

Consider the following assembly language program. …

If the input $X_{3}, X_{2}, X_{1}, X_{0}$ to the ROM in the figure are $8-4-2-1$ BCD numbers, then the outputs $Y_{3} Y_{2} Y_{1} Y_{0}$ are

Consider the following statements in connection with the CMOS inverter in the figure is where both the MOSFETs are of enhancement type and both have a thresh old voltage of $2 \mathrm{~V}$. Statement 1: $\mathrm{T}_{1}$ conducts when $\mathrm{V} i \geq 2 \mathrm{~V}$. Statement 2: $T_{1}$ is always in saturation when $\mathrm{V}_{0}=0 \mathrm{~V}$. …

The circuit in the figure is has two $\text{CMOS NOR}$-gates. This circuit functions as a

The voltage gain $\mathrm{A}_{u}=\frac{\mathrm{V}_{0}}{\mathrm{~V}_{i}}$ of the JFET amplifier shown in the figure is

A zener diode regulator in the figure is to be designed to meet the specifications: $I_{L}=10 \mathrm{~mA}$, $\mathrm{V}_{0}=10 \mathrm{~V}$ and $\mathrm{V}_{m}$ varies from $30 \mathrm{~V}$ to $50 \mathrm{~V}$. The zener diode has $V_{z}=10 \mathrm{~V}$ and $I_{z k}$ (knee current) $=1 \mathrm{~mA}$. For satisfactory operation.

The circuit in figure employs positive feedback and is intended to generate sinusoidal oscillation. If at a frequency $f_{0}, \mathrm{~B}(f)=\Delta \frac{V_{f}(f)}{V_{0}(f)}=\frac{1}{6} \angle 0^{\circ}$, then to sustain oscillation at this frequency

An amplifier using an opamp with a slew-rate $S R=1$ $V / \mu \mathrm{sec}$ has a gain of $40 \mathrm{~dB}$. If this amplifier has to faithfully amplify sinusoidal signals from dc to $20 \; \mathrm{kHz}$ without introducing any slew-rate induced distortion, then the input signal level must not exceed.

If the impulse response of a discrete-time system is $h[n]=-5^{n} u[-n-1]$, then the system function $\mathrm{H}(z)$ is equal to

The Laplace transform of a continuous-time signal $x(t)$ is $X(s)=\frac{5-s}{s^{2}-s-2}$. If the Fourier transform of this signal exists, then $x(t)$ is

If the $3$-phase balanced source in the figure is delivers $1500 \mathrm{~W}$ at a leading power factor of $0.844$, then the value of $Z_{L}$ (in ohm) is approximately

In the network of the figure is the maximum power is delivered to $R_{\mathrm{L}}$ if its value is

The dominant mode in a rectangular waveguide is $\text{TE10,}$ because this mode has

The phase velocity of waves propagating in a hollow metal waveguide is

If a plane electromagnetic wave satisfies the equation $\frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{z}^{2}}=\mathrm{c}^{2} \frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{t}^{2}}$, the wave propagates in the

A transmission line is distortionless if

If a signal $f(t)$ has energy $E$, the energy of the signal $f(2 t)$ is equal to