GATE EC question library

Which of the following cannot be the Fourier series expansion of a periodic signal ?

Convolution of $x(t+5)$ with impulse function $\delta(t-7)$ is equal to

In given figure $1.2,$ the switch was closed for a long time before opening at $t=0$. The voltage $V x$ at $t=0^{+}$ is

The dependent current source shown in given figure.

A person with a receiver is $5 \; \mathrm{Km}$ away from the transmitter. What is the distance that this person must move further to detect a $3-d B$ decrease in signal strength?

The electric field on the surface of a perfect conductor is $2 \mathrm{~Vm}$. The conductor is immersed in water with $\epsilon=80 \epsilon_{0}$. The surface charge density on the conductor is $\left(\epsilon_{0}=10^{-4} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

Distilled water at $25^{\circ} \mathrm{C}$ is characterized by $\sigma=1.7 \times 10^{-1} \mathrm{mho} / \mathrm{m}$ and $\epsilon=78 \; \epsilon_{0}$ at a frequency of $3 \; \mathrm{GHz}.$ Its loss tangent $\tan\delta$ is $\left(\epsilon=10^{-9} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

A plane wave is characterized by $\overline{\mathrm{E}}=\left(0.5 \hat{x}+\hat{y} e^{jz} / 2 \right)e^{jzet – jkz}.$ This wave is

If the variance $\sigma_{x}^{2}$ of $d(n)=x(n)-x(n-1)$ is one-tenth the variance $\sigma_{x}^{2}$ of a stationary zero-mean discrete-time signal $x(n)$, then the normalized autocorrelation function $R_{x x}(k) / \sigma_{x}^{2}$ at $k=1$ is

A signal $x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t$ is ideally sampled with a sampling period of $50 \; \mu \mathrm{sec}$ and then passed through an ideal lowpass filter with cut-off frequency of $15 \; \mathrm{kHz}$. Which of the following frequencies is/are present at the filter output?

In the figure $m(t)=\frac{2 \sin 2 \pi t}{t}, s(t)=\cos 200 \pi t$ and $n(t)$ $=\frac{\sin 199 \pi t}{t}$. The output $y(t)$ will be

An angle-modulated signal is given by $s(t)=\cos 2 \pi\left(2 \times 10^{6} t+30 \sin 150 t+40 \cos 150 t\right)$.The maximum frequency and phase deviations of $s(t)$ are

The system with the open loop transfer function $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)=\frac{1}{s\left(s^{2}+s+1\right)}$ has a gain margin of

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