GATE EC question library

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

Let $x(t)= \cos(10\pi t)+\cos(30\pi t)$ be sampled at $20 Hz$ and reconstructed using an ideal low-pass filter with cut-off frequency of $20 Hz$. The frequency/frequencies present in the reconstructed signal is/are

For an all-pass system $H(z)= \frac{(z^{-1}-b)}{(1-az^{-1})}$, where $\mid H(e^{-j\omega }) \mid= 1,$ for all $\omega$. If $\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,$then $b$ equals

A modulated signal is $y(t)= m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ KHz only. The minimum required rate (in KHz) at which $y(t)$ should be sampled to recover $m(t)$ is _______.

Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is

The input $-3e^{2t}u(t),$ where $u(t)$ is the unit step function, is applied to a system with transfer function $\frac{s-2}{s+3}.$ If the initial value of the output is $-2$, then the value of the output at steady state is _______.

The phase response of a passband waveform at the receiver is given by $$\varphi (f)= -2\pi \alpha (f-f_{c})-2\pi \beta f_{c}$$ where $f_{c}$ is the centre frequency, and $\alpha$ and $\beta$ are positive constants. The actual signal propagation delay from the transmitter to receiver is

Consider an $FM$ signal $f(t)= \cos\left [ 2\pi f_{c} t+\beta _{1}\sin2\pi f_{1}t+\beta _{2}\sin2\pi f_{2}t\right ].$ The maximum deviation of the instantaneous frequency from the carrier frequency $f_{c}$ is

Consider an air filled rectangular waveguide with a cross-section of $5 \: cm \times 3 \: cm$. For this waveguide, the cut-off frequency (in MHz) of $TE_{21}$ mode is __________.

In the following figure, the transmitter $Tx$ sends a wideband modulated $RF$ signal via a coaxial cable to the receiver $Rx$. The output impedance $Z_{T}$ of $Tx$, the characteristic impedance $Z_{0}$ of the cable and the input impedance $Z_{R}$ of $Rx$ are all real. Which one of the following statements is TRUE about the distortion of the …

The maximum value of $f(x)$= $2x^{3}$ – $9x^{2}$ + $12x – 3$ in the interval $0\leq x\leq 3$ is _______.

Which one of the following statements is NOT true for a square matrix $A$?

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .

Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2}\leq X_{3}\right \}$ is _________.

Consider the building block called ‘Network N’ shown in the figure. Let $C= 100\mu F$ and $R= 10 k \Omega.$ Two such blocks are connected in cascade, as shown in the figure. The transfer function $\frac{V_{3}(s)}{V_{1}(s)}$ of the cascaded network is

In the circuit shown in the figure, the value of node voltage $V_{2}$ is

In the circuit shown in the figure, the angular frequency $\omega$ (in rad/s), at which the Norton equivalent impedance as seen from terminals $b-b'$ is purely resistive, is ________.

For the $Y$-network shown in the figure, the value of $R_{1}$ (in $\Omega$) in the equivalent $\Delta$-network is __________.

The donor and accepter impurities in an abrupt junction silicon diode are $1\times 10^{16} cm^{-3}$ and $5\times 10^{18}$$cm^{-3}$, respectively. Assume that the intrinsic carrier concentration in silicon $n_{i}= 1.5\times 10^{10}cm^{-3}$ at $300K, \frac{kT}{q}= 26$ $mV$ and the permittivity of silicon $\epsilon _{si}= 1.04\times 10^{-12}F/cm.$ …

The slope of the $I_{D}$ vs. $V_{GS}$ curve of an n-channel MOSEFT in linear regime is $10^{-3}\Omega ^{-1}$ at $V_{DS}= 0.1 \: V$. For the same device, neglecting channel length modulation, the slope of the $\sqrt{I_{D} }$ vs. $V_{GS}$ curve (in $\sqrt{A}/V$) under saturation regime is approximately _________.