GATE EC question library

A four-variable Boolean function is realized using $4\times 1$ multiplexers as shown in the figure. The minimized expression for $\text{F(U,V,W,X)}$ is

A $2\times 2$ ROM array is built with the help of diodes as shown in the circuit below. Here $W0$ and $W1$ are signals that select the word lines and $B0$ and $B1$ are signals that are output of the sense amps based on the stored data corresponding to the bit lines during the read operation. …

The distance (in meters) a wave has to propagate in a medium having a skin depth of $0.1\:m$ so that the amplitude of the wave attenuates by $20\:dB$, is

A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{x}.$ The equation that describes the curve is

For the circuit given in the figure, the voltage $V_{c}$ (in volts) across the capacitor is

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) $0.5$ second after closing the switch is _______.

A $dc$ current of $26\:\mu A$ flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of $0.5\:nF$. Its neutral region resistances can be neglected. Assume that the room temperature thermal equivalent voltage is $26\:mV$. For …

An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node $A$, connected to the negative input of the op-amp as indicated in the figure is ________.

The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below: Here $\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.$ The value (accurate to two decimal places) of $\int ^{\infty }_{-\infty } \mid y( t ) \mid ^{2}dt$ is ________.

A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ where $Z$ has uniform probability density over the interval $(-1,1).\: X$ and $Z$ are independent. If the MAP rule based detector outputs $\hat{X}$ as …

For a unity feedback control system with the forward path transfer function $$G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}$$The peak resonant magnitude $M_{r}$ of the closed-loop frequency response is $2$. The corresponding value of the gain $\text{K}$ (correct to two decimal places) is _________.

The figure below shows the Bode magnitude and phase plots of a stable transfer function $G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.$ Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop is stable for $k < k_{0}.$ The maximum value of $k_{0}$ is _________.

In the circuit shown below, the $(W/L)$ value for $M_{2}$ is twice that for $M_{1}$. The two $\text{nMOS}$ transistors are otherwise identical. The threshold voltage $V_{T}$ for both transistors is $1.0\:V$. Note that $V_{GS}$ for $M_{2}$ must be $> 1.0\:V$. Current through the $\text{nMOS}$ transistors can be modeled as …

A solar cell of area $1.0\:cm^{2},$ operating at $1.0$ sun intensity, has a short circuit current of $20\: mA$, and an open circuit voltage of $0.65\: V$. Assuming room temperature operation and thermal equivalent voltage of $26\: mV$, the open circuit voltage (in volts, correct to two decimal places) at $0.2$ sun intensity is _________.

A junction is made between $p^{-Si}$ with doping density $N_{A1}=10^{15}cm^{-3}$ and $p^{Si}$ with doping density $N_{A2}=10^{17}cm^{-3}.$ Given: Boltzmann constant $k=1.38\times 10^{-23}J\cdot K^{-1},$ electronic charge $q=1.6\times 10^{-19}C$. Assume $\text{100}\%$ acceptor ionization. At room temperature $\left ( T=300 K \right ),$ the …

In the circuit shown below, a positive edge-triggered $D$ Flip-Flop is used for sampling input data $D_{in}$ using clock $CK$. The XOR gate output $3.3$ volts for logic HIGH and $0$ volts for logic LOW levels. The data bit and clock periods are equal and the value of $\Delta T/T_{CK}=0.15,$ where the parameters $\Delta T$ and $T_{CK}$ are …

The logic gates shown in the digital circuit below use strong pull-down $\text{nMOS}$ transistors for LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are intentionally shorted to implement “wired logic”. Such shorted nodes will be HIGH …

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated at a frequency which is $25\%$ higher than the cutoff frequency of the dominant mode, the guide …

A uniform plane wave traveling in free space and having the electric field $$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \pi \times 10^{8}t-2\:\pi \left ( x+\sqrt{2} \:z\right )\right ]V/m$$ is incident on a dielectric medium (relative permittivity $>1$, relative permeability $=1$) as shown in the …

The position of a particle $y\left ( t \right )$ is described by the differential equation: $$\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$$ The initial conditions are $y\left ( 0 \right )=1$ and $\frac{dy}{dt}\mid_{t=0}=0$. The position (accurate to two decimal places) of the particle at $t=\pi$ is _________.