Recent questions tagged gate2015-ec-1

The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in thefirst quadrantsecond quadrantthird quadrantfourth quadran...

A sinusoidal signal of $2$ kHz frequency is applied to a delta modulator. The sampling rate and step-size $\Delta$ of the data modulator are $20,000$ samples per second a...

Consider the signal $s(t)=m(t) \cos(2 \pi \: f_ct)+ \hat{m}(t) \sin(2 \pi f_c t)$ where $\hat{m}(t)$ denotes the Hilbert transform of $m(t)$ and the bandwidth of $m(t)$ i...

Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the depe...

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\overrightarrow{E}(z,t) = \hat{a}_y 2 \cos \bigg( 10^st-\frac{z}{\sqr...

The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is$(2-t)e^t$$(1+2t)e^{-t}$$(2+t)e^{-t}$$(1-2t)e^t$

A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x – x^2y^2\overrightarrow{a}_y – x^2 yz \overrightarrow{a}_z$. Which one of the sta...

Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?

The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.

The damping ratio of a series RLC circuit can be expressed as$\frac{R^2C}{2L} \\$$\frac{2L}{R^2C} \\$$\frac{R}{2} \sqrt{\frac{C}{L}} \\$$\frac{2}{R} \sqrt{\frac{L}{C}}$

In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.

In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.

The built-in potential of an abrupt p-n junction is $0.75$ V. If its junction capacitance $(C_J)$ at a reverse bias $(V_R)$ of $1.25 \: V$ is $5$ pF, the value of $C_J$ (...

A MOSFET in saturation has a drain current of $1$ mA for $V_{DS} =0.5 \: V$. If the channel length modulation coefficient is $0.05 \: V^{-1}$, the output resistance (in $...

For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are $1 \times 10^{17} \:cm^{-3}$ and $1 \times 10^{15} \: cm^{-3}$, respecti...

The Boolean expression $F(X,Y,Z) = \overline{X} \: Y \: \overline{Z}+ X \: \overline{Y} \: \overline{Z}+ X \: Y \: \overline{Z} + X \: Y \: Z$ converted into the canonica...

All the logic gates shown in the figure have a propagation delay of $20$ ns. Let $A=C=0$ and $B=1$ until time $t=0$. At $t=0$, all the inputs flip (i.e., $A=C=1$ and $B=0...

For the NMOSFET in the circuit shown, the threshold voltage is $V_{th}$, where $V_{th}>0$. The source voltage $V_{SS}$ is varied from $0$ to $V_{DD}$. Neglecting the chan...

In the circuit shown, assume that the opamp is ideal. The bridge output voltage $V_0$ (in mV) for $\delta=0.05$ is __________

The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are$\frac{1}{CR}$ and $R_1=R_2 ...

In the circuit shown, $I_1=80$ mA and $I_2=4$ mA. Transistors $T_1$ and $T_2$ are identical. Assume that the thermal voltage $V_T$ is $26$ mV at $27^{\circ}C$. At $50^{\c...

Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ are related as,$$\begin{bmatrix}A \\ B \\ C \end{bmatrix} = \be...

For the discrete-time system shown in the figure, the poles of the system transfer function are located at$2,3 \\$$\frac{1}{2},3 \\$$\frac{1}{2}, \frac{1}{3} \\$$2, \frac...

The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity $4$. The impulse response of the system ...

The open-loop transfer function of a plant in a unity feedback configuration is given as $G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}$. The value of the gain $K(>0)$ for which $-1...

A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}...

A plant transfer function is given as $G(s)= \bigg( K_p+ \frac{K_1}{s} \bigg) \frac{1}{s(s+2)}$. When the plant operates in a unity feedback configuration, the condition ...

The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The cross-over probability is $1/7$. If the received bit $Y=0$, t...

A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides ...