GATE EC question library

If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$?

For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$?

The partial derivative of the function $$f(x, y, z) = e^{1-x\cos y} + xze^{-1/(1+y^{2})}$$ with respect to $x$ at the point $(1,0,e)$ is

The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is

The output $y[n]$ of a discrete-time system for an input $x[n]$ is $$y\left [ n \right ]=\underset{-\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid$$ The unit impulse response of the system is

A single crystal intrinsic semiconductor is at a temperature of $300$ $\text{K}$ with effective density of states for holes twice that of electrons. The thermal voltage is $26$ mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by

Consider the recombination process via bulk traps in a forward biased $pn$ homojunction diode. The maximum recombination rate is $U_{\text{max}}$. If the electron and the hole capture cross-sections are equal, which one of the following is $\text{FALSE}$?

The components in the circuit shown below are ideal. If the op-amp is in positive feedback and the input voltage $V_{i}$ is a sine wave of amplitude $1$ $\text{V}$, the output voltage $V_{o}$ is

In the circuit shown below, the Thevenin voltage $V_{TH}$is

The figure below shows a multiplexer where $S_{1}$ and $S_{0}$ are the select lines, $I_{0}$ to $I_{3}$ are the input data lines, $\text{EN}$ is the enable line, and $\text{F(P, Q, R)}$ is the output. $\text{F}$ is

The pole-zero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into the $G(s)$-plane, then the mapping encircles

A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The probability that the received block erroneous is

The impedances $Z=jX,$ for all $X$ in the range $\left ( -\infty ,\infty \right )$, map to the Smith chart as

Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given below? $$y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$$

In the given circuit, the two-port network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.

The current in the $\text{RL}$-circuit shown below is $i\left ( t \right )=10\cos\left ( 5t-\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.

In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.

In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the op-amp is __________ $\text{mA}$.

In an $8085$ microprocessor, the number of address lines required to access a $16$ K byte memory bank is ____________ .

A $10$-bit D/A converter is calibrated over the full range from $0$ to $10$ V. If the input to the D/A converter is $13 \:A$ (in hex), the output ( rounded off to three decimal places) is __________ $V$.