Recent questions and answers

The eigenvalues of a skew-symmetric matrix arealways zeroalways pure imaginaryeither zero or pure imaginaryalways real

All the four entries of the $2 \times 2$ matrix $\mathbf{P}=\left[\begin{array}{ll}p_{11} & p_{12} \\ p_{21} & p_{22}\end{array}\right]$ are nonzero, and one of its eigen...

Consider a system where $x_{1}(t), x_{2}(t)$, and $x_{3}(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the sys...

Consider the matrix $A$ below:$$A=\left[\begin{array}{llll}2 & 3 & 4 & 5 \\0 & 6 & 7 & 8 \\0 & 0 & \alpha & \beta \\0 & 0 & 0 & \gamma\end{array}\right]$$For which of the...

Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where $W$ is in $\mathrm{Hz}$ . Consider the following two modulation schemes for the message signal:D...

In a huge pile of apples and oranges, both ripe and unripe mixed together,$15\%$ are unripe fruits. Of the unripe fruits, $45 \%$ are apples. Of the ripe ones, $66 \%$ ar...

The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system in the figure.If $G(s)H(s)$ has one zero in the right-half of the $s$...

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_{1}[n]$ and $h_{2}[n]$ denote the impulse responses of LTI Subsystems $1$ a...

In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is$36$ Joules$16$ Joules$256$ JoulesNone of the above

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is $20 \%$ of the consultin...

A simplified small-signal equivalent circuit of a BJT-based amplifier is given below.The small-signal voltage gain $V_{o} / V_{S}$ (in $\mathrm{V} / \mathrm{V})$ is $\_\_...

Which of the following can be used as an n-type dopant for silicon?Select the correct option(s).ArsenicBoronGalliumPhosphorous

The probability that an electron in a metal occupies the Fermi-level at any temperature $(>0 \mathrm{~K})$$0$$1$$0.5$$1.0$

​​​​A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system wi...

A message signal having peak-to-peak value of $2\:V$, root mean square value of $0.1\:V$ and bandwidth of $\text{5 kHz}$ is sampled and fed to a pulse code modulation ($\...

Assume you are using a binary code error correcting code $C$. If the minimum Hamming distance between any two codewords of $C$ is $3$. ThenWe can correct and detect $2$ b...

Consider an additive white Gaussian noise (AWGN) channel with bandwidth $W$ and noise power spectral density $\frac{N_{0}}{2}$. Let $P_{a v}$ denote the average transmit ...

The generator matrix of a $(6,3)$ binary linear block code is given by$$G=\left[\begin{array}{llllll} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 ...

The Nyquist plot of a system is given in the figure below. Let $\omega_{P}, \omega_{Q}, \omega_{R}$, and $\omega_{S}$ be the positive frequencies at the points $\boldsymb...

The periodic modulating signal $m(t)$ is shown in the figure. Using Carson's rule. estimate $B_{F M}$ (bandwidth of the FM signal) and $B_{P M}$ (bandwidth of the PM sign...

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3 \Omega$ resistor are as indicated.The voltage (in Volt...

A full adder and an XOR gate are used to design a digital circuit with inputs $X, Y$, and $Z$, and output $F$, as shown below. The input $Z$ is connected to the carry-in ...

Decimal $43$ in Hexadecimal and $\text{BCD}$ number system is respectively$\text{B2, 01000011}$$\text{2B, 01000011}$$\text{2B, 00110100}$$\text{B2, 0100 0100}$

In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).

Let $x[n]$ and $y[n]$ be the input and output of a linear time invariant $\text{(LTI)}$ system. Then which of following system is $\text{LTI}$.$z[n]=y[n]+c$ for a constan...

$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by:$$ \begin{array}{l} P(X=0, ...

The exports and imports (in crores of $Rs$.) of a country from $2000$ to $2007$ are given in the following bar chart. If the trade deficit is defined as excess of imports...

The units of $\frac{q}{k T}$ are$\mathrm{V} $$\mathrm{V}^{-1}$$\mathrm{J} $$\mathrm{J} / \mathrm{K}$

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=\int_{-\infty}^{\infty} f(t) \exp (-j \: \omega t) d t$ exists.Which one of the f...

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration $n$ ' is:Note: The figures shown ...

A video transmission system transmits $625$ picture frames per second. Each frame consists of a $400 \times 400$ pixel grid with $64$ intensity levels per pixel. The data...

If $137+276=435$ how much is $731+672?$ $534$$1403$$1623$$1513$

​​​​​A $4$-bit priority encoder has inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$ in descending order of priority. The two-bit output $A B$ is generated as $00,01,10$, and 11...

Read the statements:All women are entrepreneurs.Some women are doctors.Which of the following conclusions can be logically inferred from the above statements?All women ar...

Here are two analogous groups, Group-$I$ and Group-$II$, that list words in their decreasing order of intensity. Identify the missing word in Group-$II$.Group-$I$: Abuse ...

The value of $$\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$$ is$\text{ln }2$$1.0$$e$$\infty$

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balanc...