Recent questions and answers

Under what conditions is the following inequality true for $a, b>0$$$\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))$$$\lambda=0.5$$0<a...

Two discrete time systems with impulse responses $h_t[n]=\delta[n-1]$ and $h_2[n]=\delta[n-2]$ are connected in cascade. The overall impulse response of the cascaded syst...

Assuming the $\text{OP-AMP}$ to be ideal. the voltage gain of the amplifier shown below is$-\frac{\mathrm{R}_2}{\mathrm{R}_1}$$-\frac{\mathrm{R}_3}{\mathrm{R}_1}$$-\left(...

For a parallel $\text{RLC}$ circuit, which one of the following statements is $\text{NOT}$ correct?The bandwidth of the circuit decreases if $\mathrm{R}$ is increasedThe ...

For the two-port network shown below, the short-circuit admittance parameter matrix is$\left[\begin{array}{cc}4 & -2 \\ -2 & 4\end{array}\right] \mathrm{S}$$\left[\begin{...

A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R,...

Two resistors are connected in a circuit loop of area $5 \mathrm{~m}^{2}$, as shown in the figure below. The circuit loop is placed on the $x-y$ plane.When a time-varying...

In the circuit below, $M_{1}$ is an ideal AC voltmeter and $M_{2}$ is an ideal AC ammeter. The source voltage (in Volts) is $v_{s}(t)=100 \cos (200 t)$.What should be the...

All the components in the bandpass filter given below are ideal. The lower $-3$ dB frequency of the filter is $1$ MHz.The upper $-3$ dB frequency (in MHz , rounded off to...

The number that least fits this set$:(324,441,97$ and $64)$ is$324$$441$$97$$64$

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic(a) Continuous, aperiod...

Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$. The system isCausal and time invariant.Non-causal and time varying.Causal and time varying.Non-...

​​​​A causal and stable $\text{LTI}$ system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5 t)$ is applied to another c...

A heavily doped $n$-type semiconductor has the following dataHole-electron mobility ratio : $0.4$Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$Intrins...

The concentration of minority carriers in an extrinsic semiconductor under equilibrium isdirectly proportional to the doping concentrationinversely proportional to the do...

In an abrupt $p-n$ junction, doping concentrations on $p$-side and $n$-side are $\mathrm{N}_{\mathrm{A}}=9 \times 10^{16} / \mathrm{cm}^{3}$ and $N_{0}=1 \times 10^{16} /...

The intrinsic carrier density at $300 \mathrm{~K}$ is $1.5 \times 10^{10}$ / $\mathrm{cm}^{3}$, in silicon. For $n$-type silicon doped to $2.25 \times$ $10^{15}$ atoms $/...

In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-...

A binary random variable $X$ takes the value of $1$ with probability $1/3$. $X$ is input to a cascade of $2$ independent identical binary symmetric channels (BSCs) each w...

Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlat...

An amplifier is assumed to have a single-pole high-frequency transfer function. The rise time of its output response to a step function input is $35\;\text{nsec}$. The up...

An $\text{npn}$ transistor (with $\mathrm{C}=0.3 \; \mathrm{pF}$ ) has a unity gain cutoff frequency $f_{\mathrm{T}}$ of $400 \; \mathrm{MHz}$ at a $\text{dc}$ bias curre...

An amplifier has an open-loop gain of $100$, an input impedance of $1 \; \mathrm{k \Omega}$, and an output impedance of $100 \; \Omega$. A feedback network with a feedbac...

The amplitude of a random signal is uniformly distributed between $-5 \mathrm{~V}$ and $5 \mathrm{~V}$.If the signal to quantization noise ratio required in uniformly qua...

If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$$2.23$$4.33$$11.37$$27.64$

In the sum of products function $f(X,Y,Z)=\sum(2,3,4,5)$, the prime implicants are$\overline{X}Y,X\overline{Y}$$\overline{X}Y,X\overline{Y}\;\overline{Z},X\overline{Y}Z$$...

Given that$A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is$15\:A+12\:I$$19\:A+30\:I$$17\:A+15\:I$...

For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold?$(M^{T})^{T} = M$$(cM)^{T} = c(M)^{T}$$(M+N)^{T} = M^{T} + N^{T}...

​​​​For the Boolean function\[F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text {, }\]the essential prime implicants are $\_\_\_\_\_\_$.$B D, \bar{B} \bar{D}$$B D, A B...

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...

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index $\text{(BMI)}$ in $2003$ and $2023$. Based on the...

$40 \%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is$120$$144$$160$$212$

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...

Let $\mathbb{R}$ and $\mathbb{R}^{3}$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set...

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 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...