Recent questions tagged numerical-answers

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both...

Consider a function $f(z)=z^{2}+z+1$ where $z \in \mathbb{C}$ is a complex variable. A simple closed contour $\gamma$ in $z$-plane encloses the point $z=1+0 j$.The value ...

An electric field has a potential of $V(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \mathrm{~V}$. A charge of $1$ coulomb placed at $(\hat{\imath}+\hat{\jmath}+\hat{k})$ experience...

Given $x(t)=4 \sin (15 \pi t)+7 \cos (4 \pi t)$, where $t$ is in seconds.The fundamental period of $x(t)$ is $\_\_\_\_\_\_$ seconds.$15$$60$$30$$2$

In the circuit shown, the BJT has a $\beta$ of $100$. The base-emitter junction voltage is $0.65$ $\mathrm{V}$. The quiescent collector current, $I_{C}$ is $\_\_\_\_$ $\m...

The maximum signal to quantization noise ratio (SQNR) for a $16$-bit analog-todigital converter is approximately $\_\_\_\_\_\_$ $\mathrm{dB}$.$48$$68$$88$$98$

An analog speech signal contains signals from $200$ $\mathrm{Hz}$ to $2400$ $\mathrm{Hz}$. It is sampled at $6$ $\mathrm{kHz}$ and quantized with $512$ levels for pulse c...

The slope efficiency of a laser diode is $0.5 \mathrm{~W} / \mathrm{A}$, and the output optical power at a current of $100$ $\mathrm{mA}$ is $30$ $\mathrm{mW}$. Assuming ...

In a linear element, the measured current is $100 \mathrm{~mA} \pm 2.5 \%$ and the measured voltage is $5 \mathrm{~V} \pm 5 \%$. Which of the following options show $(\ma...

A data set is given to be $[1,2,0,-1,-3,1,2,0,1]$.The median of the data set is $\_\_\_\_$ . (rounded off to the nearest integer)

The potential difference between nodes $A$ and $B$ in a circuit is $v_{A}-v_{B}=5 \mathrm{~V}$. The work done in moving a charge of $1$ coulomb from point $B$ to $A$ is $...

In a series $R L$ circuit shown in the figure, the current through the resistor lags the AC source voltage by $45^{\circ}$. Let $R=100 \pi \Omega$ and $L=2 \mathrm{H}$.Th...

The minimum number of comparators required in a $6$-bit flash analog-to-digital converter is $\_\_\_\_\_\_$. (answer in integer)

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\...

An electric field in free space is$\vec{E}=(2 x+5 y+6 z) \hat{\imath}+(5 x+4 y+10 z) \hat{\jmath}+(6 x+10 y+2 z) \hat{k} \mathrm{~V} / \mathrm{m}.$The charge density is $...

A straight thin wire carrying a current of $I=1 \mathrm{~A}$ in the direction $\widehat{n}=\dfrac{1}{\sqrt{6}} \hat{\imath}+\dfrac{2}{\sqrt{6}} \hat{\jmath}+\dfrac{1}{\sq...

A two-port network has $\mathrm{z}$-parameters $z_{11}=z_{22}=10 \Omega$, and $z_{12}=z_{21}=5 \Omega$.The value of $R_{L}$ such that maximum power is transferred to $R_{...

In the circuit shown below, the value of the output voltage $V_{0}$ is $\_\_\_\_$ $\mathrm{V}$.$2$$3$$4$$8$

A linear time invariant (LTI) system is described by:$$\begin{array}{c}{\left[\begin{array}{l}\dot{x}_{1} \\\dot{x}_{2}\end{array}\right]=\left[\begin{array}{cc}0 & 1 \\-...

In the circuit shown below, $R$ is $1 \mathrm{k} \Omega$ and $R_{f}$ is $10 \mathrm{k} \Omega$. If $V_{\text {in }}$ is 100 mV and the op-amps have supply voltages of $\p...

In the following active filter circuit with ideal op-amps, $R$ is $1 \mathrm{k} \Omega, C$ is $1 \mu \mathrm{~F}$, and $V_{\text {in }}$ has an amplitude of $1$ $\mathrm{...

A closed Lissajous pattern observed on an oscilloscope in the $\mathbf{X}-\mathbf{Y}$ mode has three horizontal tangencies and two vertical tangencies in steady state. If...

A parallel plate capacitive displacement sensor has a plate area of $2 \mathrm{~cm}^{2}$. The air gap between the plates is decreased by $0.1$ mm from an initial value of...

An amplitude modulated voltage signal $x(t)$ drives a load of $1 \Omega$.$$x(t)=K \cos (300 \pi \: t)+L \cos (240 \pi \: t)+L \cos (360 \pi \: t) .$$If the efficiency is ...

Given a differential equation $\dfrac{d^{2} x}{d t^{2}}+x=0$ with $x(0) \neq 0$.Which of the following statements is/are true?$\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d ...

Let $f(t)=\left\{\begin{array}{cc}1, & t \in[0,2] \\ -t+3, & t \in[2,3] \\ 0, & \text { otherwise }\end{array}\right.$Then$\int_{-\infty}^{\infty} f(\tau) d \tau=$ $\_\_\...

A single phase transformer has a rating of $10 \mathrm{kVA}, 50 \mathrm{~Hz}, 1100 \mathrm{~V} / 220 \mathrm{~V}$. In an open circuit test with the high voltage side open...

A linear time invariant (LTI) system has a transfer function$$G(s)=\frac{10(s+1)}{s\left(s^{2}+2 s+5\right)}$$The system is placed in unity negative feedback configuratio...

The system $G(s)=\dfrac{K}{(s+1)^{4}}$ has a gain margin of $20$ dB. The value of $K$ is $\_\_\_\_$. (rounded off to two decimal places)

In the phase-locked-loop circuit shown below, the output of the VCO is a digital square wave.If the input is a square wave at $10$ $\mathrm{kHz}$, the steady state freque...

A digital counter increments its count every $0.1 \mu \mathrm{~s}$. The counter is used in an instrument to measure frequency. The counter is operated for one period of t...

A current carrying semiconductor of thickness $0.7$ mm is placed in a transverse magnetic field. The measured Hall voltage is $0.9$ $\mathrm{mV}$ and the current is $6$ $...

For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives information about the value of the measurand. For a Bragg wavelength of $1550$ $\mathrm{nm...

A photodiode has a responsivity $0.8 \mathrm{~A} / \mathrm{W}$. If the input optical power to the photodiode is $2$ $\mathrm{mW}$, the power delivered to a $50 \: \Omega$...