# Recent questions and answers

A second order system has closed loop poles located at $s=-3\pm j4$. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places) is ________
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Assume that the opamp in the circuit shown is ideal. The value of $\frac{V_x}{I_x} (\text{in k}\Omega)$ is ____________.
A sinusoid of $\text{10 kHz}$ is sampled at $\text{15 k samples/s}.$ The resulting signal is passed through an ideal low pass filter $(LPF)$ with cut-off frequency of $\text{25 kHz}$. The maximum frequency component at the output of the $\text{LPF (in kHz)}$ is _________.
A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\text{100 ms.}$ The $\text{DS-ADC}$ is operated in the continuous conversion mode. The conversion time of the $\text{DS-ADC}$ for an input voltage of $\text{123.4 mV (in ms, rounded off to one decimal place)}$ is _____.
The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{10 sin(100}\pi\: t) V$. The other terminal of the sensor is tied to the input of a high input impedance ... $\text{100 pF}$. The peak of the voltage $V_A$ at the input of the amplifier when $\text{x=0.1 (in volts)}$ is _________.
Two $100\: \Omega$ resistors having tolerance $3\%$ and $4\%$ are connected in series. The effective tolerance of the series combination $\text{(in % rounded off to one decimal place)}$ is ___________.
Consider the matrix $M=\begin {bmatrix} 1&-1&0\\1&-2&1\\0&-1&1\end{bmatrix}$. One of the eigenvectors of $M$ is $\begin {bmatrix} 1\\-1\\1\end{bmatrix}$ $\begin {bmatrix} 1\\1\\-1\end{bmatrix}$ $\begin {bmatrix} -1\\1\\-1\end{bmatrix}$ $\begin {bmatrix} 1\\1\\1\end{bmatrix}$
Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0.$ The solution to this ordinary differential equation is __________ $x(t)=0$ $x(t)=\sin(t)$ $x(t)=\cos(t)$ $x(t)=\sin(t)-\cos(t)$
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line is __________. $\text{y=-0.5x+1}$ $\text{y=x-0.5}$ $\text{y=0.5x-1}$ $\text{y=2x+1}$
The loop transfer function of a negative feedback system is $G(s)H(s)=\frac{1}{s(s-2)}$. The Nyquist plot for the above system _________. encircles $(-1+j0)$ point once in the clockwise direction encircles $(-1+j0)$ point once in the counterclockwise direction does not encircles $(-1+j0)$ point encircles $(-1+j0)$ point twice in the counterclockwise direction
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
Consider two identical bags $B1$ and $B2$ each containing $10$ balls of identical shapes and sizes. Bag $B1$ contains $7$ Red and $3$ Green balls, while bag $B2$ contains $3$ Red and $7$ Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag $B1$ $\text{(rounded off to one decimal place)}$ is ______.
The rms value of the phasor current $\underline{I}$ in the circuit shown $\text{(in amperes)}$ is _____.
In the circuit shown, the rms value of the voltage across the $100 \Omega$ resistor $\text{(in volts)}$ is _________.
Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right.$ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \end{array}\right.$ Consider $y[n]=h[n]\otimes g[n]$, where $\otimes$ denotes the convolution operator. The value of $y[2]$ is ___________
The loop transfer function of a negative feedback system is given by $G(s)H(s)=\frac{K}{s(s+2)(s+6)}$, where $K>0$. The value of $K$ at the breakaway point of the root locus for the above system $\text{(rounded off to one decimal place)}$ is __________.
The system shown in Fig.(a) has a time response y(t) to an input $r(t)=10u(t)$ as shown in Fig. (b), $u(t)$ being the unit step input. Both $K, t$ are positive. The gain $K$ of the system is __________
Assuming that the opamp used in the circuit shown is ideal, the reading of the $1\;Hz$ bandwidth, permanent magnet moving coil $(PMMC)$ type voltmeter $\text{(in volts)}$ is __________
If the opamps in the circuit shown are ideal and $V_x=0.5\;mV$, the steady state value of $V_\circ \; \text{(in volts, rounded off to two decimal places)}$ is ___________
Two flip-flops are interconnected as shown in the figure. The present state of the flip flops are: $A=1, B=1$. The input x is given as $1,0,1$ in the next three clock cycles. The decimal equivalent of $(ABy)_2$ with A beign the $MSB$ and y being the $LSB$, after the 3rd clock cycle is ___________
The address lines $A_9 \dots A_2$ of a 10 bit, 1.023 V full-scale digital to analog converter $(DAC)$ is connected to the data lines $D_7$ to $D_0$ of an 8-bit microprocessor, with $A_1$ and $A_0$ of the $DAC$ grounded. Now, $D_7 \dots D_0$ is changed ... $\text{DAC (in mV, rounded off to one decimal place)}$ is __________.
The real power drawn by a balanced load connected to a $\text{400 V, 50 Hz,}$ balanced, symmetrical 3-phase, 3-wire, $RYB$ sequence mains is measured using the two-wattmeter method. Wattmeter $W_1$ is connected in the $R$ line and wattmeter $W_2$ is connected in the $B$ ... current is measured as $\frac{1}{\sqrt3}A$. If the wattmeter $W_1$ reads zero, the reading on $W_2$ (in watts) is _______.
A $6\frac{1}{2}$ digit timer-counter is set in the ‘time period’ mode of operation and the range is set as ‘ns’. For an input signal, the timer-counter displays $1000000$. With the same input signal, the timer-counter is changed to ‘frequency’ mode of operation and the range is set as ‘Hz’. the display will show the number _______.
The circuit shown uses ideal opamp powered from a supply $V_{CC}=5 V$. If the charge $q_p$ generated by the piezoelectric sensor is of the form $q_p=0.1 \sin(10000\pi t) \mu C$, the peak detector output after 10 cycles of $q_p$ $\text{(in volts, rounded off to one decimal place)}$ is ______.
A metallic strain gauge of resistance $R_X$ with a gauge factor of 2 is bonded to a structure made of a metal with modulus of elasticity of $200\: GN/m^2$. The value of $R_X$ is $1\:k\Omega$ when no stress is applied. $R_X$ is a part of a quarter bridge with ... subjected to a stress of $100\:MN/m^2$. Magnitude of the output of the bridge (in mV, rounded off to two decimal places) is _________.
A laser beam of 10 mm beam diameter is focused onto an optical fiber using a thin biconvex lens as shown in the figure. The refractive index of the lens is $1.5$. The refractive indices of the core and cladding of the fiber are $1.55 \;and \;1.54$ respectively. ... the focal length of the lens to attain he maximum coupling to the fiber $\text{(in mm, rounded off to one decimal place)}$ is ______
As shown in the figure, a slab of finite thickness $t$ with refractive index $n_2=1.5$, has air $(n_1=1)$ above and below it. Light of free space wavelength $600 nm$ is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in nm) is __________.
Consider the finite sequence $X=(1,1,1).$ The Inverse Discrete Fourier Transform (IDFT) of X is given as $\text{(x(0), x(1), x(2)).}$ The value of $x(2)$ is _______
A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and B $\text{(in$\mu$F, rounded off to one decimal place)}$ is ________
Consider the following state variable equations: $\dot{x_1}(t)=x_2(t)$ $\dot{x_2}(t)=-6x_1(t)-5x_2(t)$ The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ second, the value of $x_2(1)$ $\text{(rounded off to two decimal places)}$ is ___________
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is ___________
A $\text{1000/1 A, 5 VA, UPF}$ bar-primary measuring current transformer has $1000$ secondary turns. The current transformer exhibits a ratio error of $-0.1\%$ and a phase error of $3.438$ minutes when the primary current is $1000 A.$ At this ... condition, the rms value of the magnetization current of the current transformer $\text{(in amperes, rounded off to two decimal places)}$ is _________
The mutual inductances between the primary coil and the secondary coils of linear variable differential transformer (LVDT) shown in the figure are $M_1$ and $M_2$. Assume that the self-inductances $L_{s1}$ and $L_{s2}$ remain constant and are independent of $x$ ... detector becoms zero when $|V_2|=1.25|V_1|$. The value of $D$ (in mm, rounded off to one decimal place) is _______
In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______
The loop transfer function of a negative feedback system is $G(s)H(s)=\frac{2(s+1)}{s^2}$. The phase margin of the system $\text{(in degrees, rounded off to one decimal place)}$ is __________
The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrightarrow{a} and\;\overrightarrow{b}$ on that plane such that $\overrightarrow{a}\neq \alpha \overrightarrow{b}$ ... both $\overrightarrow{a} and\;\overrightarrow{b}$ is ___________ $\hat{k}$ $\hat{i}-\hat{j}$ $-\hat{j}$ $\hat{i}$
Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation ________ $\dot{X}=-F(X), X(0)=1$ $\dot{X}=-F(X)+X, X(0)=1$ $\dot{X}=F(X), X(0)=1$ $\dot{X}=F(X)+X, X(0)=1$
A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and obtain a unique solution by multiplying both left and right sides of the equation ... a unique solution provided the matrix $A^T A$ is well conditioned Yes, can obtain a unique solution provided the matrix $A$ is well conditioned
In the circuit shown below, the safe maximum value for the current $I$ is _______ $\text{1.0 A}$ $\text{0.5 A}$ $\text{0.1 A}$ $\text{0.05 A}$