# Recent activity A coil having an impedance of (10 + j100) $\Omega$ is connected in parallel to a variable capacitor as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor is changed so that parallel resonance occurs. The impedance across terminals p-q at resonance (in $\Omega$) is $\_\_\_\_$.
Consider signal x(t) = . Let $\delta$ denote the unit impulse (Dirac-delta) function. The value of the integral $\int^5_0$ 2x(t- 3)$\delta$(t-4)dt is 2 1 0 3
Two periodic signals x(t) and y(t) have the same fundamental period of 3 seconds. Consider the signals z(t) = x(-t) + y(2t + 1). The fundamental period of z(t) in seconds is 1 1.5 2 3
The Thevenin equivalent circuit representation across terminals p – q of the circui shown in the figure is a 1 V source in series with 150k$\Omega$ 1 V source in parallel with 100k$\Omega$ 2 V source in series with 150k$\Omega$ 2 V source in parallel with 200k$\Omega$
A series R-C circuit is excited by a 1 <0 V sinusoidal ac voltage source. The locus diagram of the phasor current L = (x + jy)A, when C is varied , while keeping R fixed, is
Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is $\frac{5}{16}$ $\frac{3}{16}$ $\frac{3}{5}$ $\frac{9}{16}$
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is 0 1 2 3
Let f$_1$(Z) =Z$^2$ and f$_2$(Z) = $\overline{z}$ be two complex variable functions. Here $\overline{z}$ is the complex conjugate of z. Choose the correct answer Both of f$_1$(Z) and f$_2$(Z) are analytic Only f$_1$(Z) is analytic Only f$_2$(Z) is analytic Both f$_1$(Z) and f$_2$(Z) are not analytic
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 0 0,0,1 0,1,1 1,1,1
An ideal square wave with period of 20ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate description of the output? Output is zero Output consists of both 50 Hz and 100 Hz frequency components. Output is a pure sinusoid of frequency 50Hz Output is a square wave of fundamental frequency 50Hz.
An input p(t) = sin(t) is applied to the system G(s) = $\frac{s-1}{s+1}$. The corresponding steady state output is y(t) = sin(t + $\varphi$), where the phase $\varphi$ (in degrees), when restricted to 0$^o$ $\leq$ $\varphi$ $\leq$ 360$^o$, is $\_\_\_\_\_\_$
The approximate phase response of $\frac{100^2e^-0.01s}{s^2+0.2s+100^2}$ is
Consider the transfer function G(s) = $\frac{2}{(s+1)(s+2)}$. The phase margin of G(s) in degrees is $\_\_\_\_\_$
In the circuit, assume that the opamp is ideal and the transistor has a $\beta$ of 20. The current I${_0}$( in $\mu A$) flowing through the load Z${_L}$ is $\_\_\_\_\_\_$.
The diodes given in the circuit are ideal. At t = 60ms, V$_{pq}$(in Volts) is $\_\_\_\_\_\_\_$
For the 3-bit binary counter shown in the figure, the output increments at every positive transition in the clock(CLK). Assume ideal diodes and the starting state of the counter as 000. If output is 1 V and output low is 0 V, the current I(in mA) flowing through the 50 $\Omega$ resistor during the 5$^{th}$ clock cycle is(up to one decimal place) $\_\_\_\_\_\_$
The representation of the decimal number (27.625)$_{10}$ in base -2 number system is 11011.110 11101.101 11011.101 10111.110
A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time delay. The processor is driven by a 5 MHz clock. The time delay (in $\mu$s) introduced by the ... Label LOOP if zero flag is not set. Takes 10 clock periods when jump is performed and 7 clock periods when jump is not performed.
A voltage of 6 cos(100$\pi$t) V is field as y-input to a CRO. The waveform seen on the seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively 1 V/div and 1 ms/div 1 V/div and 2 ms/div 2 V/div and 1 ms/div 2 V/div and 2 ms/div
A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100$^{th}$ division. The power consumed by the load (in Watts) is $\_\_\_\_\_$
As shown in the figure, temperature $\theta$ is measured using a K type thermocouple. It has a sensitivity of 40 $\mu V$^{0}$C. The gain (G) of the ideal instrumentations amplifier is 25. If the output V$_0$is 96 mV, then the value of$\theta$(in$^0$C) is$\_\_\_\_\_$0 votes 0 answers A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a static constant pressure of 100kpa. Its steady-state output will be 0 V 0.1 V 1 V 10 V 0 votes 0 answers An amplitude modulated signal is shown in the figure. The modulation index is(up to one decimal place)$\_\_\_\_\_$0 votes 0 answers An optical pulse containing 6 x 10$^6$photons is incident on a photodiode and 4.5 x 10$^6$electron-hole pairs are created. The maximum possible quantum efficiency (in %) of the photodiode is$\_\_\_\_$. 0 votes 0 answers Given$\overrightarrow{F}$= (x$^2$– 2y)$\overrightarrow{i}$– 4yz$\overrightarrow{j}$+ 4xx$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$. d$\overrightarrow{l}$along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1 0 votes 0 answers Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red? 20% 25% 30% 40% 0 votes 0 answers Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2 Here x and y are the unknows and k is real constant. The value of k for which there are infinite number of solutions is 3 1 -3 -6 0 votes 0 answers Consider the following equations$\frac {\partial {V(x,y)}}{\partial x}$= px$^2$+ y$^2$+ 2xy$\frac {\partial {V(x,y)}}{\partial y}$= x$^2$+ qy$^2$+ 2xy where p and q are constant ,V(x,y) that satisfies the above equation is p$\frac{x^3}{3}$+ q$\frac{x^2}{3}$+ 2xy + 6 p$\frac{x^3}{3}$...$\frac{x^2}{3}$+ x$^2$y + xy$^2$+ xy p$\frac{x^3}{3}$+ q$\frac{x^2}{3}$+ x$^2$y + xy$^2$0 votes 0 answers In the given circuit, superposition is applied.When V$_2$is set to 0 V, the current I$_2$is -6 A. When V$_1$is set to v, the current I$_1$is + 6A. Current i$_3$(in A) when both sources are applied will be (up to two decimal places)$\_\_\_\_\_$. 0 votes 0 answers Consider a standard negative feedback configuration with G(s) =$\frac{1}{(s+1)(s+2)}$and H(s) =$\frac{s+a}{s}$, For the closed loop system to have poles on the imaginary axis, the value of$\alpha$should be equal to (up to one decimal place)$\_\_\_\_\_\_$. 0 votes 0 answers Consider the linear system x =$\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix}$x, with initial condition x(0) =$\begin{bmatrix}-1 \\1\end{bmatrix}$. The solution x(t) for this system is x(t) =$\begin{bmatrix}e^{-t} & te^{-2t} \\0 & e^{-2t}\end{bmatrix}$...$\begin{bmatrix}e^{-t} & 0 \\0 & e^{-2t}\end{bmatrix}\begin{bmatrix}1 \\1\end{bmatrix}$0 votes 0 answers Consider the standard negative feedback configuration with G(s) =$\frac{s^2+0.2s+100}{s^2 – 0.2s +100}$and H(s) =$\frac{1}{2}$. The number of clockwise encirclements of (-1,0) in he Nyquist plot of the Loop transfer-function G(s)H(s) is$\_\_\_\_\_$0 votes 0 answers For the sequence x[n] = {1, -1,1, -1}, with n = 0,1,2,3, the DFT is computed as X(k) =$\Sigma^3_{n=1}$x[n]e^$-j\frac2{\pi}{4}$nk, for k = 0,1,2,3. The value of k for which X(k) is not zero is 0 1 2 3 0 votes 0 answers Let y[n] = x[n] + h[n], where * denotes convolution and x[n] and h[n] are two discrete time sequences, Given that then z-transform of y[n] s y(z) = 2+ 3z$^{-1}$+ z$^{-2}$, the z- transform of p[n] = x[n] * h [n-2] is 2 + 3z + z$^{-2}$3z +z$^{-2}$2z$^2$+ 3z + 1 2z$^{-2}$+ 3z$^{-3}$+ z$^{-4}$0 votes 0 answers The Fourier transform of a signal x(t), denoted by X(j$\omega$), is shown in the figure Let y(t)) = x(t) + e$^jt$x(t). The value of Fourier transform of y(t) evaluated at the angular frequency$\omega$= 0.5 rad /s is 0.5 1 1.5 2.5 0 votes 0 answers In the given circuit, the mesh currents I${_1}$,I${_2}$and I${_3}$are${_1}$= 1 A,${_2}$=2 A and${_3}$= 3A${_1}$= 2 A,${_2}$= 3 A and${_3}$= 4A${_1}$= 3 A,${_2}$= 4 A and${_3}$= 5A${_1}$= 4 A,${_2}$= 5 A and${_3}$= 6A 0 votes 0 answers In the figure, and RLC load supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is$\_\_\_\_\_$. 0 votes 0 answers Unit step response of a linear time invariant (LTI) system is,given by y(t) = (1 – e$^{-2t}$)u(t). Assuming zero initial condition,the transfer function of the system is$\frac{1}{s+1}\frac{2}{(s+1)(s+2)}\frac{1}{s+2}\frac{2}{s+2}\$