Question:

Question 1

A differential equation didt?0.2i=0didt-0.2i=0 is applicable over ?10

Question 2

Consider a signal defined by

x(t)={ej10t0for |t|?1for |t|>1xt=ej10tfor t?10for t>1

Its Fourier Transform

Question 3

The coils of a wattmeter have resistances 0.01?? and 1000??; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25A at power factor 0.8. The voltage across the load terminals is 30V. The percentage error on the wattmeter reading is?

Question 4

A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage V0V0 is 36 V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current (iL) just continuous is?

Question 5

For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is TsTs. If the voltage VLVL is as shown, the duty cycle of the switch S is?

Question 6

In the given rectifier, the delay angle of the thyristor T1T1 measured from the positive going zero crossing of VsVs is 30. If the input voltage VsVs is 100sin(100?t)V100sin?(100?t)V, the average voltage across R (in Volt) under steady-state is?

Question 7

For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?

Question 9

The z-Transform of a sequence x[n]x[n] is given as X(z)=2z+4?4/z+3/z2X(z)=2z+4?4/z+3/z2. If y[n]y[n] is the first difference of x[n]x[n] , then Y(z)Y(z) is given by?

Question 10

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is Q24??0Kd2Q24??0Kd2 where K is given by?

Question 11

In the following sequential circuit, the initial state (before the first clock pulse ) of the circuit is Q1Q0Q1Q0= 00. The state (Q1Q0Q1Q0), immediately after the 333rd333rd clock pulse is?

Question 12

A Boolean funcation f(A,B,C,D)=f(A,B,C,D)= ??(1, 5, 12, 15) is to be implemented using an 81 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S2S1S0S2S1S0 of the multiplexer respectively. Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?

Question 13

The saturation voltage of the ideal op-amp shown below is 10 V. The output voltage v0v0 of the following circuit in the steady-state is?

Question 14

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers P1P1 and P2P2 in MW, and are given by

dC1dP1=0.2P1+50dC1dP1=0.2P1+50

dC2dP2=0.24P2+40dC2dP2=0.24P2+40

Where

20MW?P1??P1?150 MW

20MW?P2??P2?150MW.

For a certain load demand, P1P1 and P2P2 have been chosen such that dC1/dP1dC1/dP1 = 76 Rs/MWh and dC2/dP2dC2/dP2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P2P2 is?

Question 15

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is?

A sequence of 1000 equally spaced samples of a Gauss-Markov process using the recursive relation: 1-) Xn = axn-1+ Win = 1,2, ...,1000. Here assume that Xo = 0, and {W, ) is a sequence of independent identically distributed Gaussian random variables. In order to estimate the autocorrelation function of this discrete process, one can apply the formula: N-co N 2-) Rx(m) = lim = En=1XXn-m = E(Xn*n-m). However, since we have a finite number of samples an approximation would be 3) Rx(m) =- N-m 2n=1 XinXin-mim = 0,1, ..., 64 Notice we shorten the data and consider only the overlapping samples in the window starting at n=1 and the window starting at n=m+1. The theoretical autocorrelation for such a signal model is also known as: 4-)Rx(m) = on all, where On is the input process variance. Write Rx(m) correlation functions using equation 1 and equation 4Answer the following questions about the Classical Assumptions. The Gauss Markov theorem states that if certain assumptions are met, OLS is BLUE, or the "Best Linear Unbiased Estimator." a. (5 points) Define "Best" in terms of the Gauss-Markov theorem. b. (5 points) Define "Unbiased" in terms of the Gauss-Markov theorem. c. (5 points) Which of the following pairs of independent variables would violate the fourth classical assumption of "no perfect collinearity?" Circle. i. X1 and 2X1 ii. X1 and (X1)2 iii. Consumption and Disposable income in the US over the last 30 yearsConsider a standard chessboard with an 8 x 8 grid of possible locations. We define a Markov chain by randomly moving a single chess piece on this board. The initial location Xo is sampled uniformly among the 82 = 64 squares. At time t, the piece then chooses Xt+1 by sampling uniformly from the set of legal moves given its current location Xt. For a description of legal chess moves, see: http://en. wikipedia. org/wiki/Rules_of_chess#Basic_moves. a) Suppose the chess piece is a king, which can move to any of the 8 adjacent squares. Is the Markov chain irreducible? Is the Markov chain aperiodic? b) Suppose the chess piece is a bishop. Is the Markov chain irreducible? Is the Markov chain aperiodic? c) Suppose the chess piece is a knight. Is the Markov chain irreducible? Is the Markov chain aperiodic?. Consider a zero-mean WSS complex Gauss-Markov process of order 1 defined by the following equation r =-ar _tv, n=0,1,.... where v ~ /(0, o') and Ela, v* ] = 0 for 1 = +1, 12, .... Multiply both sides by * and take expectation values to find Er, *]. Note that E[rv*] = Ex*v,]. Multiply both sides by r* and take expectation values to show R., [0] = -aR_ [-1] + 0) = -aR* [1]+02. This process is also known as the auto-regressive process of order 1 and is denoted by AR(1). . Now multiply both sides by e* , I = 1, 2...., and take expec- tation values to show R, [!] = -aR,, [[ - 1], 1 =1, 2. .... This result, for a Gauss-Markov process of order P, or an AR(P) process. forms the basis for high resolution spectral estimation of zero-mean WSS random signals