Question 1:

A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance, R, and a very large inductance, L. The two most dominant frequency components in the source current are?

Question 2:

Consider a signal x[n]=(12)n1[n],x[n]=(12)n1[n], where 1[n]=01[n]=0 if n0isz?k1?12z?1x[n?k],k>0isz?k1?12z?1 with region of convergence being

Question 3:

The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is: ?Cz2+1z2+2zdz

Question 4:

A lossless transmission line with 0.2 pu reactance per phase uniformly distributedd along the length of the line, connecting a generator bus to a bus, is protected up to 80 % of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:

Question 5:

Consider a linear time-invariant system whose input r(t)r(t) and output y(t)y(t) are related by the following differential equation: d2y(t)d(t)2+4y(t)=6r(t)d2y(t)d(t)2+4y(t)=6r(t)

The poles of this system are at?

Question 6:

Which of the following is true for all possible non-zero choices of integers m,n;m?nm,n;m?n or all possible non-zero choices of real numbers p,q;p?qp,q;p?q, as applicable ?

Question 7:

A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence (1,0,1) and input data (1,1,0,1,0,0,1,1,0,1,0,1,1,0), what is the output of this detector ?

Question 8:

A three-phase, 50 Hz, 4-pole induction motor runs at no-load with a slip of 1 % With full load, the slip increaseas to 5 % The % speed regulation of the motor (rounded off to 2 decimal places) is?

Question 9:

A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diaode, D, represented approximately as a piecewise linear plot of current vs time at diode turn-off. Lpar is a parasitic inductance dur to the wiring of the cirucit, and is in series with the diode. The point on the plot (indicate your choice by entering 1, 2, 3 or 4) at which the IGBT experiences the highest current stress is

Question 10:

A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be ____________ W (rounded off to 2 decimal places).

Let (Yl, Y2, ..., YK) ~ Multinomial(n, 71, 72, ..., Wk), then (a) Calculate the moment generating function (This will be a multivariate MGF). 3 Marks] (b) Show that E(Y;) = naj [2 Marks] (c) Show that Var(Y;) = na; (1 -nj) [4 Marks (d) Show that Cov(Y;, Y;) = -main; [6 Marks] Hint: You can use the Multivariate MGF. Recall if Y = (Y1, Y2, ..., Y-) be a multivariate random variable. Then the MGF is defined as, MY(1, ..., the) = E(exp(ti Yit ... + YA)) Now use partial derivative on t; or to, b; to achieve the resultsState whether the function is a probability mass function or not. If not, explain why not. 1 f(x) = 35X, for x =5, 7, 9, 11 Select all that apply. A. The function f(x) is not a probability mass function because it does not satisfy the third condition of probability mass functions. B. The function f(x) is not a probability mass function because it does not satisfy the first condition of probability mass functions. [)C. The function f(x) is not a probability mass function because it does not satisfy the second condition of probability mass functions. [)D. The function f(x) is a probability mass function.Suppose that the joint probability mass function of X and Y is P(X = 2, Y = j) - (2) e 2X/j!, OKi