Indian Institute of Technology Kharagpur (IIT-K) 2006 M.E Electronics and Telecommunications Gate ece - Question Paper

19. For the function of a complex variable W = lnZ
(where, W=u+jv and Z=x+jy),the u=constant lines get mapped in Z-plane as
(A) set of radial straight lines
(B) set of concentric circles
(C) set of confocal hyperbolas
(D) set of confocal ellipses
20. 3 companies, X, Y and Z supply computers to a university. The percentage of
computers supplied by them and the probability of those being defective are tabulated beneath.
provided that a computer is defective, the probability that it was supplied by Y is:
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
21. For the matrix [ jthe eigenvalue corresponding to the eigenvector is:
(A) 2
(B) 4
(C) 6
(D) 8
22. For the differential formula + k2y = 0 the boundary conditions are
Compan
y
°h of computers
supplied
Probability of being defective
X 60°h 0.01
Y 30°h 0.02
Z 10°h 0,03
(i) y=Oforx=Oand
(ii) y=Oforx=a
The form of non-zero solutions of y (where mvaries over all integers) are m,rx
(A) y=AmsIn
m a
m,rx
(B) y= AmCO5
m a
(C) Y=4m
mrx
(D) y=Amea
23. Consider the function f (t) having Laplace transform
2 two Re[sl>O
S +a)0
The final value of f(t)would be:
(A) 0
(B) 1
(C) —1 f(oo) 1
(D)
24. As x is increased from — to 00, the function
ex
f(x)=
1 + ex
(A) monotonically increases
(B) monotonically reduces
(C) increases to a maximum value and then reduces
(D) reduces to a minimum value and then increases
25. The 1st and the last critical frequencies (singularities) of a driving point impedance
function of a passive network having 2 types of elements, are a pole and a zero
respectively. The above property will be satisfied by
(A) RL network only
(B) RC network only
(C) LC network only
(D) RC as well as RL networks
26. In the figure shown below, presume that all the capacitors are initially uncharged. If
v,(t)=lOu(t) Volts,v0(t) is provided by
(A) Se °°° Volts
(B) 8(1 — e °°°) Volts
(C) 8u(t) Volts

Earning:   Approval pending.