All India Institute of Medical Sciences 2007 B.Com Computer Science Auto cad University - Question Paper

(C) 0
(D) m(t)(t)
40. The minimum sampling frequency (in samples/sec) needed to reconstruct the subsequent
signal from its samples without distortion.
(sin2,r1OOOt3 (sin2,r1OOOt2
x(t)=5i I i would be:
Tt }
(A) 2x103
(B) 4x103
(C) 6x103
(D) 8x103

41. A uniformly distributed random variable X with probability density function
f (x) =±(u(x+5)-u(x-5))
Where u(.)is the unit step function is passed through a transformation provided in the figure
below. The probability density function of the transformed random variable Y would be
(A) (y)=(u(y+2.5)-u(y-2.5))
(B) i,(y)=O.5Y(y)+O.5Y(y—l)
(C) f(y)= O.255(y+2.5)+O.255(y —2.5)+O.55(y)
(D) f(y) = O.258(y+2.5)+O.258(y —2.5)+(u(y+2.5)—u(y —2.5))
42. A system with input x[nl and output y[n is provided as y[n=sinrnx(n). The
system is:
(A) linear, stable and invertible
(B) non-linear, stable and non-invertible
(C) linear, stable and non-invertible
(D) linear, unstable and invertible
43. The unit-step response of a system starting from rest is provided by
c(t)=1—e2 for t!=0
The transfer function of the system is:
(A)1 + 2s
(B) 2+s
(C) 2+s
(D) 2s one + 2s
44. The Nyquist plot of G(ja)H(ja)for a closed loop control system, passes through (—1, j0)
point in the GH plane. The gain margin of the system in dB is equal to
(A) infinite
(B) greater than zero
(C) less than zero
(D) zero
45. The positive values of “K” and “a” so that the system
oscillates at a frequency of two rad/sec respectively are
shown in the figure beneath
(A) 1, 0.75
(B) 2, 0.75
(C) 1, 1
(D) 2, 2
46. The unit impulse response of a system is:
For this system, the steady-state value of the output for unit step input is equal
to
(A) -1
(B) 0
(C) 1
(D)
47. A linear system is defined by the subsequent state formula
k(t)=Ax(t)+Bu(t), A=[°
The state-transition matrix of the system is:
(A) rcost sint
L—sint cost
(B) r_cost sint
L—sint —cost

Earning:   Approval pending.