# EC GATE 2007 (Test 6)

Tag: ec gate 2007
Q.1
A unity feedback control system has an open-loop transfer function . The gain K for which s = +j will lie on the root locus of this system is
A. 4
B. 5.5
C. 6.5
D. 10
Explaination / Solution: Workspace
Report
Q.2
The state space representation of a separately excited DC servo motor dynamics is given as where ω is the speed of the motor, ia is the armature current and u is the armature voltage. The transfer function ω(s)/U(s) of the motor is
A. B. C. D. Explaination / Solution:  Workspace
Report
Q.3
An independent voltage source in series with an impedance Zs = Rs + jXs delivers a maximum average power to a load impedance ZL when
A. ZL = Rs + jXs
B. ZL = Rs
C. ZL = jXs
D. ZL = Rs - jXs
Explaination / Solution:

According to maximum Power Transform Theorem
ZLZ= (Rs - jXs)

Workspace
Report
Q.4
If the Laplace transform of a signal then its final value is
A. -1
B. 0
C. 1
D. Unbounded
Explaination / Solution: Final value theorem is applicable only when all poles of system lies in left half of S -plane. Here s = 1 is right s −plane pole. Thus it is unbounded.

Workspace
Report
Q.5
Three functions f(t), f2(t) and f3(t) which are zero outside the interval [0, T] are shown in the figure. Which of the following statements is correct? A. f(t) and f2(t) are orthogonal
B. f(t) and f3(t) are orthogonal
C. f2(t) and f3(t) are orthogonal
D. f(t) and f2(t) are orthonormal
Explaination / Solution:

For two orthogonal signal f (x) and g(x) i.e. common area between f x  and g x  is zero.

Workspace
Report
Q.6
The 3-dB bandwidth of the low-pass signal e-t u(t), where u(t) is the unit step function, is given by
A. 1/2π Hz
B. C.
D. 1 Hz
Explaination / Solution: Workspace
Report
Q.7
A Hilbert transformer is a
A. non-linear system
B. non-causal system
C. time-varying system
D. low-pass system
Explaination / Solution:
No Explaination.

Workspace
Report
Q.8
The frequency response of a linear, time-invariant system is given by The step response of the system is
A. 5(1 - e-5t) u(t)
B. 5(1 - e-t/5) u(t)
C. 1/2 (1 - e-5t) u(t)
D. 1/5 (1 - e-t/5) u(t)
Explaination / Solution: Workspace
Report
Q.9
The z −transform X(z) of a sequence x n is given by X It is given that the region of convergence of X(z) includes the unit circle. The value of x is
A. −0.5
B. 0
C. 0.25
D. 05
Explaination / Solution: Workspace
Report
Q.10
Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is then the system response is If the itial state vector of the system changes to the system response becomes The eigenvalue and eigenvector pairs (λivi)for the system are
A. B. C. D.    