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
Answer : Option D
Explaination / Solution:



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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.
Answer : Option D
Explaination / Solution:




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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
Answer : Option D
Explaination / Solution:

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

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Q.4
If the Laplace transform of a signal  then its final value is
A. -1
B. 0
C. 1
D. Unbounded
Answer : Option D
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.

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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
Answer : Option C
Explaination / Solution:

For two orthogonal signal f (x) and g(x)

i.e. common area between f x  and g x  is zero.

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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
Answer : Option A
Explaination / Solution:



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Q.7
A Hilbert transformer is a
A. non-linear system
B. non-causal system
C. time-varying system
D. low-pass system
Answer : Option A
Explaination / Solution:
No Explaination.


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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)
Answer : Option B
Explaination / Solution:



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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
Answer : Option B
Explaination / Solution:



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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.
Answer : Option A
Explaination / Solution:





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