# Networks, Signals and Systems (Test 3)

## Gate Exam : Ec Electronics And Communication Engineering

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Q.1
The fourier series expansion of the periodic signal shown below will contain the following nonzero terms A. B. C. D. Explaination / Solution:

⇒ it satisfies the half wave symmetry, so that it contains only odd harmonics.
⇒ It satisfies the even symmetry. So bn = 0

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Q.2
For a periodic signal the fundamental frequency in radians/s is
A. 100
B. 300
C. 500
D. 1500
Explaination / Solution:
No Explaination.

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Q.3
Consider a signal defined by Its Fourier Transform is
A. B. C. D. Explaination / Solution: Workspace
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Q.4
Consider a linear time invariant system x = Ax, with initial condition x(0) at t = 0. Suppose α and β are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues λ1 and λ2 respectively. Then the response x(t) of the system due to initial condition x(0) = α is
A. B. C. D. Explaination / Solution: Workspace
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Q.5
The system ẋ = Ax + Bu with is
A. stable and controllable
B. stable but uncontrollable
C. unstable but controllable
D. unstable and uncontrollable
Explaination / Solution:
No Explaination.

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Q.6
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
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Q.7
{ x(n)} is a real - valued periodic sequence with a period N . x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence is
A. B. C. D. 0
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Q.8
The result of the convolution is
A. x ( t + t0)
B. x ( t - t0)
C. x ( -t + t0)
D. x ( -t - t0)
Explaination / Solution:

From the convolution property, Now, we replace t by -t to obtain Workspace
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Q.9
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh‟s Table of the system characteristic equation X: The system is stable … P: … when all elements are positive Y: The system is unstable … Q: … when any one element is zero Z: The test breaks down … R: … when there is a change in sign of coefficients
A. X→P, Y→Q, Z→R
B. X→Q, Y→P, Z→R
C. X→R, Y→Q, Z→P
D. X→P, Y→R, Z→Q
Explaination / Solution:
No Explaination.

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Q.10
The input voltage given to a converter is The current drawn by the converter is The active power drawn by the converter is
A. 181W
B. 500W
C. 707W
D. 887W 