# Networks, Signals and Systems (Test 1)

## Gate Exam : Ec Electronics And Communication Engineering

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Networks, Signals and Systems
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Q.1
A plane wave of wavelength λ is traveling in a direction making an angle 300 with positive x − axis and 900 with positive y − axis. The  field of the plane wave can be represented as (E is constant)
A.
B.
C.
D.
Explaination / Solution:

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Q.2
The state variable description of an LTI system is given by
where y is the output and u is the input. The system is controllable for

A.
B.
C.
D.
Explaination / Solution:

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Q.3
A discrete system is represented by the difference equation

It has initial condition X1(0) = 1; X2(0) = 0. The pole location of the system for a = 1, are
A. 1 ± j0
B. −1 ± j0
C. ±1 + j0
D. 0 ± j1
Explaination / Solution:

from the given difference equation,

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Q.4
Consider the function ݂f(z) = z + z* where z is a complex variable and z* denotes its complex conjugate. Which one of the following is TRUE?
A. f(z) is both continuous and analytic
B. f(z) is continuous but not analytic
C. f(z) is not continuous but is analytic
D. f(z) is neither continuous nor analytic
Explaination / Solution:

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Q.5
x(t)is a positive rectangular pulse from t = −1 to t = +1 with unit height as shown in the figure. The value of  { where X(ω) is the Fourier transform of x(t)} is

A. 2
B.
C. 4
D.
Explaination / Solution:
No Explaination.

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Q.6
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.

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Q.7
A discrete time linear shift - invariant system has an impulse response h[n] with h[0] = 1,h[1] =- 1,h[2] = 2, and zero otherwise The system is given an input sequence x[n] with x[0] = x[2] = 1, and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are respectively
A. 5, 2
B. 6, 2
C. 6, 1
D. 5, 3
Explaination / Solution:

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Q.8
Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as

Which one of the following statements is true about the system?

A. It is causal and stable
B. It is causal but not stable
C. It is not causal but stable
D. It is neither causal nor stable
Explaination / Solution:

For an input-output relation if the present output depends on present and past input values then the given system is “Causal”.
For the given relation,

For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.
Stability
If x[n] is bounded for the given finite range of n i.e. 0 ≤ n ≤ 10 y[n] is also bounded.
Similarly x[n] - x[n-1] is also bounded at all other values of n
Thus the system is “stable”.

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Q.9
Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems u(t) denotes the unit-step function)?
A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.10
A three – bus network is shown in the figure below indicating the p.u. impedances of each element.

The bus admittance matrix, Y – bus, of the network is
A.
B.
C.
D.