# Networks, Signals and Systems (Test 2)

## Gate Exam : Ec Electronics And Communication Engineering

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Q.1
A dual trace oscilloscope is set to operate in the Alternate mode. The control input of the multiplexer used in the y-circuit is fed with a signal having a frequency equal to
A. the highest frequency that the multiplexer can operate properly
B. twice the frequency of the time base (sweep) oscillator
C. the frequency of the time base (sweep) oscillator
D. haif the frequency of the time base (sweep) oscillator
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.2
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is
A. 5
B. 12
C. 15
D. 20
Answer : Option A
Explaination / Solution:
No Explaination.

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Q.3
For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?
A. The impulse response will be integral, but may not be absolutely integrable.
B. The unit impulse response will have finite support.
C. The unit step response will be absolutely integrable.
D. The unit step response will be bounded.
Answer : Option B
Explaination / Solution:
No Explaination.

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Q.4
Let f(x) be a real, periodic function satisfying f(−x) = −f(x). The general form of its Fourier series representation would be
A.
B.
C.
D.
Answer : Option B
Explaination / Solution:

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Q.5
Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is

A.
B.
C.
D.
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.6
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.7
Let x(t) be the input and y(t) be the output of a continuous time system.
Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4
Properties                                               Relations
P1 : Linear but NOT time - invariant R1 : y(t) = t2x(t)
P2 : Time - invariant but NOT linear R2 : y(t) = t|x(t)|
P3 : Linear and time - invariant        R3 : y(t) = |x(t)|
R4 : y(t) = x(t-5)
A. (P1, R1), (P2, R3), (P3, R4)
B. (P1, R2), (P2, R3), (P3, R4)
C. (P1, R3), (P2, R1), (P3, R2)
D. (P1, R1), (P2, R2), (P3, R3)
Answer : Option B
Explaination / Solution:

Mode function are not linear. Thus y(t) = |x(t)|  is not linear but this functions is time invariant. Option (A) and (B) may be correct.
The y(t) = t|x(t)| is not linear, thus option (B) is wrong and (a) is correct. We can see that
R1 : y(t) = t2x(t) Linear and time variant.
R2 : y(t) = t|x(t)| Non linear and time variant.
R3 : y(t) = |x(t)| Non linear and time invariant.
R4 : y(t) = x(t-5) Linear and time invariant.

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Q.8
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I.   The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued
II.  The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6𝜋 rad/s
For the three statements above, which one of the following is correct?
A. only II and III are true
B. only I and III are true
C. only III is true
D. only I is true
Answer : Option B
Explaination / Solution:

Fourier series coefficient ak is unaffected by scaling operating. Thus (I) is true and (II) is false.
T = 1sec for x(t) and if it compressed by '3' then the resultant period T = 1/3
Fundamental frequency = 2𝜋/T1= = 6𝜋 rad/sec
Thus (III) is correct.

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Q.9
A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period TS. In which one of the following cases is the sampled signal periodic?
A. T = √2Ts
B. T = 1.2Ts
C. Always
D. Never
Answer : Option B
Explaination / Solution:

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Q.10
The input voltage given to a converter is
The current drawn by the converter is

The input power factor of the converter is
A. 0.31
B. 0.44
C. 0.5
D. 0.71
Answer : Option C
Explaination / Solution:

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