# Networks, Signals and Systems (Test 5)

## Gate Exam : Ec Electronics And Communication Engineering

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Networks, Signals and Systems
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Q.1
Given two continuous time signals  which exist for t > 0, the convolution z(t) = x(t)* y(t) is
A.
B.
C.
D.
Explaination / Solution:

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Q.2
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.3
A function y(t), such that y(0) = 1 and y(1) = 3e-1, is a solution of the differential equation  Then y(2) is
A. 5e-1
B. 5e-2
C. 7e-1
D. 7e-2
Explaination / Solution:

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Q.4
Consider the system with following input-output relationwhere, x[n] is the input and y[n] is the output. The system is
A. invertible and time invariant
B. invertible and time varying
C. non-invertible and time invariant
D. non-invertible and time varying
Explaination / Solution:

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Q.5
Given f(t) and g(t) as shown below:

The Laplace transform of g(t) is
A. 1/s(e3s – e5s)
B. 1/s(e-5s – e-3s)
C. 1/s(e-3s – e-2s)
D. 1/s(e5s – e3s)
Explaination / Solution:
No Explaination.

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Q.6
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 system matrix A is

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

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Q.7
The Fourier series of a real periodic function has only (P) cosine terms if it is even (Q) sine terms if it is even (R) cosine terms if it is odd (S) sine terms if it is odd Which of the above statements are correct ?
A. P and S
B. P and R
C. Q and S
D. Q and R
Explaination / Solution:

The Fourier series of a real periodic function has only cosine terms if it is even and sine terms if it is odd.

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Q.8
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
A.  product of h1(t)  and h2(t)
B.  sum of h1(t)  and h2(t)
C.  Convolution of h1(t)  and h2(t)
D.  Subtraction  of h1(t)  and h2(t)
Explaination / Solution:

If the two systems with impulse responseh1(t)  and h2(t)   are connected in cascaded configuration as shown in figure, then the overall response of the system is the convolution of the individual impulse responses.

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Q.9
The impulse response of a continuous time system is given by   The value of the step response at t = 2 is
A. 0
B. 1
C. 2
D. 3
Explaination / Solution:

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Q.10
An RLC circuit with relevant data is given below.

The current Ic in the figure above is
A. − j2 A
B.
C.
D. + j2A