# Networks, Signals and Systems (Test 4)

## Gate Exam : Ec Electronics And Communication Engineering

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Q.1
The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is A. 0
B. 0.1
C. 1
D. 10
Explaination / Solution: Workspace
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Q.2
A continuous random variable X has a probability density function is
A. 0.368
B. 0.5
C. 0.632
D. 1.0
Explaination / Solution:
No Explaination.

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Q.3
The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. The integration time step is h. For this discrete-time system, which one of the following statements is TRUE?
A. The system is not stable for h>0
B. The system is stable for h>1/π
C. The system is stable for 0<h<1/2π
D. The system is stable for 1/2π<h<1/π
Explaination / Solution:
No Explaination.

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Q.4
Let z(t) = x(t) * y(t), where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).
A. c.x(ct) * y(ct)
B. x(ct) * Y(ct)
C. c.x(t) * y(ct)
D. c.x(ct) * y(t)
Explaination / Solution: Workspace
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Q.5
Given f(t) and g(t) as shown below: g(t) can be expressed as
A. g(t) = f(2t − 3)
B. g(t) = f((t/2) − 3)
C. g(t) = f(2t − (3/2))
D. g(t) = f((t/2) − (3/2))
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 eigenvalue and eigenvector pairs (λivi)for the system are
A. B. C. D. Explaination / Solution:   Workspace
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Q.7
Group I lists a set of four transfer functions. Group II gives a list of possible step response y(t). Match the step responses with the corresponding transfer functions. A. P - 3,Q - 1,R - 4,S - 2
B. P - 3,Q - 2,R - 4,S - 1
C. P - 2,Q - 1,R - 4,S - 2
D. P - 3,Q - 4,R - 1,S - 2
Explaination / Solution: Workspace
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Q.8
A discrete time signal x[n] = sin (π2n) n being an integer, is
A. periodic with period π
B.  periodic with period π2
C. periodic with period π/2
D. not periodic
Explaination / Solution:

In the given options (A), (B) and (C), we have the periods respectively as
N1 = π

N2 = π2

N3 = π/3

None of the above period is an integer. Since, a discrete time signal has its period an integer. So, all the three options are incorrect. Hence, we are left with the option (D). i.e. the discrete time signal x[n] = sin (π2n) is not periodic.

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Q.9
A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for t ≥ 0:
X: Impulse                           P: 1 – e-t/T
Y: Unit step                          Q: t – T(1 – e(-t/T)
Z :Ramp                               R: e-t/T
A. X→R, Y→Q, Z→P
B. X→Q, Y→P, Z→R
C. X→R, Y→P, Z→Q
D. X→P, Y→R, Z→Q
Explaination / Solution:

In general the first order, L.P.F filter transfer function is because G(0) = k and G(∞) = ∞ if we take this transfer function as reference and give different input such as s(t).r(t).u(t)  Workspace
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Q.10
An RLC circuit with relevant data is given below. The power dissipated in the resistor R is
A. 0.5W
B. 1W
C. √2 W
D. 2W 