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.

**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

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

For this discrete-time system, which one of the following statements is TRUE?

No Explaination.

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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

**Answer : ****Option B**

**Explaination / Solution: **

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Consider a continuous-time system with input x(t) and output y(t) given by
y(t) = x(t) cos(t)
This system is

**A. ** linear and time-invariant

**B. ** non-linear and time-invariant

**C. ** linear and time-varying

**D. ** non-linear and time-varying

**Answer : ****Option C**

**Explaination / Solution: **

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The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is
the input signal. A signal z(t) is called eigen-signal of the system T , when T{z(t)} = γz(t),
where γ is a complex number, in general, and is called an eigenvalue of T. Suppose the impulse
response of the system T is real and even. Which of the following statements is TRUE?

**A. ** cos(t) is an eigen-signal but sin(t) is not

**B. ** cos(t) and sin(t) are both eigen-signals but with different eigenvalues

**C. ** sin(t) is an eigen-signal but cos(t) is not

**D. ** cos(t) and sin(t) are both eigen-signals with identical eigenvalues

**Answer : ****Option D**

**Explaination / Solution: **

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Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems ?

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option C**

**Explaination / Solution: **

Transfer function for the given pole zero plot is:

Transfer function for the given pole zero plot is:

From the plot Re (P_{1} and P_{2})>(Z_{1} and Z_{2})

So, these are two lead compensator.

Hence both high pass filters and the system is high pass filter

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A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil (PMMC) meter connected across the same load reads

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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) = t^{2}x(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)

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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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

**Answer : ****Option D**

**Explaination / Solution: **

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Let the signal be passed through an LTI system with frequency
response H(𝜔), as given in the figure below

**A. ** 4000 + 4000cos(2000πt) + 4000cos(4000πt)

**B. ** 2000 + 2000cos(2000πt) + 2000cos(4000πt)

**C. ** 4000cos(2000πt)

**D. ** 2000cos(2000πt)

**Answer : ****Option C**

**Explaination / Solution: **

The Fourier series representation of the output is given as

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A system is defined by its impulse response The system is

**A. ** stable and causal

**B. ** causal but not stable

**C. ** unstable and non-causal

**D. ** stable but not causal

**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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