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

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A continuous random variable X has a probability density function is

**A. ** 0.368

**B. ** 0.5

**C. ** 0.632

**D. ** 1.0

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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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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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)

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

**Explaination / Solution: **

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Given f(t) and g(t) as shown below:

g(t) can be expressed as

No Explaination.

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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

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

The eigenvalue and eigenvector pairs (λ_{i}v_{i})for the system are

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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.

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A discrete time signal x[n] = sin (π^{2}n) n being an integer, is

**A. ** periodic with period π

**B. ** periodic with period π^{2}

**C. ** periodic with period π/2

**D. ** not periodic

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

**Explaination / Solution: **

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

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

N1 = π

N2 = π^{2}

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 (π^{2}n) is not periodic.

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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:

**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

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

**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)

X: Impulse P: 1 – e^{-t/T}

Y: Unit step Q: t – T(1 – e^{(-t/T)}

Z :Ramp R: e^{-t/T}

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)

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An RLC circuit with relevant data is given below.

**A. ** 0.5W

**B. ** 1W

**C. ** √2 W

**D. ** 2W

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

**Explaination / Solution: **

The power dissipated in the resistor R is

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**Preparation Study Material**- Circuit Analysis (Study/Preparation)
- Digital Electronics (Study/Preparation)
- Signals and Systems (Study/Preparation)
- Communication Theory (Study/Preparation)
- Basic Electrical and Instrumentation Engineering (Study/Preparation)
- Electrical Engineering and Instrumentation (Study/Preparation)
- Electronic Devices (Study/Preparation)
- Linear Integrated Circuits LIC (Study/Preparation)
- Electronic Circuits I (Study/Preparation)
- Electronic Circuits II (Study/Preparation)
- Control System Engineering (Study/Preparation)
- Digital Communication (Study/Preparation)
- Digital Signal Processing (Study/Preparation)
- Microprocessors and Microcontrollers (Study/Preparation)
- Electromagnetic Theory (Study/Preparation)