For the discrete-time system shown in the figure, the poles of the system transfer function are located at

We have the discrete time system as shown in figure below.

The circuit is minimized as

Hence, poles are at

z = 1/2, 1/3

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A plant transfer function is given as When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
**A. **
**B. **
**C. **
**D. **
**Answer : ****Option A**

**Explaination / Solution: **

Given plant transfer function,

K_{P}
> K_{1} > 0

2K_{1}
> K_{P} > 0

2K_{1} < K_{P}

2K_{1}
> K_{P}

Given plant transfer function,

So, closed loop transfer function is

Therefore, characteristics equation is

For stability, we form the Routh array.

For stability, we must have

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The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude

From the pole-zero plot, we obtain the transfer function as

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The result of the convolution is

**A. ** x ( t + t_{0})

**B. ** x ( t - t_{0})

**C. ** x ( -t + t_{0})

**D. ** x ( -t - t_{0})

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

**Explaination / Solution: **

From the convolution property,

From the convolution property,

Now, we replace t by -t to obtain

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Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of H_{ϕ} on r , where H_{ϕ} is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor ?

No Explaination.

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A vector is given by Which one of the following statements is TRUE?
**A. ** is solenoidal, but not irrotational

**B. ** is irrotational, but not solenoidal

**C. ** is neither solenoidal nor irrotational

**D. ** is both solenoidal and irrotational

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

**Explaination / Solution: **

Given vector,

Given vector,

If divergence then vector is solenoidal. So, we obtain

Hence, it is solenoidal.

Again, if curl then is irrotational. So, we obtain

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In the given circuit, the values of V_{1} and V_{2} respectively are

**A. ** 5 V, 25 V

**B. ** 10 V, 30 V

**C. ** 15 V, 35 V

**D. ** 0 V, 20 V

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

**Explaination / Solution: **

By Nodal analysis

By Nodal analysis

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A function 1 – x^{2} + x^{3 }is defined in the closed interval [-1, 1]. The value of x , in the open interval (-1, 1) for which the mean value theorem is satisfied, is

**A. ** -1/2

**B. ** -1/3

**C. ** 1/3

**D. ** 1/2

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

**Explaination / Solution: **

Lagrange’s mean value theorem states that if a function f(x) is continuous in close interval [a, b] and differentiable in open interval (a + b), then for point c in the interval, we may define

Since, polynomial function is always continuous and differentiable, so

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The damping ratio of a series RLC circuit can be expressed as

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

Damping ratio is given by

Damping ratio is given by

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Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let and be their complements. Which one of the following statements is FALSE?
**A. ** P(A ∩ B) = P(A) P(B)

**B. **

**C. ** P( A U B) = P(A) + P(B)

**D. **

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

**Explaination / Solution: **

A and B are two independent events with probabilities, P(A) ≠ 0 and P(B) ≠ 0

A and B are two independent events with probabilities, P(A) ≠ 0 and P(B) ≠ 0

Now, we check the given options.

True

True

False

True

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