A uniformly distributed random variable X with probability density function fx(x) = 1/10 (u(x + 5) -u(x - 5))  where u(.)  is  the unit step  function  is passed  through a  transformation given  in  the  figure below. The probability density function of the transformed random variable Y would be

1.  fY (y) = 1/5 (u(y + 2.5) -u(y -  2.5))

2.  fY (y) = 0.5 δ(y) + 0.5 δ(y - 1)

3.  fY (y) = 0.25 δ(y + 2.5) + 0.25 δ(y - 2.5) + 0.5 δ(t)

4.  fY (y) = 0.25 δ(y + 2.5) + 0.25 δ(y - 2.5) + 1/10(u(y + 2.5) - u(y - 2.5))

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Correct Answer :

fY (y) = 0.25 δ(y + 2.5) + 0.25 δ(y - 2.5) + 0.5 δ(t)


Explanation :
No Explanation available for this question

A system with input x[n] and output y[n] is given as y[n] = (sin (5/6) π n) x(n).The system is

1.  linear, stable and invertible

2.  non-linear, stable and non-invertible

3.  linear, stable and non-invertible

4.  linear, unstable and invertible

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Correct Answer :

linear, stable and non-invertible


Explanation :
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The unit-step response of a system starting from rest is given by C(t) = 1 - e-2t for t ≥ 0  The transfer function of the system is

1.  1/(1 + 2s)

2.  2/(2 + s)

3.  1/(2 + s)

4.  2s/(1 + 2s)

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Correct Answer :

2/(2 + s)


Explanation :
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The Nyquist plot of G (jω) H (jω) for a closed loop control system, passes through (-1, j0) point in the GH plane. The gain margin of the system in dB is equal to

1.  infinite

2.  greater than zero

3.  less than zero

4.  zero

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Correct Answer :

zero


Explanation :
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The positive values of "K" and "a" so  that  the system shown  in  the  figure below oscillates at a frequency of 2 rad/sec respectively are

1.  1, 0.75

2.  2, 0.75

3.  1, 1

4.  2, 2

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Correct Answer :

2, 0.75


Explanation :
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The unit impulse response of a system is h(t) = e-t , t ≥ 0  For this system, the steady-state value of the output for unit step input is equal to

1.  -1

2.  0

3.  1

4.  ∞

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4
Correct Answer :

1


Explanation :
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The transfer function of a phase-lead compensator is given by Ge(s) = (1 + 3Ts)/(1 + Ts) where T > 0 The maximum phase-shift provided by such a compensator is

1.  π/2

2.  π/3

3.  π/4

4.  π/6

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4
Correct Answer :

π/6


Explanation :
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The minimum step-size  required  for a Delta-Modulator operating at 32 K samples/sec  to track the signal (here u(t) is the unit-step function) x(t) = 125 t(u(t) - u(t - 1)) + (250 - 125t) (u(t - 1) - u(t - 2)) so that slope-overload is avoided, would be

1.  2-10

2.  2-8

3.  2-6

4.  2-4

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Correct Answer :

2-8


Explanation :
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A zero-mean white Gaussian noise is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is the uniformly sampled with sampling period ts = 0.03 msec.The samples so obtained would be

1.  correlated

2.  statistically independent

3.  uncorrelated

4.  orthogonal

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4
Correct Answer :

statistically independent


Explanation :
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A  source  generates  three  symbols  with  probabilities  0.25,  0.25,  0.50  at  a  rate  of  3000symbols  per  second.  Assuming  independent  generation  of  symbols,  the  most  efficient source encoder would have average bit rate as

1.  6000 bits/sec

2.  4500 bits/sec

3.  3000 bits/sec

4.  1500 bits/sec

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Correct Answer :

4500 bits/sec


Explanation :
No Explanation available for this question
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