For the differential equation (d2y/dx2) + k2y = 0, the boundary conditions are (i)   y = 0 for x = 0, and (ii)  y = 0 for x = a The form of non-zero solutions of y (where m varies over all integers) are

1.  

2.  

3.  

4.  

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4
Correct Answer :


Explanation :
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A Hilbert transformer is a

1.  non-linear system

2.  non-causal system

3.  time-varying system

4.  low-pass system

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4
Correct Answer :

non-linear system


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The frequency response of a linear, time-invariant system is given by H(f) = 5/(1 + j10 πf). The step response of the system is

1.  5(1 - e-5t)u(t)

2.  5(1 - e-(t/5))u(t)

3.  1/5(1 - e-5t)u(t)

4.  1/5(1 - e-(t/5))u(t)

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4
Correct Answer :

5(1 - e-(t/5))u(t)


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A 5-point sequence x[n] is given as x[-3] = 1, x[-2] = 1, x[-1] = 0, x[0] = 5, x[1] = 1. Let X(ejω) denote the discrete-time Fourier transform of x[n]. The value of 

1.  5

2.  10 π

3.  16 π

4.  5 + j10π

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4
Correct Answer :

10 π


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The z-transform X[z] of a sequence X[n] is given by X[z] = 0.5/(1 - 2z-1). It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is

1.  -0.5

2.  0

3.  0.25

4.  0.5

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4
Correct Answer :

0.5


Explanation :
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A control system with a PD controller is shown in the figure. If the velocity error constant Kv= 1000 and the damping ratio ζ = 0.5, then the values of KP and KD are

1.  KP = 100, KD = 0.09

2.  KP = 100, KD = 0.9

3.  KP = 10, KD = 0.09

4.  KP = 10, KD = 0.9

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4
Correct Answer :

KP = 100, KD = 0.9


Explanation :
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The  transfer  function  of  a  plant  is T(s)  =  5/((s  +  5)(s2  +  s  +  1)).  The  second-order approximation of T(s) using dominant pole concept is

1.  1/((s + 5)(s + 1))

2.  5/((s + 5)(s + 1))

3.  5/(s2 + s + 1)

4.  1/(s2 + s + 1)

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4
Correct Answer :

5/(s2 + s + 1)


Explanation :
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The  open-loop  transfer  function  of  a  plant  is  given as G(s)  =  1/(s2  -  1).  If  the  plant  is operated  in a unity  feedback configuration,  then  the  lead compensator  that can stabilize this control system is

1.  (10(s - 1))/(s + 2)

2.  (10(s + 4))/(s + 2)

3.  (10(s + 2))/(s + 10)

4.  (1(s + 2))/(s + 10)

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4
Correct Answer :

(10(s - 1))/(s + 2)


Explanation :
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The following differential equation has 3(d2y/dt2) + 4(dy/dt)3 + y2 + 2 = x

1.  degree = 2, order = 1

2.  degree = 3, order = 2

3.  degree = 4, order = 3

4.  degree = 2, order = 3

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4
Correct Answer :

degree = 3, order = 2


Explanation :
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A unity  feedback control system has an open-loop  transfer  function G(s) = K/(s(s2 + 7s +12)). The gain K for which  s = -1 + j1 will lie on the root locus of this system is 

1.  4

2.  5.5

3.  6.5

4.  10

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4
Correct Answer :

10


Explanation :
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