56. Fourier Series coefficient of time-domain signal is
    

    X[k] =		- 1		|k|	, ωo = 1
    		3

    
    then corresponding time domain signal will be

1. 1. 4

      5 + 3sin t

   
   
   

   2. 5

      4 + 3sin t

   
   
   

   3. 5

      4 + 3cos t

   
   
   

   4. 4

      5 + 3cos t

   
   
   

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   Correct Option: D

   
   

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57. Fourier Series coefficient of time-domain signal is
    X[k] = jδ[k – 1]– jδ[k + 1] + δ[k + 3] + δ[k – 3], ω_o = 2π
    then corresponding time domain signal will be

1. 1. 2(cos 3πt – sin πt)

   
   
   

   2. – 2(cos 3πt – sinπt)

   
   
   

   3. 2(cos 6πt – sin 2πt)

   
   
   

   4. – 2(cos 6πt – sin 2πt)

   
   
   

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   = je^j2πt – je^{– j2πt} + e^j6πt + e^{– j6πt}
   = – 2sin 2πt + 2cos 6πt

   Correct Option: C

   
   = je^j2πt – je^{– j2πt} + e^j6πt + e^{– j6πt}
   = – 2sin 2πt + 2cos 6πt

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58. Laplace transform of sin2 t is

1. 1. 4

      s² + 2

   
   
   

   2. 4

      s² + 4

   
   
   

   3. 2

      s² + 4

   
   
   

   4. 2

      s² + 2

   
   
   

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   NA

   Correct Option: C

   NA

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59. The average value of the voltage waveform shown below is
    

1. 1. 0.632 K

   
   
   

   2. 0.368 K

   
   
   

   3. 2.71 K

   
   
   

   4. None of these

   
   
   

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   Correct Option: A

   

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60. A linear time invariant system has an impulse response e^2t, t > 0. If the initial conditions are zero and the input is e^3t ,the output for t > 0 is

1. 1. e^3t – e^2t

   
   
   

   2. e^5t

   
   
   

   3. e^3t + e^2t

   
   
   

   4. None of these

   
   
   

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   H(s) =	1	, R(s) =	1
   	(s - 2)		(s - 3)

   
   

   Output =	1	.	1	=	1	-	1
   	(s - 2)		(s - 3)		(s - 3)		(s - 2)

   
   C(t) = e^3t – e^2t

   Correct Option: A

   H(s) =	1	, R(s) =	1
   	(s - 2)		(s - 3)

   
   

   Output =	1	.	1	=	1	-	1
   	(s - 2)		(s - 3)		(s - 3)		(s - 2)

   
   C(t) = e^3t – e^2t

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