131. Let X(s) =	3s + 5
     	s² + 10s + 21

     
     be the Laplace Transform of a signal x(t). Then, x(0+) is

1. 1. 0

   
   
   

   2. 3

   
   
   

   3. 5

   
   
   

   4. 21

   
   
   

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   Correct Option: B

   
   

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132. Consider a signal defined by
     

     x(t) =		ej10t,	for	|t| ≤ 1
     		0	for	|t| > 1

     
     Its Fourier Transform is

1. 1. 	2sin(ω - 10)
      	ω - 10

   
   
   

   2. 	2ej10tsin(ω - 10)
      	ω - 10

   
   
   

   3. 	2sin ω
      	ω - 10

   
   
   

   4. 	2ej10tsin ω
      	ω

   
   
   

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   Correct Option: A

   

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133. The unit step response of a system with the transfer function
     

     G(s) =	1 - 2s
     	1 + s

     
     is given by which one of the following waveforms?

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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   Y(s) = G(s) × U(s)
   

   ∴ Y(s) =	1 - 2s	.	1
   	(1 + s)		s

   
   Now using partial fraction concept
   

   ∴ Y(s) =	A	+	B
   	(s)		(s + 1)

   
   A = 1, B = -3
   ∴ y(t) = u(t) – 3e^–t u(t)
   ∴ y(t) = (1 – 3e – t) u(t)

   Correct Option: A

   
   Y(s) = G(s) × U(s)
   

   ∴ Y(s) =	1 - 2s	.	1
   	(1 + s)		s

   
   Now using partial fraction concept
   

   ∴ Y(s) =	A	+	B
   	(s)		(s + 1)

   
   A = 1, B = -3
   ∴ y(t) = u(t) – 3e^–t u(t)
   ∴ y(t) = (1 – 3e – t) u(t)

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134. The z-Transform of a sequence x[n] is given as X(z) = 2z + 4 – 4/z + 3/z². If y[n] is the first difference of x[n], then Y(z) is given by

1. 1. 2z + 2 – 8/z + 7/z² – 3/z³

   
   
   

   2. – 2z + 2 – 6/z + 1/z² – 3/z³

   
   
   

   3. – 2z – 2 + 8/z – 7/z² + 3/z³

   
   
   

   4. 4z – 2 – 8/z – 1/z² + 3/z³

   
   
   

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   y[n] is first difference of x[n]
   ∴ y[n] = x(n)– x(n – 1)
   From z transform
   ∴ Y(z) = x(Z) (1 – z – 1) = X(z) – z^–1X(z)
   ∴ Y(z) = [2z + 4 – 4z^–1 + 3z^–2] – [2 + 4z^–1 – 4z^–2]
   = 2z + 4 – 4z^–1 +3 z^–2 – 2 – 4z^–1 + 4z^–2 – 3z^–3
   = 2z + 2 – 8z^–1 + 7z – 2 – 3^–3
   

   = 2z + 2 -	8	+	7	-	3
   	z		z2		z3

   Correct Option: A

   y[n] is first difference of x[n]
   ∴ y[n] = x(n)– x(n – 1)
   From z transform
   ∴ Y(z) = x(Z) (1 – z – 1) = X(z) – z^–1X(z)
   ∴ Y(z) = [2z + 4 – 4z^–1 + 3z^–2] – [2 + 4z^–1 – 4z^–2]
   = 2z + 4 – 4z^–1 +3 z^–2 – 2 – 4z^–1 + 4z^–2 – 3z^–3
   = 2z + 2 – 8z^–1 + 7z – 2 – 3^–3
   

   = 2z + 2 -	8	+	7	-	3
   	z		z2		z3

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135. For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?

1. 1. The impulse response will be integral, but may not be absolutely integrable.

   
   
   

   2. The unit impulse response will have finite support.

   
   
   

   3. The unit step response will be absolutely integrable.

   
   
   

   4. The unit step response will be bounded.

   
   
   

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   NA

   Correct Option: D

   NA

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