91. The signal flow diagram of a system is shown in the given figure. The number of forward paths and the number of pairs of non-touching loops are respectively
    

1. 1. 3, 1

   
   
   

   2. 3, 2

   
   
   

   3. 4, 2

   
   
   

   4. 2, 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   C = RG – H₂C
   

   ∴	C	=	G
   	R		1 + H2

   Correct Option: C

   C = RG – H₂C
   

   ∴	C	=	G
   	R		1 + H2

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92. Consider a feedback control system with loop transfer function
    

    G(s) H(s) =	K(1 + 0.5s)
    	s(1 + s)(1 + 2s)

    
    The type of the closed loop system is
    

1. 1. zero

   
   
   

   2. one

   
   
   

   3. two

   
   
   

   4. three

   
   
   

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1. View Hint View Answer Discuss in Forum

   Type of closed loop system having a feedback control system as
   

   G(s) H(s) =	K(1 + 0.5s)	is one.
   	s(1 + s)(1 + 2s)

   Correct Option: B

   Type of closed loop system having a feedback control system as
   

   G(s) H(s) =	K(1 + 0.5s)	is one.
   	s(1 + s)(1 + 2s)

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93. The transfer function of the system described by
    

    	d2y	+	dy	=	du	+ 2u
    	dt2		dt		dt

    
    with u as input and y as output is

1. 1. 	(s + 2)
      	(s2 + s)

   
   
   

   2. 	(s + 1)
      	(s2 + s)

   
   
   

   3. 	s
      	(s2 + s)

   
   
   

   4. 	2s
      	(s2 + s)

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   	d2y	+	dy	=	du	+ 2u
   	dt2		dt		dt

   
   ∴ s²y(s) + sy(s) = su(s) + 2u(s)
   

   ⇒	y(s)	=	s + 2
   	u(s)		s2 + s

   
   

   Correct Option: A

   	d2y	+	dy	=	du	+ 2u
   	dt2		dt		dt

   
   ∴ s²y(s) + sy(s) = su(s) + 2u(s)
   

   ⇒	y(s)	=	s + 2
   	u(s)		s2 + s

   
   

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94. The overall transfer function of the system in the given figure is
    
    

1. 1. 	G
      	1 - GH

      
      

   
   
   

   2. 	2G
      	1 - GH

      
      

   
   
   

   3. 	GH
      	1 - GH

      
      

   
   
   

   4. 	2G
      	1 - H

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Y₁ = U + X₂H
   Y₂ = U + X₁H
   and X₁ = GY₁ = GU + GX₂H
   X₂ = GY₂ = GU + GX₁H
   ⇒ Y = X₁ + X₂ = 2 GU + GH (X₁ + X₂)
   = 2 GU + GHY
   

   ⇒ Y =	2GU
   	1 - GH

   
   

   ⇒	Y	=	2G
   	U		1 - GH

   
   

   Correct Option: B

   
   Y₁ = U + X₂H
   Y₂ = U + X₁H
   and X₁ = GY₁ = GU + GX₂H
   X₂ = GY₂ = GU + GX₁H
   ⇒ Y = X₁ + X₂ = 2 GU + GH (X₁ + X₂)
   = 2 GU + GHY
   

   ⇒ Y =	2GU
   	1 - GH

   
   

   ⇒	Y	=	2G
   	U		1 - GH

   
   

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95. The transfer function of a linear system is
    

1. 1. ratio of the output, v_o (t), and input v_i (t)

   
   
   

   2. ratio of the derivatives of the output and the input

   
   
   

   3. ratio of the Laplace transform of the output and that of the input with all initial conditions zeros

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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