71. Given a unity feedback system with open-loop transfer function.
    

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

    
    the root locus plot of the system is of the form—

1. 1. Fig:- A
      

   
   
   

   2. Fig:- B
      

   
   
   

   3. Fig:- C
      

   
   
   

   4. Fig:- D
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that
   

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

   
   ∴ H(s) = 1
   C.E. 1 + G(s) H(s) = 0
   ⇒ s³ + 3s² + 2s + K = 0
   Routh Hurwitz array
   s3 1 2 s2 3 K s1 6 – K 6 s0 K 6 – K 6 ≥ 0 K=6
   since there is nothing given in question in the form of numerical value, so we must calculate the intersection of root locus on the imaginary axis by using auxiliary equation i.e.,
   3s² + K = 0
   3s² + 6 = 0
   or
   s² = 2
   s = ± √2 j
   since only plot (A) intersects imaginary axis.
   Hence plot (A) is the correct choice.

   Correct Option: A

   Given that
   

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

   
   ∴ H(s) = 1
   C.E. 1 + G(s) H(s) = 0
   ⇒ s³ + 3s² + 2s + K = 0
   Routh Hurwitz array
   s3 1 2 s2 3 K s1 6 – K 6 s0 K 6 – K 6 ≥ 0 K=6
   since there is nothing given in question in the form of numerical value, so we must calculate the intersection of root locus on the imaginary axis by using auxiliary equation i.e.,
   3s² + K = 0
   3s² + 6 = 0
   or
   s² = 2
   s = ± √2 j
   since only plot (A) intersects imaginary axis.
   Hence plot (A) is the correct choice.

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72. Signal flow graph is used to find—
    

1. 1. stability of the system
      

   
   
   

   2. controllability of the system
      

   
   
   

   3. transfer function of the system
      

   
   
   

   4. poles of the system

   
   
   

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1. View Hint View Answer Discuss in Forum

   Refer synopsis.

   Correct Option: C

   Refer synopsis.

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73. The transfer function of a linear system is the—
    

1. 1. ratio of the output V₀1 (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

   Refer synopsis.

   Correct Option: C

   Refer synopsis.

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74. Non-minimum phase transfer function is defined as the transfer function—
    

1. 1. which has zeros in the right-half s-plane
      

   
   
   

   2. which has zeros only in the left-half s-plane
      

   
   
   

   3. which has poles in the right-half s-plane
      

   
   
   

   4. which has poles in the left-half s-plane

   
   
   

   5. A and C both

   
   
   

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1. View Hint View Answer Discuss in Forum

   Non-minimum transfer function can have zeros in the right half s-plane and poles in the right half s-plane.
   

   Correct Option: E

   Non-minimum transfer function can have zeros in the right half s-plane and poles in the right half s-plane.
   

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75. The transfer function of a tacheometer is of the form—
    

1. 1. Ks
      

   
   
   

   2. K/ s
      

   
   
   

   3. K/ (s+1)
      

   
   
   

   4. K/ [s (s+1)]

   
   
   

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1. View Hint View Answer Discuss in Forum

   Techeometer is basically a differentiator.
   Hence transfer function is of the form Ks.

   Correct Option: A

   Techeometer is basically a differentiator.
   Hence transfer function is of the form Ks.

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