56. The phase margin of a system with the open-loop transfer function
    

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

    
    

1. 1. 0°

   
   
   

   2. 63.4°

   
   
   

   3. 90°

   
   
   

   4. ∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   | G(jω) H(jω)| ≠ 1, for any value of ω,
   Therefore phase margin ∞ .

   Correct Option: D

   | G(jω) H(jω)| ≠ 1, for any value of ω,
   Therefore phase margin ∞ .

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57. A linear discrete-time system has t he characteristic equation, z³ – 0.81z = 0
    The system
    

1. 1. is stable

   
   
   

   2. is marginally stable

   
   
   

   3. is unstable

   
   
   

   4. stability cannot be assessed from the given information

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here linear discrete time system has characteristic equation
   z³ – 0. 81 z = 0
   ⇒ z (z² – 0.92) = 0
   ⇒ z (z – 0.9) (z + 0.9) = 0
   Hence z = 0, 0.9, – 0.9
   All roots lie inside unit circle. Hence the system is stable .

   Correct Option: A

   Here linear discrete time system has characteristic equation
   z³ – 0. 81 z = 0
   ⇒ z (z² – 0.92) = 0
   ⇒ z (z – 0.9) (z + 0.9) = 0
   Hence z = 0, 0.9, – 0.9
   All roots lie inside unit circle. Hence the system is stable .

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58. The characteristic equation of a closed-loop system is given by
    s⁴ + 6s³ + 11s² + 6s + K = 0
    Stable closed loop behaviour can be ensured when gain K is such that
    

1. 1. 0 < K < 10

   
   
   

   2. K > 10

   
   
   

   3. – ∞ < K < ∞

   
   
   

   4. 0 < K < 20

   
   
   

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1. View Hint View Answer Discuss in Forum

   s⁴ + 6s³ + 11s² + 6s + K = 0
   

   s4	1	11	K
   s3	6	6	–
   s2	10	K	–
   s1	6 – 0.6 K	–	–
   s0	K	–	–

   
   For stability
   K ≥ 0 and also 6 (1 – 0.1 K) ≥ 0
   Thus, 0 ≤ K ≤ 10.
   

   Correct Option: A

   s⁴ + 6s³ + 11s² + 6s + K = 0
   

   s4	1	11	K
   s3	6	6	–
   s2	10	K	–
   s1	6 – 0.6 K	–	–
   s0	K	–	–

   
   For stability
   K ≥ 0 and also 6 (1 – 0.1 K) ≥ 0
   Thus, 0 ≤ K ≤ 10.
   

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59. Match List-I with List-II and select the correct answer using the codes given below the Lists :
    
    

1. 1. A - 4 , B - 3 , C - 2 , D - 1

   
   
   

   2. A - 3 , B - 4 , C - 1 , D - 2

   
   
   

   3. A - 3 , B - 4 , C - 2 , D - 1

   
   
   

   4. A - 4 , B - 2 , C - 3 , D - 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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60. The feedback system with characteristic equation
    s⁴ + 20 Ks³ + 5s² + 10s + 15 = 0 is
    

1. 1. stable for all value of K

   
   
   

   2. stable for positive value of K

   
   
   

   3. stable for ∞ > K > 7.0

   
   
   

   4. unstable for all values of K

   
   
   

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1. View Hint View Answer Discuss in Forum

   By Routh criterion
   
   For this, any value at K the system is unstable.

   Correct Option: D

   By Routh criterion
   
   For this, any value at K the system is unstable.

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