1. The system with transfer function
   

   K

   s2(1 + sT)

   
   is operated in closed-loop with unity feedback. The closed-loop system is—
   

1. 1. stable
      

   
   
   

   2. unstable
      

   
   
   

   3. marginally stable
      

   
   
   

   4. conditionally stable

   
   
   

---

1. View Hint View Answer Discuss in Forum

   C.E. = 1 + G (s) H (s) = 0
   

   = 1 +	K	1 = s2 + s3T + K = 0
   	s2(1 + sT)

   
   There is missing term of s¹. Hence the system is unstable.

   Correct Option: B

   C.E. = 1 + G (s) H (s) = 0
   

   = 1 +	K	1 = s2 + s3T + K = 0
   	s2(1 + sT)

   
   There is missing term of s¹. Hence the system is unstable.

---

2. Given that the transfer function G (s) is

   K

   s2(1 + sT)

   State the type and order of the system—
   

1. 1. 2 and 3
      

   
   
   

   2. 3 and 2
      

   
   
   

   3. 3 and 3
      

   
   
   

   4. 2 and 2

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Type = 2, Order = 3
   

   Correct Option: A

   Type = 2, Order = 3
   

---

---

3. The transfer function G (s) is

   K

   s2(1 + sT)

   . This open-loop system will be—
   

1. 1. stable
      

   
   
   

   2. unstable
      

   
   
   

   3. marginally stable
      

   
   
   

   4. conditionally stable

   
   
   

---

1. View Hint View Answer Discuss in Forum

   C.E. of the given O.L.T.F. ⇒ 1 + G (s) = 0
   

   ⇒ 1 +	K	= 0
   	s2(1 + sT)

   
   ⇒ s² + s³T + K = 0
   ⇒ s³ T + s² + K = 0
   system is unstable since there is missing terms of s¹.

   Correct Option: A

   C.E. of the given O.L.T.F. ⇒ 1 + G (s) = 0
   

   ⇒ 1 +	K	= 0
   	s2(1 + sT)

   
   ⇒ s² + s³T + K = 0
   ⇒ s³ T + s² + K = 0
   system is unstable since there is missing terms of s¹.

---

4. A system has the transfer function (1 – s)/ (1 + s). It is a—
   

1. 1. non-minimum phase system
      

   
   
   

   2. minimum phase system
      

   
   
   

   3. low-pass system
      

   
   
   

   4. second order system

   
   
   

---

1. View Hint View Answer Discuss in Forum

   A system with
   

   T.F =	1 - s
   	T + s

   
   is a non-minimum phase system because a non-minimum phase system have at least one pole and/or zero in the R.H. side plane for nonminimum phase system as ω → ∞, phase angle φ ≠ – 90° (n – m). In this case, phase is – tan^–1 ωT – tan^–1 ωT
   = – 2 tan^–1 ωT = – 180° as ω → ∞.

   Correct Option: A

   A system with
   

   T.F =	1 - s
   	T + s

   
   is a non-minimum phase system because a non-minimum phase system have at least one pole and/or zero in the R.H. side plane for nonminimum phase system as ω → ∞, phase angle φ ≠ – 90° (n – m). In this case, phase is – tan^–1 ωT – tan^–1 ωT
   = – 2 tan^–1 ωT = – 180° as ω → ∞.

---

---

5. An all pass network imparts only—
   

1. 1. negative phase to the input
      

   
   
   

   2. positive phase to the input
      

   
   
   

   3. ± 90º phase shift to the input
      

   
   
   

   4. ± 180º phase shift to the input

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Transfer function of an all pass network,
   = 1 – s 1 + s = 1 – jω 1 + jω, ∠ φ = tan– 1 (ω) – tan– 1 ω
   As ω → ∞, ∠ φ → – 180°
   However, if the transfer function
   

   =	1 - s	=	1 -jω
   	1 + s		1 – jω

   
   ∠ φ = tan^–1 ω – tan^–1 (– ω) = 2 tan^–1 ω,
   as ω → ∞, ∠ φ → + 180°.
   Thus, an all pass transfer function impart ± 180° phase shift to the input. Hence alternative .

   Correct Option: D

   Transfer function of an all pass network,
   = 1 – s 1 + s = 1 – jω 1 + jω, ∠ φ = tan– 1 (ω) – tan– 1 ω
   As ω → ∞, ∠ φ → – 180°
   However, if the transfer function
   

   =	1 - s	=	1 -jω
   	1 + s		1 – jω

   
   ∠ φ = tan^–1 ω – tan^–1 (– ω) = 2 tan^–1 ω,
   as ω → ∞, ∠ φ → + 180°.
   Thus, an all pass transfer function impart ± 180° phase shift to the input. Hence alternative .

---