A. stable and of the minimum phase type

**B. stable and of the non-minimum phase type**

C. unstable and of the minimum phase type

D. unstable and of the non-minimum phase type

[2] The open loop transfer function G(s) of a unity feedback control system is given as,

G(s) = [ k(s+2/3) / s2(s+2) ] From the root locus, it can be inferred that when k tends to positive infinity,

**A. three roots with nearly equal real parts exist on the left half of the s-plane**

B. one real root is found on the right half of the s-plane

C. the root loci cross the jω axis for a finite value of k; k≠0

D. three real roots are found on the right half of the s-plane

[5] The input x(t) of a system are related as y(t) = ∫t-∞

**x(τ)cos(3τ)dτ. The system is [GATE2012]**

A. time-invariant and stable

**B. stable and not time-invariant**

C. time-invariant and not stable

D. not time-invariant and not stable

[7] The Fourier transform of a signal h(t) is H(jω) = (2cosω)(sin2ω)/ω. The value of h(0) is [GATE2012]

A. 1/4

B. 1/2

**C. 1**

D. 2

[14] Consider the following statements with reference to the phase plane:

1. They are general and applicable to a system of any order.

2. Steady state accuracy and existence of limit cycle can be predicteD.

3. Amplitude and frequency of limit cycle if exists can be evaluateD.

4. Can be applied to discontinuous time system. Which of the above statements are correct [IES2010]

A. 1,2,3 and 4

B. 2 and 3 only

C. 3 and 4 only

D. 2,3 and 4 only

**Ans: B**

[18] The open loop transfer function of a unity feedback system is given by G(s) =(e-0.1s)/s.The gain margin of this system is [GATE 2009]

A. 11.95 dB

B. 17.67 dB

C. 21.33 dB

D. 23.9 dB

**Ans: D**

[21]The trace and determinant of a 2x2 matrix are known to be -2 and -35 respectively. Its eigen values are [GATE 2009]

A.-30 and -5

B.-37 and -1

C.-7 and 5

D.17.5 and -2

**Ans:C**

[22]A Linear Time Invariant system with an impulse response h(t) produces output y(t) when input x(t) is applied. When the input x(t-τ) is applied to a system with impulse response h(t-τ), the output will be [GATE 2009]

A.y(t)

B.y(2(t-τ))

C.y(t-τ)

D.y(t-2τ)

**Ans:D**

[25] For the driving point impedance function, Z(s)=[as2+7s+3]/[s2+3s+b], the circuit realization is shown below. The values of 'a' and 'b' respectively are [IES2010]

A. 4 and 5

B. 2 and 5

C. 2 and 1

D. 2 and 3

**Ans: C**

[29] The system represented by the input-output relationship y(t)= 5t∫-∞ x(τ)dτ, t>0 is

A. Linear and casual

**B. Linear but not casual**

C. Casual but not linear

D. Neither linear nor casual

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