**In this post we are providing some MCQ on control system that asked in previous year GATE examination. if you have any queries or doubts then you can ask in our Facebook group, and for detail theory lectures of control system subscribe our you-tube channel ENGINEER TREE. all links given below to follow us**

**answer key will be provided within 48 hour of this post **

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# Time response previous year gate questions

**GATE 2000**

(1) An amplifier with resistive negative feedback has two left half plane poles in its open loop transfer function. the amplifier

- will always be unstable at high frequency
- will be stable for all frequency
- may be unstable, depending on the feedback factor
- will oscillate at low frequency

**GATE 2001 **

(2) If the characteristic equation of a closed loop system is \({ s }^{ 2 }+2s+2=0\), then system is

- over damped
- critically damped
- under damped
- undamped

**GATE 2002**

(3) consider a system with transfer function \(G(s)=\frac { (s+6) }{ k{ s }^{ 2 }+s+6 } \). its damping ratio will be 0.5 when the value of k is

- 2/6
- 3
- 1/6
- 6

**GATE 2002**

(4) The transfer function of a system is

\(G(s)=\frac { 100 }{ (s+1)(s+100) } \)

For a unit step input to the system the approximate settling time for 2% criterion is

- 100 sec
- 4 sec
- 1 sec
- 0.01 sec

**GATE 2004**

(5) A system described by the following differential equation \(\frac { { d }^{ 2 }y }{ d{ t }^{ 2 } } +3\frac { dy }{ dt } +2y=x(t)\) is initially at rest. for input x(t)=2u(t), the output y(t) is

- \((1-2{ e }^{ -t }+{ e }^{ -2t })u(t)\)
- \((1+2{ e }^{ -t }-2{ e }^{ -2t })u(t)\)
- \((0.5+{ e }^{ -t }+1.5{ e }^{ -2t })u(t)\)
- \((0.5+{ 2e }^{ -t }+2{ e }^{ -2t })u(t)\)

**GATE 2005**

(6) In the derivation of expression for peak percent overshoot \({ M }_{ P }={ e }^{ \frac { -\delta \pi }{ \sqrt { 1-{ \delta }^{ 2 } } } }\times 100%\), which of the following condition is not required?

- system is linear and time invariant
- the system transfer function has a pair of complex conjugate poles and no zeros
- there is no transportation in this system
- the system has zero initial condition

**GATE 2005**

(7) A ramp input applied to an unity feedback system results in 5% steady state error, the type number and zero frequency gain of the system are respectively

- 1 and 20
- 0 and 20
- 0 and 1/20
- 1 and 1/20

**GATE 2006 **

(8) The unit step response of a system starting from rest is given by

\(c(t)=1-{ e }^{ -2t }\quad for\quad t\le 0\)

The transfer function of the system is

- \(\frac { 1 }{ 2+2s } \)
- \(\frac { 2 }{ 2+s } \)
- \(\frac { 1 }{ 2+s } \)
- \(\frac { 2s }{ 1+2s } \)

**GATE 2006**

(9) Consider two transfer functions

\({ G }_{ 1 }(s)=\frac { 1 }{ { s }^{ 2 }+as+b } \quad and\quad { G }_{ 2 }(s)=\frac { s }{ { s }^{ 2 }+as+b } \)

The 3-db bandwidths of their frequency response are, respectively

- \(\sqrt { { a }^{ 2 }-4b } ,\sqrt { { a }^{ 2 }+4b } \)
- \(\sqrt { { a }^{ 2 }+4b } ,\sqrt { { a }^{ 2 }-4b } \)
- \(\sqrt { { a }^{ 2 }-4b } ,\sqrt { { a }^{ 2 }-4b } \)
- \(\sqrt { { a }^{ 2 }+4b } ,\sqrt { { a }^{ 2 }+4b } \)

**GATE 2007**

(10) A control system with PD controller is shown in the figure, if the velocity error constant Kv =1000 and the damping ratio δ=0.5, the values of Kp and Kd are

- Kp=100, Kd=0.09
- Kp=100, Kd=0.9
- Kp=10, Kd=0.09
- Kp=10, Kd=0.9

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where is answer key ? … i m not able to find it out