NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

GATE EE 2014 Set 2

MCQ (Single Correct Answer)
The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr } } \right]\,\,Q = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:
A
Controllable and observable
B
Not controllable but observable
C
Controllable but not observable
D
Not controllable and not observable
2

GATE EE 2013

MCQ (Single Correct Answer)
The state variable formulation of a system is given as
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$

The response $$y(t)$$ to a unit step input is

A
$${1 \over 2} - {1 \over 2}{e^{ - 2t}}$$
B
$$1 - {1 \over 2}{e^{ - 2t}} - {1 \over 2}{e^{ - t}}$$
C
$${e^{ - 2t}} - {e^{ - t}}$$
D
$$1 - {e^{ - t}}$$
3

GATE EE 2013

MCQ (Single Correct Answer)
The state variable formulation of a system is given as
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$

The system is

A
controllable but not observable
B
not controllable but obserable
C
both controllable and observable
D
both not controllable and not Observable
4

GATE EE 2012

MCQ (Single Correct Answer)
The state variable description of an $$LTI$$ system is given by $$$\left( {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr {\mathop {{x_3}}\limits^ \bullet } \cr } } \right) = \left( {\matrix{ 0 & {{a_1}} & 0 \cr 0 & 0 & {{a_2}} \cr {{a_3}} & 0 & 0 \cr } } \right)\left( {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right) + \left( {\matrix{ 0 \cr 0 \cr 1 \cr } } \right)u,$$$ $$$y = \left( {\matrix{ 1 & 0 & 0 \cr } } \right)\left( {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right)$$$

where $$y$$ is the output and $$u$$ is the input. The system is controllable for

A
$${a_1} \ne 0,\,\,{a_2} = 0,\,\,{a_3} \ne 0$$
B
$${a_1} = 0,\,\,{a_2} \ne 0,\,\,{a_3} \ne 0$$
C
$${a_1} = 0,\,\,{a_2} \ne 0,\,\,{a_3} = 0$$
D
$${a_1} \ne 0,\,\,{a_2} \ne 0,\,\,{a_3} = 0$$

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12