1
GATE EE 2012
+1
-0.3
A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}}$$ is excited by $$\sin \left( {\omega t} \right).$$ The steady-state output of the system is zero at
A
$$\omega = 1\,\,rad/s$$
B
$$\omega = 2\,\,rad/s$$
C
$$\omega = 3\,\,rad/s$$
D
$$\omega = 4\,\,rad/s$$
2
GATE EE 2012
+2
-0.6
The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

$${G_c}\left( s \right)$$ is a lead compensator if

A
$$a = 1,b = 2$$
B
$$a = 3,b = 2$$
C
$$a = -3,b = -1$$
D
$$a = 3,b = 1$$
3
GATE EE 2012
+2
-0.6
The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

The phase of the above lead compensator is maximum at

A
$$\sqrt 2 \,rad/s$$
B
$$\sqrt 3 \,rad/s$$
C
$$\sqrt 6 \,rad/s$$
D
$$1/$$ $$\sqrt 3 \,rad/s$$
4
GATE EE 2012
+2
-0.6
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
$${a_1} \ne 0,\,\,{a_2} \ne 0,\,\,{a_3} = 0$$
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