1
GATE EE 2004
+2
-0.6
The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of $$‘a’$$ to give a phase margin of $${45^0}$$ is equal to
A
$$0.141$$
B
$$0.441$$
C
$$0.841$$
D
$$1.141$$
2
GATE EE 2004
+2
-0.6
In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will be
A
$${K \over {\sqrt 2 }}\sin \left( {t - {{45}^0}} \right)$$
B
$${K \over {\sqrt 2 }}\sin \left( {t + {{45}^0}} \right)$$
C
$$K\,\sin \left( {t - {{45}^0}} \right)$$
D
$$K\,\sin \left( {t + {{45}^0}} \right)$$
3
GATE EE 2004
+2
-0.6
The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ is the two dimensional state vector and $$A$$ is the system matrix given by $$A = \left[ {\matrix{ 0 & 2 \cr 2 & 0 \cr } } \right].$$ The roots of the characteristic equation are
A
$$-2$$ and $$+2$$
B
$$-j2$$ and $$+j2$$
C
$$-2$$ and $$-2$$
D
$$+2$$ and $$+2$$
4
GATE EE 2004
+2
-0.6
The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline B \overline C } \right)$$ can be written as
A
$$\overline A D + \overline B \overline C D$$
B
$$AD + B\overline C D$$
C
$$\left( {\overline A + D} \right)\left( {\overline B C + \overline D } \right)$$
D
$$A\overline D + BC\overline D$$
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