1
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The root locus of the feedback control system having the characteristic equation $${s^2} + 6Ks + 2s + 5 = 0$$ where $$K>0,$$ enters into the real axis at
A
$$s=-1$$
B
$$s = - \sqrt 5$$
C
$$s=-5$$
D
$$s = \sqrt 5$$
2
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The transfer function $$C(s)$$ of a compensator is given below: $$C\left( s \right) = {{\left( {1 + {s \over {0.1}}} \right)\left( {1 + {s \over {100}}} \right)} \over {\left( {1 + s} \right)\left( {1 + {s \over {10}}} \right)}}$$

The frequency range in which the phase (lead) introduce by the compensator reaches the maximum is

A
$$0.1 < \omega < 1$$
B
$$1 < \omega < 10$$
C
$$10 < \omega < 100$$
D
$$\omega > 100$$
3
GATE EE 2017 Set 2
Numerical
+2
-0
Consider the system described by the following state space representation
\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr}

If $$u(t)$$ is a unit step input and $$\left[ {\matrix{ {{x_1}\left( 0 \right)} \cr {{x_2}\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr } } \right],$$ the value of output $$y(t)$$ at $$t=1$$ sec (rounded off to three decimal places) is _____________.

4
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
For a $$3$$ -input logic circuit shown below, the output $$Z$$ can be expressed as
A
$$Q + \overline R$$
B
$$P\overline Q + R$$
C
$$\overline Q + R$$
D
$$P + \overline Q + R$$
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