1
GATE EE 2017 Set 2
+1
-0.3
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as + b}},\,\left( {a > 0,\,b > 0,\,K > 0} \right),$$ the steady state error will be
A
$$0$$
B
$${a \over b}$$
C
$${{a + K} \over b}$$
D
$${{a - K} \over b}$$
2
GATE EE 2017 Set 2
+2
-0.6
The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the complex $$s$$-plane is
A
$$0 < K < 6$$
B
$$0 < K < 16$$
C
$$6 < K < 36$$
D
$$6 < K < 16$$
3
GATE EE 2017 Set 2
+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
$$s = \sqrt 5$$
4
GATE EE 2017 Set 2
+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
$$\omega > 100$$
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