1
GATE EE 2003
+2
-0.6
The circuit of fig shows a $$555$$ Timer $$IC$$ connected as an Astable multivibrator. The value of the capacitor $$C$$ is $$10$$ $$nF.$$ The values of the resistors $${R_A}$$ and $${R_B}$$ for a frequency of $$10$$ $$kHz$$ and a duty cycle of $$0.75$$ for the output voltage waveform are
A
$${R_A} = 3.62\,k\Omega ,\,\,{R_B} = 3.62\,k\Omega$$
B
$${R_A} = 3.62\,k\Omega ,\,\,{R_B} = 7.25\,k\Omega$$
C
$${R_A} = 7.25\,k\Omega ,\,\,{R_B} = 3.62\,k\Omega$$
D
$${R_A} = 7.25\,k\Omega ,\,\,{R_B} = 7.25\,k\Omega$$
2
GATE EE 2003
+2
-0.6
The block diagram of a control system is shown in Fig. The transfer function $$G(s) = Y(s)/U(s)$$ of the system is
A
$${1 \over {18\left( {1 + {s \over {12}}} \right)\left( {1 + {s \over 3}} \right)}}$$
B
$${1 \over {27\left( {1 + {s \over 6}} \right)\left( {1 + {s \over 9}} \right)}}$$
C
$${1 \over {27\left( {1 + {s \over {12}}} \right)\left( {1 + {s \over 9}} \right)}}$$
D
$${1 \over {27\left( {1 + {s \over 9}} \right)\left( {1 + {s \over 3}} \right)}}$$
3
GATE EE 2003
+1
-0.3
A control system is defined by the following mathematical relationship $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$\$

The response of the system as $$\,t \to \infty$$ is

A
$$x=6$$
B
$$x=2$$
C
$$x=2.4$$
D
$$x=-2$$
4
GATE EE 2003
+2
-0.6
The block diagram shown in fig given is a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is
A
$$25\%$$
B
$$0.75\%$$
C
$$6\%$$
D
$$33\%$$
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