1
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition matrix

A
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {1 - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
B
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {{e^{ - t}} - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - t}}} \cr } } \right)$$
C
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {{e^{ - t}} - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
D
$$\left( {\matrix{ 1 & {\left( {1 - {e^{ - t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
2
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition equation

A
$$X\left( t \right) = \left( {\matrix{ {t - {e^{ - t}}} \cr {{e^{ - t}}} \cr } } \right)$$
B
$$X\left( t \right) = \left( {\matrix{ {t - {e^{ - t}}} \cr {3{e^{ - 3t}}} \cr } } \right)$$
C
$$X\left( t \right) = \left( {\matrix{ {t - {e^{ - 3t}}} \cr {3{e^{ - 3t}}} \cr } } \right)$$
D
$$X\left( t \right) = \left( {\matrix{ {t - {e^{ - 3t}}} \cr {{e^{ - t}}} \cr } } \right)$$
3
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
In the figure, as long as $${X_1} = 1$$ and $${X_2} = 1,$$ the output $$Q$$ remains GATE EE 2005 Digital Electronics - Logic Gates Question 4 English
A
at $$1$$
B
at $$0$$
C
at its initial value
D
unstable
4
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
The digital circuit shown in the figure works as a GATE EE 2005 Digital Electronics - Sequential Circuits Question 16 English
A
$$JK$$ flip-flop
B
Clocked $$RS$$ flip-flop
C
$$T$$ flip-flop
D
Ring counter
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