1
GATE EE 2014 Set 2
+1
-0.3
The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u$$ is
A
$$\left[ {\matrix{ {{e^t}} & 0 \cr {{e^t}} & {{e^t}} \cr } } \right]$$
B
$$\left[ {\matrix{ {{e^t}} & 0 \cr {{t^2}{e^t}} & {{e^t}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{e^t}} & 0 \cr {t{e^t}} & {{e^t}} \cr } } \right]$$
D
$$\left[ {\matrix{ {{e^t}} & {t{e^t}} \cr 0 & {{e^t}} \cr } } \right]$$
2
GATE EE 2014 Set 2
+2
-0.6
The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr } } \right]\,\,Q = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:
A
Controllable and observable
B
Not controllable but observable
C
Controllable but not observable
D
Not controllable and not observable
3
GATE EE 2014 Set 2
+2
-0.6
The $$SOP$$ (sum of products) from of a Boolean function is $$\sum \left( {0,1,3,7,11} \right),$$ where inputs are $$A,B,C,D$$ ($$A$$ is $$MSB$$, and $$D$$ is $$LSB$$). The equivalent minimized expression of the function is
A
$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline B } \right)\left( {\overline C + D} \right)$$
B
$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline C } \right)\left( {\overline C + D} \right)$$
C
$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline C } \right)\left( {\overline C + \overline D } \right)$$
D
$$\left( {\overline B + C} \right)\left( {A + \overline B } \right)\left( {\overline A + \overline B } \right)\left( {\overline C + D} \right)$$
4
GATE EE 2014 Set 2
+2
-0.6
A $$JK$$ flip flop can be implemented by $$T$$ flip flops. Identify the correct implementation.
A
B
C
D
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