1
GATE ECE 2009
MCQ (More than One Correct Answer)
+1
-0.3
Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \right],$$

where p and q are arbitrary real numbers. Which of the following statesments about the controllability of the system is true?

A
The system is completely state controllable for any nonzero values of p and q.
B
Only p =0 and q=0 result in controllability.
C
The system is uncontrollable for all values of p and q.
D
We cannot conclude about controllability from the given data.
2
GATE ECE 2009
+2
-0.6
If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then
A
Y=Z
B
Y= $${\overline Z }$$
C
Z= 1
D
Z= 0
3
GATE ECE 2009
+2
-0.6
What are the minimum number of 2-to 1 multiplexers required to generate a 2-input AND gate and a 2-input EX-OR gate?
A
1 and 2
B
1 and 3
C
1 and 1
D
2 and 2
4
GATE ECE 2009
+2
-0.6
What are the counting states (Q1, Q2) for the counter shown in the figure below?
A
11, 10, 00, 11, 10,......
B
01,1011,00,01........,
C
00,11,01,10,00........
D
01,10,00,01,10........
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