1
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
The characteristic equation of a closed-loop system is $$s\left( {s + 1} \right)\left( {s + 3} \right) + \,\,k\left( {s + 2} \right) = 0,\,\,k > 0.$$

Which of the following statements is true?

A
Its roots are always real
B
It cannot have a breakaway point in the range $$ - 1 < {\mathop{\rm Re}\nolimits} \left[ s \right] < 0$$
C
Two of its roots tend to infinity along the asymptotes $${\mathop{\rm Re}\nolimits} \left[ s \right] = - 1$$
D
It may have complex roots in the right half plane
2
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
The system $$\mathop X\limits^ \bullet = AX + BU$$ with $$A = \left[ {\matrix{ { - 1} & 2 \cr 0 & 2 \cr } } \right],$$ $$B = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$ is
A
stable and controllable
B
stable but uncontrollable
C
unstable but controllable
D
unstable and uncontrollable
3
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
A minimized form of the function $$F$$ is GATE EE 2010 Digital Electronics - Minimization Question 5 English
A
$$F = \overline X \overline Y + YZ$$
B
$$F = \overline {XY} + YZ$$
C
$$F = \overline {XY} + Y\overline Z $$
D
$$F = \overline {XY} + \overline Y Z$$
4
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
Which of the following circuits is a realization of the previous function $$F$$ $$?$$
A
GATE EE 2010 Digital Electronics - Minimization Question 4 English Option 1
B
GATE EE 2010 Digital Electronics - Minimization Question 4 English Option 2
C
GATE EE 2010 Digital Electronics - Minimization Question 4 English Option 3
D
GATE EE 2010 Digital Electronics - Minimization Question 4 English Option 4
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