1
GATE EE 2010
+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
+2
-0.6
The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( {j\omega } \right)$$ plane $$\left( {for\,\,0 < \omega < \infty } \right)$$ is
A
B
C
D
3
GATE EE 2010
+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
4
GATE EE 2010
+2
-0.6
A minimized form of the function $$F$$ is
A
$$F = \overline X \overline Y + YZ$$
B
$$F = \overline {XY} + YZ$$
C
$$F = \overline {XY} + Y\overline Z$$
D
$$F = \overline {XY} + \overline Y Z$$
GATE EE Papers
2023
2022
2021
2020
2019
2018
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
EXAM MAP
Medical
NEET