1
GATE EE 2004
+2
-0.6
The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ is the two dimensional state vector and $$A$$ is the system matrix given by $$A = \left[ {\matrix{ 0 & 2 \cr 2 & 0 \cr } } \right].$$ The roots of the characteristic equation are
A
$$-2$$ and $$+2$$
B
$$-j2$$ and $$+j2$$
C
$$-2$$ and $$-2$$
D
$$+2$$ and $$+2$$
2
GATE EE 2004
+2
-0.6
The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline B \overline C } \right)$$ can be written as
A
$$\overline A D + \overline B \overline C D$$
B
$$AD + B\overline C D$$
C
$$\left( {\overline A + D} \right)\left( {\overline B C + \overline D } \right)$$
D
$$A\overline D + BC\overline D$$
3
GATE EE 2004
+2
-0.6
A digital circuit which compares two numbers $${A_3}{A_2}{A_1}{A_0},\,\,{B_3}{B_2}{B_1}{B_0}$$ is shown in Fig. To get output $$Y=0,$$ choose one pair of correct input numbers
A
$$1010, 1010$$
B
$$0101,0101$$
C
$$0010, 0010$$
D
$$0010, 1011$$
4
GATE EE 2004
+1
-0.3
The digital circuit using two inverters shown in figure will act as
A
a bistable multi-vibrator
B
an astable mutli-vibrator
C
a Monostable multi-vibrator
D
an oscillator
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