1
GATE EE 2015 Set 2
+2
-0.6
For the system governed by the set of equations: \eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = - 2{x_1} + u \cr & \,\,\,\,\,\,y = 3{x_1} \cr}\$
the transfer function $$Y(s)/U(s)$$ is given by
A
$$3\left( {s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
B
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
C
$$\left( {s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
D
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
2
GATE EE 2015 Set 2
+1
-0.3
Consider the following Sum of products expression, $$F.$$
$$F = ABC + \overline A \overline B C + A\overline B C + \overline A BC + \overline A \overline B \overline C$$

The equivalent Product of Sums expression is

A
$$F = \left( {A + \overline B + C} \right)\left( {\overline A + B + C} \right)\left( {\overline A + \overline B + C} \right)$$
B
$$F = \left( {A + \overline B + \overline C } \right)\left( {A + B + C} \right)\left( {\overline A + \overline B + \overline C } \right)$$
C
$$F = \left( {\overline A + B + \overline C } \right)\left( {A + \overline B + \overline C } \right)\left( {A + B + C} \right)$$
D
$$F = \left( {\overline A + \overline B + C} \right)\left( {A + B + \overline C } \right)\left( {A + B + C} \right)$$
3
GATE EE 2015 Set 2
+2
-0.6
A Boolean function $$f\left( {A,B,C,D} \right) = \Pi \left( {1,5,12,15} \right)$$ is to be implemented using an $$8 \times 1$$ multiplexer ($$A$$ is $$MSB$$). The inputs $$ABC$$ are connected to the select inputs $${S_2}{S_1}{S_0}$$ of the multiplexer respectively.

Which one of the following options gives the correct inputs to pins $$0,1,2,3,4,5,6,7$$ in order?

A
$$D,\,0,\,D,\,0,\,0,\,0,\,\overline D ,D$$
B
$$\overline D ,\,1,\,\overline D ,\,1,\,1,\,1,\,D,\overline D$$
C
$$D,1,D,1,1,1,\overline D ,D$$
D
$$\overline D ,\,0,\,\overline D ,\,0,\,0,\,0,\,D,\,\overline D$$
4
GATE EE 2015 Set 2
+2
-0.6
In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $${Q_1}{Q_0}$$ $$=00.$$ The state $$\left( {{Q_1}{Q_0}} \right),$$ immediately after the $${333^{rd}}$$ clock pulse is
A
$$00$$
B
$$01$$
C
$$10$$
D
$$11$$
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