GATE EE 2014 Set 2 | GATE EE Year Wise Previous Years Questions

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

For the transfer function $$G\left( s \right) = {{5\left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {{s^2} + 4s + 25} \right)}}.$$ The values of the constant gain term and the highest corner frequency of the Bode plot respectively are

$$3.2, 5.0$$

$$16.0, 4.0$$

$$3.2, 4.0$$

$$16.0, 5.0$$

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-0.3

The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u$$ is

$$\left[ {\matrix{ {{e^t}} & 0 \cr {{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & 0 \cr {{t^2}{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & 0 \cr {t{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & {t{e^t}} \cr 0 & {{e^t}} \cr } } \right]$$

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr } } \right]\,\,Q = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:

Controllable and observable

Not controllable but observable

Controllable but not observable

Not controllable and not observable

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

The $$SOP$$ (sum of products) from of a Boolean function is $$\sum \left( {0,1,3,7,11} \right),$$ where inputs are $$A,B,C,D$$ ($$A$$ is $$MSB$$, and $$D$$ is $$LSB$$). The equivalent minimized expression of the function is

$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline B } \right)\left( {\overline C + D} \right)$$

$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline C } \right)\left( {\overline C + D} \right)$$

$$\left( {\overline B + C} \right)\left( {\overline A + C} \right)\left( {\overline A + \overline C } \right)\left( {\overline C + \overline D } \right)$$

$$\left( {\overline B + C} \right)\left( {A + \overline B } \right)\left( {\overline A + \overline B } \right)\left( {\overline C + D} \right)$$

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