1
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A second order LTI system is described by the following state equation. $$$\eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr & {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr} $$$

When x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t)=X1(t). The systyem is

A
undamped (oscillatory)
B
under damped
C
critically damped
D
over damped
2
GATE ECE 2017 Set 2
Numerical
+1
-0
Consider the state space realization $$$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr {\mathop x\limits^ \bullet } & {\left( t \right)} \cr } } \right] = \left[ {\matrix{ 0 & 0 \cr 0 & { - 9} \cr } } \right]\left[ {\matrix{ {{x_1}} & {\left( t \right)} \cr {{x_2}} & {\left( t \right)} \cr } } \right] + \left[ {\matrix{ 0 \cr {45} \cr } } \right]u\left( t \right),$$$ with the initial condition $$\left[ {\matrix{ {{x_1}} & {\left( 0 \right)} \cr {{x_2}} & {\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 0 \cr 0 \cr } } \right];$$
Where u(t) denotes the unit step function.
The value of $$\mathop {Lt}\limits_{x \to \infty } \left| {\sqrt {{x_1}^2\left( t \right) + {x_2}^2\left( t \right)} } \right|$$ is ______
Your input ____
3
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the circuit shown in the figure. GATE ECE 2017 Set 2 Digital Circuits - Combinational Circuits Question 34 English The Boolean expression F implemented by the circuit is
A
$$\overline X \,\overline Y \,\overline Z + XY + \,\overline Y \,Z$$
B
$$\overline X \,Y\,\overline Z + XZ + \,\overline Y \,Z$$
C
$$\overline X \,Y\,\overline Z + XY + \,\overline Y \,Z$$
D
$$\overline X \,\overline Y \,\overline Z + XZ + \,\overline Y \,Z$$
4
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A programmable logic array (PLA) is shown in the figure. GATE ECE 2017 Set 2 Digital Circuits - Combinational Circuits Question 16 English The Boolean function F implemented is
A
$$\overline P \,\overline {Q\,} R + \overline P QR + P\overline {Q\,} \overline R $$
B
$$(\overline P \, + \overline {Q\,} + \,R)(\overline P \, + Q + R) + (P + \overline P \, + \overline R )$$
C
$$\overline P \,\overline {Q\,} R + \overline P QR + P\overline {Q\,} \,\overline R $$
D
$$(\overline P + \,\overline {Q\,} \, + R)(\overline P + Q + R) + (P + \overline {Q\,} + R)$$
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