1
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is:
$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 1 & 2 \cr 2 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 1 \cr 2 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr} $$
A
$${{\left( {s + 2} \right)} \over {\left( {{s^2} - 2s - 2} \right)}}$$
B
$${{\left( {s + 2} \right)} \over {\left( {{s^2} + s - 4} \right)}}$$
C
$${{\left( {s - 4} \right)} \over {\left( {{s^2} + s - 4} \right)}}$$
D
$${{\left( {s + 4} \right)} \over {\left( {{s^2} - s - 4} \right)}}$$
2
GATE EE 2016 Set 1
Numerical
+2
-0
Consider the following state - space representation of a linear time-invariant system.
$$\mathop x\limits^ \bullet \left( t \right) = \left[ {\matrix{ 1 & 0 \cr 0 & 2 \cr } } \right]\,\,x\left( t \right),\,\,y\left( t \right) = {c^T}x\left( t \right),\,c = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$ and
$$x\left( 0 \right) = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$

The value of $$y(t)$$ for $$t\,\,\, = \,\,{\log _e}2$$ ___________.

Your input ____
3
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+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
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
4
GATE EE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
In the signal flow diagram given in the figure, $${u_1}$$ and $${u_2}$$ are possible inputs whereas $${y_1}$$ and $${y_2}$$ are possible outputs. When would the $$SISO$$ system derived from this diagram be controllable and observable? GATE EE 2015 Set 1 Control Systems - State Variable Analysis Question 9 English
A
When $${u_1}$$ is the only input and $${y_1}$$ is the only output
B
When $${u_2}$$ is the only input and $${y_1}$$ is the only output
C
When $${u_1}$$ is the only input and $${y_2}$$ is the only output
D
When $${u_2}$$ is the only input and $${y_2}$$ is the only output
GATE EE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12