GATE ECE 2013 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2013

MCQ (Single Correct Answer)

-0.6

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations GATE ECE 2013 Control Systems - State Space Analysis Question 20 English

GATE ECE 2013 Control Systems - State Space Analysis Question 20 English

The state-variable equations of the system shown in the figure above are

$$\eqalign{ & \mathop X\limits^ \bullet = \left[ {\matrix{ { - 1} & 0 \cr 1 & { - 1} \cr } } \right]X + \left[ {\matrix{ { - 1} \cr 1 \cr } } \right]u \cr & y = \left[ {\matrix{ 1 & { - 1} \cr } } \right]X + u \cr} $$

$$\eqalign{ & \mathop X\limits^ \bullet = \left[ {\matrix{ { - 1} & 0 \cr { - 1} & { - 1} \cr } } \right]X + \left[ {\matrix{ { - 1} \cr 1 \cr } } \right]u \cr & y = \left[ {\matrix{ { - 1} & { - 1} \cr } } \right]X + u \cr} $$

$$\eqalign{ & \mathop X\limits^ \bullet = \left[ {\matrix{ { - 1} & { - 1} \cr 0 & { - 1} \cr } } \right]X + \left[ {\matrix{ { - 1} \cr 1 \cr } } \right]u \cr & y = \left[ {\matrix{ 1 & { - 1} \cr } } \right]X - u \cr} $$

GATE ECE 2013

MCQ (Single Correct Answer)

-0.6

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations GATE ECE 2013 Control Systems - State Space Analysis Question 19 English

GATE ECE 2013 Control Systems - State Space Analysis Question 19 English

The state transition matrix e^At of the system shown in the figure above is

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

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

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

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

GATE ECE 2013

MCQ (Single Correct Answer)

-0.3

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

$$\overline X \,Y,X\overline Y $$

$$\overline X \,Y,X\overline Y $$$$\overline Z ,X\overline Y Z$$

$$\overline X Y\overline Z $$,$$\overline X YZ,X\overline Y $$

$$\overline X Y\overline Z $$ ,$$\overline X YZ,X\overline Y $$$$\overline Z ,X\overline Y Z$$

GATE ECE 2013

MCQ (Single Correct Answer)

-0.3

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles.

an AND gate

an OR gate

an XOR gate

a NAND gate

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