GATE ECE 2013 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2013

MCQ (Single Correct Answer)

-0.3

A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has

no real roots

no negative real root

odd number of real roots

at least one positive and one negative real root

GATE ECE 2013

MCQ (Single Correct Answer)

-0.3

The Bode plot of a transfer function G (s) is shown in the figure below. GATE ECE 2013 Control Systems - Frequency Response Analysis Question 54 English

GATE ECE 2013 Control Systems - Frequency Response Analysis Question 54 English

The gain (20 log $$\left| {G(s)} \right|$$ ) is 32 dB and -8dB at 1rad/s and 10rad/s respectively. The phase is negative for all $$\omega .$$ Then G(s) is

$${\textstyle{{39.8} \over s}}$$

$${\textstyle{{39.8} \over {{s^2}}}}$$

$${\textstyle{{32} \over {{s}}}}$$

$${\textstyle{{32} \over {{s^2}}}}$$

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 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)

-0.6

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 21 English

GATE ECE 2013 Control Systems - State Space Analysis Question 21 English

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

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

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

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

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