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1

GATE EE 2017 Set 1

MCQ (Single Correct Answer)
A closed loop system has the characteristic equation given by
$${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, which one of the following conditions should be satisfied?
A
$$0 < K < 0.5$$
B
$$0.5 < K < 1$$
C
$$0 < K < 1$$
D
$$K > 1$$
2

GATE EE 2014 Set 3

MCQ (Single Correct Answer)
A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$𝐻(𝑠).$$ It is given that $$\left| {G\left( s \right)H\left( s \right)} \right| < 1.$$ Which of the following is true about the stability of the system?
A
The system is always stable
B
The system is stable if all zeros of $$𝐺(𝑠)𝐻(𝑠)$$ are in left half of the $$s$$-plane
C
The system is stable if all poles of $$𝐺(𝑠)𝐻(𝑠)$$ are in left half of the s-plane
D
It is not possible to say whether or not the system is stable from the information given
3

GATE EE 2014 Set 1

MCQ (Single Correct Answer)
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of
A
only one root at the origin
B
imaginary roots
C
only positive real roots
D
only negative roots
4

GATE EE 2009

MCQ (Single Correct Answer)
The first two rows of Routh's tabulation of a third order equation are as follows $$$\left. {\matrix{ {{s^3}} \cr {{s^2}} \cr } } \right|\matrix{ 2 & 2 \cr 4 & 4 \cr } $$$
this means there are

A
two roots at $$s$$ $$ = \pm j$$ and one root in right half $$s$$ - plane
B
two roots at $$s$$ $$ = \pm j2$$ and one root in left half $$s$$ - plane
C
two roots at $$s$$ $$ = \pm j2$$ and one root in right half $$s$$ - plane
D
two roots at $$s$$ $$ = \pm j$$and one root in left half $$s$$ - plane

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