# Signals and Systems for GATE EC Quiz 6

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Here is Signals Systems GATE EC Quiz 6 to help you prepare for your upcoming GATE exam. The GATE EC paper has several subjects, each one as important as the last. However, one of the most important subjects in GATE EC is Signals and Systems. The subject is vast, but practice makes tackling it easy.

This quiz contains important questions which match the pattern of the GATE exam. Check your preparation level in every chapter of Signals and Systems for GATE. Simply take the quiz and comparing your ranks. Learn about control system, Feedback principle and more.

Signals and Systems for GATE EC Quiz 6

Que. 1

A periodic variable x is shown in the figure as a function of time. The root mean square (rms) value of x is

Que. 2

For a function g(t), it is given that $$\mathop \smallint \limits_{ – \infty }^{ + \infty } g\left( t \right){e^{ – j\omega t}}dt = \omega {e^{ – 2{\omega ^2}}}$$ for any real value $$\omega$$.
If, $$y\left( t \right) = \mathop \smallint \limits_{ – \infty }^t g\left( \tau \right)d\tau$$, then $$\mathop \smallint \limits_{ – \infty }^\infty y\left( t \right)dt$$ is:

1.
0
2.
$$-j$$
3.
$$-\frac{j}{2}$$
4.
$$\frac{j}{2}$$

Que. 3

The FT of $$\rm h\left( t \right)$$ is  $$\rm H\left( {j\omega } \right) = \frac{{\left( {2cos\omega } \right)\left( {sin2\omega } \right)}}{\omega }$$ The value of  $$\rm h(0)$$ is

1.
$$\rm 1/4$$
2.
$$\rm 1/2$$
3.
$$\rm 1$$
4.
$$\rm 2$$

Que. 4

The input $$x(t)$$ and  output  $$y(t)$$ of a system are related as

$$y\left( t \right) = \mathop \smallint \limits_{ – \infty }^t x\left( \tau \right)cos\left( {3\tau } \right)d\tau$$

1.
Time – invariant & stable
2.
Stable & not time – invariant
3.
Time – invariant & not stable
4.
Not time invariant & not stable

Que. 5

A system with Transfer Function $$G(s) = \frac{{\left( {{s^2} + 9} \right)\left( {s + 2} \right)}}{{\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}}$$ is excited by sin (ωt). The steady-state output of the system is zero at:

1.
ω = 1
2.
ω = 2
3.
ω = 3
4.
ω = 4
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