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1

### GATE EE 2011

The steady state error of a unity feedback linear system for a unit step input is $$0.1.$$ The steady state error of the same system, for a pulse input $$r(t)$$ having a magnitude of $$10$$ and a duration of one second, as shown in the figure is A
$$0$$
B
$$0.1$$
C
$$1$$
D
$$10$$
2

### GATE EE 2010

For the system $${2 \over {\left( {s + 1} \right)}},$$ the approximate time taken for a step response to reach $$98$$% of its final value is
A
$$1\,s$$
B
$$2\,s$$
C
$$4\,s$$
D
$$8\,s$$
3

### GATE EE 2008

A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$

Where $$\delta \left( t \right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by $$u(t),y(t)$$ can be of the form

A
$${e^{ t}}$$
B
$${e^{ - t}}$$
C
$${e^{ t}}$$$$u(t)$$
D
$${e^{ - t}}$$$$u(t)$$
4

### GATE EE 2004

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to
A
$$5$$
B
$$5/2$$
C
$$5/3$$
D
$$0$$
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