1
GATE ECE 2010
+2
-0.6
Given f(t) = $${L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {K - 3} \right)s}}} \right].$$ If $$\matrix{ {Lim\,f\,\left( t \right) = 1,} \cr {t \to \infty } \cr } \,\,$$ then the value of K is
A
1
B
2
C
3
D
4
2
GATE ECE 2009
+2
-0.6
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau }$$ is
A
$$sF\left( s \right) - f\left( 0 \right)$$
B
$$\,{1 \over s}F\left( s \right)\,$$
C
$$\int\limits_0^s {F\left( \tau \right)d\tau }$$
D
$${1 \over s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$
3
GATE ECE 2006
+2
-0.6
Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$

The final value of f(t) would be:

A
0
B
1
C
$$- e\,\,\, - 1 \le f\left( \infty \right) \le 1$$
D
$$\infty$$
4
GATE ECE 2005
+2
-0.6
In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists?
A
Re(s) > a+2
B
Re(s) > a+7
C
Re(s) < 2
D
Re(s) > a+5
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