1
GATE CE 2011
MCQ (Single Correct Answer)
+2
-0.6
If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of $$f(t)$$ are respectively
A
$$0,2$$ $$0,{2 \over 7}$$
B
$$2,0$$
C
$$0,{2 \over 7}$$
D
$${2 \over 7},\,0$$
2
GATE CE 2005
MCQ (Single Correct Answer)
+2
-0.6
Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is
A
$${{s\,\cos \,q - p\,\sin \,q} \over {{s^2} + {p^2}}}$$
B
$${{s\,\cos \,q - p\,\sin \,q} \over {{s^2} + {p^2}}}$$
C
$${{s\,\sin \,q - p\,\cos \,q} \over {{s^2} + {p^2}}}$$
D
$${{s\,\sin \,q + p\,\cos \,q} \over {{s^2} + {p^2}}}$$
3
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
The Laplace transform of the following function is $$$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0 \le t \le \pi } \cr 0 & {for\,\,t > \pi } \cr } } \right.$$$
A
$$1/\left( {1 + {s^2}} \right)\,$$ for all $$\,s > 0$$
B
$$1/\left( {1 + {s^2}} \right)\,$$ for all $$\,s < \pi $$
C
$$\left( {1 + {e^{ - \pi s}}} \right)/\left( {1 + {s^2}} \right)$$ for all $$s>0$$
D
$${e^{ - \pi s}}/\left( {1 + {s^2}} \right)$$ for all $$s > 0$$
4
GATE CE 2002
Subjective
+2
-0
Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$
given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$
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Fluid Mechanics and Hydraulic Machines
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