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 $$t=0$$
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
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Civil Services
UPSC Civil Service
CBSE
Class 12