1
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
The Laplace transform of the following function is
$$$f\left( t \right) = \left\{ {\matrix{
{\sin t} & {for\,\,0 \le t \le \pi } \cr
0 & {for\,\,t > \pi } \cr
} } \right.$$$
2
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 $$t=0$$
given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$
3
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
Let $$F\left( s \right) = L\left[ {f\left( t \right)} \right]$$ denote the Laplace transform of the function $$f(t)$$. Which of the following statements is correct?
4
GATE CE 1996
Subjective
+2
-0
Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$
$$y\left( 0 \right) = 3$$ and $${y^1}\left( 0 \right) = 1,$$ where prime denotes derivative with respect to $$t.$$
$$y\left( 0 \right) = 3$$ and $${y^1}\left( 0 \right) = 1,$$ where prime denotes derivative with respect to $$t.$$
Questions Asked from Transform Theory (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude