1
GATE ME 1993
+1
-0.3
Simpson's rule for integration gives exact result when $$f(x)$$ is a polynomial function of degree less than or equal to ________.
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
2
GATE ME 1993
Fill in the Blanks
+1
-0
The laplace transform of the periodic function $$f(t)$$ described by the curve below
$$i.e.\,\,f\left( t \right) = \left\{ {\matrix{ {\sin \,t,} & {if\left( {2n - 1} \right)\pi < t < 2n\pi \left( {n = 1,2,3,...} \right)} \cr 0 & {otherwise\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$ is ___________. 3
GATE ME 1993
+1
-0.3
The cylinder shown below rolls without slipping. In which direction does the friction force act? Towards which of the following points is the acceleration of the point of contact A on the cylinder directed? A
The mass centre
B
The geometric centre
C
The point P as marked
D
None of the above
4
GATE ME 1993
+2
-0.6
A velocity field is given as $$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$\$
Where $$x,y,z$$ are in $$m$$ and $$V$$ $$m/s.$$ Determine if

(i) It represents an incompressible flow
(ii) The flow is irrotational
(iii) The flow is steady .

A
(i) and (iii)
B
(i) and (ii)
C
(ii) and (iii)
D
(i) only
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