1
GATE CE 2003
+1
-0.3
The vector field $$\,F = x\widehat i - y\widehat j\,\,$$ (where $$\widehat i$$ and $$\widehat j$$ are unit vectors) is
A
divergence free, but not irrotational
B
irrotational, but not divergence free
C
divergence free and irrotational
D
neither divergence free nor irrotational
2
GATE CE 1999
+1
-0.3
For the function $$\phi = a{x^2}y - {y^3}$$ to represent the velocity potential of an ideal fluid, $${\nabla ^2}\,\,\phi$$ should be equal to zero. In that case, the value of $$'a'$$ has to be
A
$$-1$$
B
$$1$$
C
$$-3$$
D
$$3$$
3
GATE CE 1996
+1
-0.3
The directional derivative of the function $$f(x, y, z) = x + y$$ at the point $$P(1,1,0)$$ along the direction $$\overrightarrow i + \overrightarrow j$$ is
A
$$1/\sqrt 2$$
B
$$\sqrt 2$$
C
$$- \sqrt 2$$
D
$$2$$
4
GATE CE 1995
+1
-0.3
The derivative of $$f(x, y)$$ at point $$(1, 2)$$ in the direction of vector $$\overrightarrow i + \overrightarrow j$$ is $$2\sqrt 2$$ and in the direction of the vector $$- 2\overrightarrow j$$ is $$-3.$$ Then the derivative of $$f(x,y)$$ in direction $$- \overrightarrow i - 2\overrightarrow j$$ is
A
$$2\sqrt 2 + 3/2$$
B
$$- 7/\sqrt 5$$
C
$$- 2\sqrt 2 - 3/2$$
D
$$1/\sqrt 5$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
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