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
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination