1
GATE CE 2011
+1
-0.3
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are two arbitrary vectors with magnitudes $$a$$ and $$b$$ respectively, $${\left| {\overrightarrow a \times \overrightarrow b } \right|^2}$$ will be equal to
A
$${a^2}\,{b^2} - {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
B
$$ab - \overrightarrow a .\,\overrightarrow b$$
C
$${a^2}\,{b^2} + {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
D
$$ab + \overrightarrow a .\,\overrightarrow b$$
2
GATE CE 2009
+1
-0.3
For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is
A
$$2\widehat i + 6\widehat j + 4\widehat k$$
B
$$2\widehat i + 12\widehat j - 4\widehat k$$
C
$$2\widehat i + 12\widehat j + 4\widehat k$$
D
$$\sqrt {56}$$
3
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
4
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
$$3$$
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
NEET