1
GATE IN 2015
+1
-0.3
The magnitude of the directional derivative of the function $$f\left( {x,y} \right) = {x^2} + 3{y^2}$$ in a direction normal to the circle $$\,{x^2} + {y^2} = 2,$$ at the point $$(1,1),$$ is
A
$$4\sqrt 2$$
B
$$5\sqrt 2$$
C
$$7\sqrt 2$$
D
$$9\sqrt 2$$
2
GATE IN 2014
Numerical
+1
-0
$$A$$ vector is defined as $$f = y\widehat i + x\widehat j + z\widehat k\,\,$$. Where $$\widehat i,\widehat j,$$ and $$\widehat k$$ are unit vectors in cartesian $$(x, y, z)$$ coordinate system. The surface integral - -over the closed surface $$S$$ of a cube with vertices having the following coordinates: $$(0,0,0), (1, 0, 0), (0, 1, 0), (0,0,1), (1, 0, 1), (1,1,1), (0, 1, 1), (1, 1, 0)$$ is _______.
3
GATE IN 2013
+1
-0.3
For a vector $$E,$$ which one of the following statements is NOT TRUE?
A
If $$\nabla .E = 0,E$$ is called
B
If $$\nabla \times E = 0,$$ $$E$$ is called conservative
C
If $$\nabla \times E = 0,$$ $$E$$ is called irrotational
D
If $$\nabla .E = 0,E$$ is called irrotational
4
GATE IN 2009
+1
-0.3
A sphere of unit radius is centered at the origin. The unit normal at a point $$(x, y, z)$$ on the surface of the sphere is the vector.
A
$$(x, y, z)$$
B
$$\left( {{1 \over {\sqrt 3 }},{1 \over {\sqrt 3 }},{1 \over {\sqrt 3 }}} \right)$$
C
$$\left( {{x \over {\sqrt 3 }},{y \over {\sqrt 3 }},{z \over {\sqrt 3 }}} \right)$$
D
$$\left( {{x \over {\sqrt 2 }},{y \over {\sqrt 2 }},{z \over {\sqrt 2 }}} \right)$$
GATE IN Subjects
EXAM MAP
Medical
NEET