1
GATE ME 2014 Set 1
+2
-0.6
The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,}$$ is evaluated along the circle $${x^2} + {y^2} = {1 \over 4}\,$$ traversed in counter clockwise direction. The integral is equal to
A
$$0$$
B
$$- {\pi \over 4}$$
C
$$- {\pi \over 2}$$
D
$${\pi \over 4}$$
2
GATE ME 2013
+2
-0.6
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $$F = xi + yj + zk$$ defined with respect to a Cartesian coordinate system having $$i, j$$ and $$k$$ as unit base vectors. $$\int {\int\limits_S {{1 \over 4}\left( {F.n} \right)dA} }$$\$

Where $$S$$ is the sphere, $$\,\,{x^2} + {y^2} + {z^2} = 1\,\,$$ and $$n$$ is the outward unit normal vector to the sphere. The value of the surface integral is

A
$$\pi$$
B
$$2$$$$\pi$$
C
$$3$$ $$\pi$$$$/4$$
D
$$4$$ $$\pi$$
3
GATE ME 2009
+2
-0.6
The divergence of the vector field $$\,3xz\widehat i + 2xy\widehat j - y{z^2}\widehat k$$ at a point $$(1,1,1)$$ is equal to
A
$$7$$
B
$$4$$
C
$$3$$
D
$$0$$
4
GATE ME 2008
+2
-0.6
The directional derivative of the scalar function $$f(x, y, z)$$$$= {x^2} + 2{y^2} + z\,\,$$ at the point $$P = \left( {1,1,2} \right)$$ in the direction of the vector $$\,\overrightarrow a = 3\widehat i - 4\widehat j\,\,$$ is
A
$$-4$$
B
$$-2$$
C
$$-1$$
D
$$1$$
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
EXAM MAP
Joint Entrance Examination