1
GATE ME 2015 Set 2
Numerical
+2
-0
The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the sphere given by $${x^2} + {y^2} + {z^2} = 9\,\,$$ is __________.
2
GATE ME 2015 Set 1
Numerical
+2
-0
The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j\,$$ $$+ \left( {{c_1}x + {c_2}y + {c_3}z} \right)k,\,\,$$
where $${{a_1} = 2}$$ and $${{c_3} = - 4.}$$ The value of $${{b_2}}$$ is ________.
3
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
$${\pi \over 4}$$
4
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
$$4$$ $$\pi$$
GATE ME Subjects
EXAM MAP
Medical
NEET