1
GATE ECE 2016 Set 2
Numerical
+2
-0
Suppose $$C$$ is the closed curve defined as the circle $$\,\,{x^2} + {y^2} = 1\,\,$$ with $$C$$ oriented anti-clockwise. The value of $$\,\,\oint {\left( {x{y^2}dx + {x^2}ydx} \right)\,\,}$$ over the curve $$C$$ equals _______.
2
GATE ECE 2014 Set 4
Numerical
+2
-0
Given $$\,\,\overrightarrow F = z\widehat a{}_x + x\widehat a{}_y + y\widehat a{}_z.\,\,$$ If $$S$$ represents the portion of the sphere $${x^2} + {y^2} + {z^2} = 1$$ for $$\,z \ge 0,$$ then $$\int\limits_s {\left( {\nabla \times \overrightarrow F .} \right)\overrightarrow {ds} \,\,}$$ is ________.
3
GATE ECE 2013
+2
-0.6
The divergence of the vector field $$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$ is
A
$$0$$
B
$$1/3$$
C
$$1$$
D
$$3$$
4
GATE ECE 2012
+2
-0.6
The direction of vector $$A$$ is radially outward
from the origin, with $$\left| A \right| = K\,{r^n}$$
where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant.
The value of $$n$$ for which $$\nabla .A = 0\,\,$$ is
A
$$-2$$
B
$$2$$
C
$$1$$
D
$$0$$
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