1
GATE ECE 2014 Set 2
Numerical
+1
-0
If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarrow r } \right| = r,$$ then div $$\left( {{r^2}\nabla \left( {\ln \,r} \right)} \right)$$ = ________.
2
GATE ECE 2013
+1
-0.3
Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint {\overrightarrow A \bullet \overrightarrow {dl} }$$ can be expressed as
A
over the closed surface bounded by the loop
B
over the closed volume bounded by the loop
C
over the open volume bounded by the loop
D
over the open surface bounded by the loop
3
GATE ECE 2011
+1
-0.3
Consider a closed surface $$'S'$$ surrounding a volume $$V.$$ If $$\overrightarrow r$$ is the position vector of a point inside $$S$$ with $$\overrightarrow n$$ the unit normal on $$'S',$$ the value of the integral is
A
$$3V$$
B
$$5V$$
C
$$10$$
D
$$15V$$
4
GATE ECE 2005
+1
-0.3
$$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to
A
$$P \times \nabla \times P \to {\nabla ^2}P$$
B
$${\nabla ^2}P + \nabla \left( {\nabla .P} \right)\,$$
C
$${\nabla ^2}P + \left( {\nabla \times P} \right)\,\,$$
D
$$\nabla \left( {\nabla .P} \right) \to {\nabla ^2}P$$
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