1
GATE ECE 2013
MCQ (Single Correct Answer)
+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
GATE ECE 2013 Engineering Mathematics - Vector Calculus Question 15 English Option 1 over the closed surface bounded by the loop
B
GATE ECE 2013 Engineering Mathematics - Vector Calculus Question 15 English Option 2 over the closed volume bounded by the loop
C
GATE ECE 2013 Engineering Mathematics - Vector Calculus Question 15 English Option 3 over the open volume bounded by the loop
D
GATE ECE 2013 Engineering Mathematics - Vector Calculus Question 15 English Option 4 over the open surface bounded by the loop
2
GATE ECE 2011
MCQ (Single Correct Answer)
+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 GATE ECE 2011 Engineering Mathematics - Vector Calculus Question 17 English is
A
$$3V$$
B
$$5V$$
C
$$10$$
D
$$15V$$
3
GATE ECE 2005
MCQ (Single Correct Answer)
+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
$$\nabla \left( {\nabla .P} \right) \to {\nabla ^2}P$$
4
GATE ECE 1993
Fill in the Blanks
+1
-0
If the linear velocity $${\overrightarrow V }$$ is given by $$\overrightarrow V = {x^2}y\overrightarrow i + xyz\overrightarrow j - y{z^2}\overrightarrow k $$ then the angular velocity $$\overrightarrow W $$ at the point $$\left( {1,1, - 1} \right)$$ is _______.
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